NDA - Page 2 of 4 - Vidhyarthi Darpan

NDA/NA(I) Exam 2019 Mathematics Previous Year Paper

NDA/NA(I) Exam 2019 Mathematics Previous Year Paper

Q. 1. अनुक्रम 25, -125, 625, -3125, … का nवाँ पद क्या है ?

(a) (-5)^2n-1

(b) (-1)²ⁿ 5ⁿ⁺¹

(d) (-1)^n-1 5ⁿ⁺¹

Q. 2. मान लीजिए x = {1, 2, 3, 4) है और R, X पर एक संबंध है । यदि R = {(1, 1), (2, 2), (3, 3), (1, 2), (2,1), (2,3),(8,2) है, तो निम्नलिखित में से कौन-सा एक सही है ?

(a) R स्वतुल्य और सममित है, किन्तु संक्रामक नहीं है

(b) R सममित और संक्रामक है, किन्तु स्वतुल्य नहीं है

(e) R स्वतुल्य और संक्रामक है, किन्तु सममित नहीं है

(d) R न तो स्वतुल्य है और न ही संक्रामक है, किन्तु सममित है

Q. 3. धनपूर्ण संख्याओं के समुच्चय N पर एक संबंध R इस प्रकार से परिभाषित है कि xRy =x²-4xy + 3y² = 0 है, तो निम्नलिखित में से कौन-सा एक सही है ?

(a) R स्वतुल्य और सममित है, किन्तु संक्रामक नहीं है

(b) R स्वतुल्य और संक्रामक है, किन्तु सममित नहीं है

(d) R स्वतुल्य है, किन्तु यह न तो सममित है और न ही संक्रामक है

Q. 4. यदि A = {x EZ : x³ – 1 = 0} और B = {x EZ: x² + x + 1 = 01 है, जहाँ z सम्मिश्र संख्याओं का समुच्चय है, तो A ∩ B किसके बराबर है ?

Q. 5. दो अरिक्त समुच्चयों A और B के लिए निम्नलिखित कथनों पर विचार कीजिए :

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं ?

(a) केवल 1

(b) केवल 2

(d) न तो 1, न ही 2

Q. 6. मान लीजिए X एक अरिक्त समुच्चय है और मान लीजिए A, B, C समुच्चय x के उपसमुच्चय हैं । निम्नलिखित कथनों पर विचार कीजिए :

उपर्युक्त कथनों में से कौन-से सही हैं ?

(a) केवल 1 और 2

(b) केवल 2 और 3

(d) 1,2 और 3

Q. 7. यदि है, तो B का सहखंडज आव्यूह किसके बराबर है ?

Q. 8. समीकरण |x²-x-6] = x + 2 के मूल क्या हैं ?

(a) -2, 1, 4 की

(b) 0, 2,4

(d) -2,2,4

Q. 9. यदि है, तो आव्यूह A है

(a) अव्युत्क्रमणीय आव्यूह

(b) अंतर्वलनीय आव्यूह

(d) वर्गसम आव्यूह

Q. 10. यदि है, तो x और y के मान क्रमश: क्या हैं ?

(a) -3,4

(b) 3, 4

(d) -3,-4

Q. 11. समीकरणों z³ + 2x² + 2x + 1 = 0 और Z²⁰¹⁷ + Z²⁰¹⁸ + 1 = 0 के सार्व मूल हैं

Q. 12. यदि C(20, n + 2) = C(20, n – 2) है, तो n किसके बराबर है?

(a) 8

(b) 10

(d) 16

Q. 13. एक समतल पर 10 बिन्दु हैं । इन बिन्दुओं में से कोई भी तीन बिन्दु एक सरल रेखा में नहीं हैं । उन सरल रेखाओं की कुल संख्या कितनी है जो इन बिन्दुओं को जोड़कर बनाई जा सकती हैं ?

(a) 90

(b) 45

(d) 30

Q. 14. A और b, समीकरण px² + qx + r = 0 (जहाँ p, q, r सभी धनात्मक हैं) के भिन्न वास्तविक मूल हैं । निम्नलिखित में से कौन-सा एक सही है?

(a) a> 0, b>0

(b) a<o, b<o

(d) a<o, b>0

Q. 15. यदि A = {λ.{λ, μ}} है, तो A का घात समुच्चय (पॉवर सैट) है

आगे आने वाले 02 (दो) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए:

किसी विद्यालय में, सभी छात्र तीन अंत: शाल खेलों (इनडोर गेम्स)-शतरंज. कैरम और टेबल टेनिस में से कम-से-कम एक खेल खेलते हैं। 60 छात्र शतरंज खेलते हैं, 50 टेबल टेनिस खेलते हैं, 48 कैरम खेलते हैं, 12 शतरंज और कैरम दोनों खेलते हैं, 15 कैरम और टेबल टेनिस दोनों खेलते हैं, 20 टेबल टेनिस और शतरंज दोनों खेलते हैं ।

Q. 16. विद्यालय में छात्रों की न्यूनतम संख्या क्या हो सकती

(a) 123

(b) 111

(d) 63

Q. 17. विद्यालय में छात्रों की अधिकतम संख्या कितनी हो सकती है?

(a) 111

(b) 123

(d) 135

Q. 18. यदि A कोटि 3 का एक तत्समक आव्यूह है, तो इसका/इसके प्रतिलोम (A^-1)

(a) शून्य आव्यूह के बराबर है।

(b) A के बराबर है

(d) का अस्तित्व नहीं है

Q. 19.A, कोटि 3 का इस प्रकार का एक वर्ग आव्यूह है कि इसके सारणिक का मान 4 है । इसके परिवर्त के सारणिक का मान क्या है?

(a) 64

(b) 36

(d) 4

Q. 20. 6 प्रोग्रामरों और 4 टाइपिस्टों में से, एक कार्यालय 5 व्यक्तियों को भर्ती करना चाहता है । यह कितने प्रकार से किया जा सकता है ताकि कम-से-कम एक टाइपिस्ट की भर्ती अवश्य हो ?

(a) 209

(b) 210

(d) 242

Q. 21. [(2x – 3y)² (2x + 3y²)² के विस्तार में पदों की संख्या क्या है ?

(a) 4

(b) 5

(d) 16

Q. 22. (1 + ax)ⁿ के विस्तार में, पहले तीन पद क्रमश: 1, 12x और 64x² हैं | n किसके बराबर है ?

(a) 6

(b) 9

(d) 12

Q. 23. संख्याएँ 1, 5 और 25 तीन पद (क्रमागत रूप से होना आवश्यक नहीं हो सकते हैं

(a) केवल एक AP के

(b) एक से अधिक पर परिमित संख्या में AP के

(d) परिमित संख्या में GPS के

Q. 24. किसी AP के (p + q)वें और (p-q) पदों का योगफल बराबर है

(a) (2p) पद के

(b) (24)वें पद के

(d) पवें पद के दुगुने के

Q. 25. यदि A, कोटि n > 1 का एक वर्ग आव्यूह है, तो निम्नलिखित में से कौन-सा एक सही है ?

(a) det (-A) = detA

(b) det (-A) = (-1)ⁿ det A

(d) det (-A) = n det A

Q. 26. 25 cosecx² + 36 sec² x का न्यूनतम मान क्या है ?

(a) 1

(b) 11

(d) 121

आगे आने वाले 02 (दो) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए:

मान लीजिए A और B, (3 × 3) आव्यूह हैं जहाँ det. A = 4 और det B = 3 है।

Q. 27. det (2AB) किसके बराबर है ?

(a) 96

(b) 72

(d) 36

Q. 28. det (3AB-1) किसके बराबर है ?

(a) 12

(b) 18

(d) 48

आगे आने वाले 02 (दो) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए : एक सम्मिश्र संख्या इस प्रकार दी गई है कि है।

Q. 29. Z का मापांक क्या है ?

(a) 4

(b) 2

(d) 1/2

Q. 30. z का मुख्य कोणांक क्या है ?

Q. 31. का क्या मान है ?

(a) -2

(b) -1

(d) 1

Q. 32. tan 54° को किस प्रकार अभिव्यक्त किया जा सकता है ?

आगे आने वाले 03 (तीन) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए:

Q. 33. θ का मान क्या है?

Q. 34. A का मान क्या है?

(a) 4

(b) 3

(d) 1

Q. 35 B का मान क्या है?

(a) -1

(b) 0

(d) 2

आगे आने वाले 02 (दो) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए:

यह दिया गया है कि cos (θ-α) = a, cos (θ-β) = b है

Q. 36. cos (α – β) किसके बराबर है ?

Q. 37. sin² (α-β) + 2ab cos (α-β) किसके बराबर है ?

Q. 38. यदि sin α + cos α = p है, तो cos² (2α) किसके बराबर है?

Q. 39. sin^-1 ⅘ + sec-5 5/4 – π/2 का मान क्या है ?

Q. 40.

Q. 41. यदि tan θ = ½ और tan φ = ⅓ है ) (θ + φ) का मान क्या है?

Q. 42. यदि cos A = 3/4 है, तो sin(A/2) sin(3A/2) का मान क्या है?

(a) 5/8

(b) 5/16

(d) 7/32

Q. 43. tan 75° + cot 75° का मान क्या है ?

(a) 2

(b) 4

(d) 4√3

Q. 44. cos 46° cos 47° cos 48° cos 49° cos 50° … cos 135⁰ का मान क्या है?

(a) -1

(b) 0

(d) 1 से अधिक

Q. 45. यदि sin 2θ = cos 3θ, जहाँ 0 < θ < π/2 है, तो sin θ किसके बराबर है ?

Q. 46. यदि समीकरण x² + px + q= 0 के मूल tan 19° और tan 26° हैं, तो निम्नलिखित में से कौन-सा एक सही है ?

(a) q – p = 1

(b) p – q = 1

(d) p + q = 3

Q. 47. n पदों वाली एक AP जिसके पदों का योगफल n(n + 1) है, का चौथा पद क्या है ?

(a) 6

(b) 8

(d) 20

Q. 48. (1 + tan α tan β)² + (tan α – tanβ)² sec² α sec²β किसके बराबर है?

(a) 0

(b) 1

(d) 4

49. यदि p= cosec θ-cotθ और q= (cosec θ + cotθ)^-1 है, तो निम्नलिखित में से कौन-सा एक सही है?

(a) pq = 1

(b) p=q

(d) p+q= 0

Q. 50. यदि एक त्रिभुज ABC के कोण 1:2:3 के अनुपात में हैं, तो संगत भुजाएँ किस अनुपात में हैं ?

(a) 1:2:3

(b) 3:2:1

(d) 1:√5:√2

Q. 51. निम्नलिखित कथनों पर विचार कीजिए :

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं ?

(a) केवल 1

(b) केवल 2

(d) न तो 1, न ही 2

Q. 52. एक वृत्त x² + y² = a² की एक जीवा को व्यास मानकर एक वृत्त खींचा गया है । यह जीवा, रेखा x + y = a पर स्थित है । वृत्त का समीकरण क्या है ?

Q. 53. एक दीर्घवृत्त पर किसी बिन्दु की नाभीय दूरियों का योगफल अचर है और यह बराबर है

(a) लघु अक्ष की लम्बाई के

(b) दीर्घ अक्ष की लम्बाई के

(d) अर्ध-दीर्घ और अर्ध-लघु अक्षों की लम्बाइयों के योगफल के

Q. 54. समीकरण 2x²-3y²-6 = 0 निरूपित करता है

(a) एक वृत्त

(b) एक परवलय

(d) एक अतिपरवलय

Q. 55. दो परवलय y² = 4ax और x² = 4ay प्रतिच्छेदी हैं

(a) रेखा y = x पर स्थित दो बिन्दुओं पर

(b) केवल मूल-बिन्दु पर

(d) केवल (4a, 4a) पर

Q. 56. बिन्दु (1, 3) और (5, 1), एक आयत के दो सम्मुख शीर्ष हैं । अन्य दो शीर्ष रेखा y = 2x + c पर स्थित हैं । c का मान क्या है ?

(a) 2

(b) – 2

(d) – 4

Q. 57. यदि रेखाएँ 3y+ 4x = 1, y = x + 5 और 5y + bx = 3 संगामी हैं, तो b का मान क्या है ?

(a) 1

(b) 3

(d) ½

Q. 58. उस सरल रेखा का समीकरण क्या है जो y = x पर लंब है और (3, 2) से होकर गुज़रती है ?

(a) x – y = 5

(b) x + y = 35

(d) x – y = 1

Q. 59. सरल रेखाएँ x + y – 4 = 0, 3x + y – 4 = 0 और x + By – 4 = 0 एक त्रिभुज बनाती हैं; यह त्रिभुज

(a) समद्विबाहु है

(b) समकोणीय है

(d) विषमबाहु है

Q. 60. वृत्त x² + y² + 4x -7y + 12 = 0 द्वारा y-अक्ष पर काटा गया एक अंत: खंड किसके बराबर है ?

(a) 1

(b) 3

(d) 7

Q. 61. A(2,-3, 3), B(5, -3, -4) और C(2, -3, -2) शीर्षों वाले एक त्रिभुज का केन्द्रक कौन-सा बिन्दु है ?

(a) (-3, 3, -1)

(b) (3,-3, -1)

(d) (-3,-1,-3)

Q. 62. गोले x² + y² + z² – 6x + 8y – 10z + 1 = 0 की त्रिज्या क्या है?

(a) 5

(b) 2

(d) 3

Q. 63. समतलों 2x + y + 2z = 9 और 4x – 5y – 4z = 1 के प्रतिच्छेदन और बिन्दु (3, 2, 1) से गुज़रने वाले समतल का समीकरण क्या है ?

(a) 10x – 2y+ 2x = 28

(b) 10x + 2y + 2x = 28

(d) 10x -2y-22 = 24

Q. 64. समानांतर समतलों 4x – 2y + 4z + 9 = 0 और 8x-4y + 82 + 21 = 0 के बीच की दूरी क्या है ?

(a) ¼

(b) ½

(d) 7/4

Q. 65. z-अक्ष के दिक्-कोसाइन क्या हैं ?

(a) <1, 1, 1>

(b) <1, 0,0>

(d) <0, 0, 1>

Q. 66. यदि और है, तो किसके बराबर है ?

(a) 106

(b) -106

(d) – 53

Q. 67. यदि बिन्दुओं A और B के स्थिति सदिश क्रमश: और हैं, तो की लम्बाई क्या है?

(a) √14

(b) √29

(d) √53

Q.68. यदि एक समकोण त्रिभुज ABC में, कर्ण AC = p है, तो किसके बराबर है ?

(a) p²

(b) 2p²

(d) p

Q. 69. सदिशों और के बीच के कोण का साइन (sine) है

Q. 70. λ का वह मान क्या है जिसके लिए सदिश और सदिश लंबवत् हैं ?

(a) 1

(b) 2

(d) 4

Q. 71. x के सापेक्ष sec² (tan^-1x) का व्युत्पन्न क्या है ?

(a) 2x

(b) x² + 1

(d) x²

Q. 72. यदि f(x) = log₁₀ (1 + x) है, तो 4f(4) + 5f(1) – log₁₀2 किसके बराबर है ?

(a) 0

(b) 1

(d) 4

Q. 73. f(x)=ln (x2+1-x)द्वारा परिभाषित एक फलन f, है

(a) एक सम फलन

(b) एक विषम फलन

(d) न तो सम और न ही विषम फलन

Q. 74. f(x) = log_X 10 द्वारा परिभाषित फलन f का डोमेन है

(a) x>10

(b) x = 10 को छोड़कर, x> 0

(d) x = 1 को छोड़कर, x> 0

Q. 75. x01 – cos2 4xx2 किसके बराबर है ?

(a) 0

(b) 12

(d) 36

Q. 76. r>0 के लिए, त्रिज्या के एक वृत्त के परिमाप का क्षेत्रफल से अनुपात (r) है । तब (1) + (2) किसके बराबर है?

(a) 1

(b) 2

(d) 4

Q. 77. यदि (x) = 3^1+x है, तब fix) (y) fkz) किसके बराबर है ?

(a) f(x + y + 2)

(b) f(x + y + z +1)

(d) f(x + y + z + 3)

Q. 78. समीकरण x² +9|x| + 20 = 0 के लिए वास्तविक मूलों की संख्या है ?

(a) शून्य

(b) एक

(d) तीन

Q. 79. यदि f(x) = sin (cos x) है, तो f’(x) किसके बराबर है?

(a) cos (cos x)

(b) sin (-sin x)

(d) (-sin x) cos (cos x)

Q. 80. फलन f(x) = √(2 – x) (x -3) का डोमेन है

(a) (0, ∞)

(b) [0, ∞)

(e) [2,3]

(d) (2,3)

Q. 81. अवकल समीकरण dy/dx = cos (y – x) + 1 का हल है

Q. 82. 02|sin x – cosx| dx किसके बराबर है?

(a) 0

(b) 2(√2 -1)

(d) 2(√2 + 1)

Q. 83. यदि y = a cos 2x + b sin 2x है, तो

Q. 84. धातु की एक दी गई मात्रा को एक अर्ध बेलन (अर्थात् एक आयताकार आधार और अर्धवृत्ताकार सिरों वाला) में ढालना है । यदि कुल पृष्ठीय क्षेत्रफल को न्यूनतम रखा जाए, तो अर्ध बेलन की ऊँचाई का अर्धवृत्ताकार – सिरों के व्यास से अनुपात क्या होगा ?

(a) π (π + 2)

(b) (π + 2) : π

(d) उपर्युक्त में से कोई नहीं

Q. 85. e^{sin x} – cosx dx किसके बराबर है ?

(a) e+1

(b) e-1

(d) e

Q. 86. यदि है, तब f^-1(x) किसके बराबर है ?

Q. 87. किसके बराबर है ?

Q. 88. बिन्दु (4, 2) से y² = 8x की अल्पतम दूरी किसके बराबर है ?

(a) √2

(b) 2√2

(d) 3√2

Q. 89. y-अक्ष को मूल-बिन्दु पर स्पर्श करने वाले वृत्त-निकाय का अवकल समीकरण है

Q. 90. अवकल समीकरण के संदर्भ में निम्नलिखित पर विचार कीजिए :

1. अवकल समीकरण की घात (डिग्री) 1 है।

2. अवकल समीकरण की कोटि (ऑर्डर) 2 है।

उपर्युक्त कथनों में से कौन-सा/से सही हैं ?

(a) केवल 1

(b) केवल 2

(d) न तो 1, न ही 2

Q. 91. अवकल समीकरण dy/dx + x/y = 0 का व्यापक हल क्या है ?

Q. 92. k का वह मान क्या है जो पर संतत बनाता है ?

(a) 2

(b) 1

(d) 0

Q. 93. a²x+b²y का न्यूनतम मान, जहाँ xy = c² है, क्या है ?

(a) abc

(b) 2abc

(d) 4abc

Q. 94. किसके बराबर है ?

Q. 95. वक्र y = c sin x और x-अक्ष के बीच किसी एक पाश (लूप) का क्षेत्रफल क्या है ?

(a) c

(b) 20

(d) 4c

Q. 96. यदि sin θ + cos θ = √2 cos θ है, तो (cos θ – sin θ) किसके बराबर है ?

(a) – √2 cos θ

(b) – √2 sin θ

(d) 2 sin θ

Q. 97. एक वृत्त जिसका व्यास 44 cm है, उसकी एक जीवा की लम्बाई 22 cm है । जीवा की लघु चाप की लम्बाई क्या है ?

(a) 484/21 cm

(b) 242/21 cm

(d) 44/7 cm

Q. 98. यदि sin θ = – ½ और tan θ = 1/√3 है, तो θ किस चतुर्थांश में रहता है ?

(a) प्रथम

(b) द्वितीय

(d) चतुर्थ

Q. 99. अंक 1, 2, 3, 4 और 5 का प्रयोग करके तीन अंकों की कितनी सम संख्याएँ बनायी जा सकती हैं, जबकि अंकों की पुनरावृत्ति की अनुमति नहीं है ?

(a) 36

(b) 30

(d) 12

Q. 100. h ऊँचाई की एक मीनार के एक बिन्दु A से, जो कि मीनार के सीधे दक्षिण में है, उन्नयन कोण x है और एक बिन्दु B से, जो कि A के सीधे पूर्व में है, उन्नयन कोण । है । यदि AB = z है, तो निम्नलिखित में से कौन-सा एक सही है ?

Q. 101. ताश की एक गड्डी से प्रतिस्थापन सहित पत्ते निकाले जाते हैं । चौदहवें पत्ते के एक इक्का होने की प्रायिकता है ?

(a) 1/51

(b) 4/51

(d) 1/13

Q. 102. यदि A और B दो घटनाएँ इस प्रकार हैं कि P(A) = 0.5, P(B) = 0-6 और P(A ⋂ B) = 0-4 है, तब P(A ⋃ B) किसके बराबर है ?

(a) 0.9

(b) 0.7

(d) 0.3

Q. 103. एक प्रश्न तीन विद्यार्थियों A, B और C को दिया जाता है जिनकी प्रश्न को हल करने की प्रायिकताएँ क्रमश: ½, ¾ और ¼ हैं । यदि वे सभी स्वतंत्र रूप से प्रश्न को हल करते हैं तो इस बात की प्रायिकता क्या है कि प्रश्न का हल मिल जाएगा?

(a) 29/32

(b) 27/32

(d) 23/32

Q. 104. निष्पक्ष पासों के एक युग्म को फेंका (लुढ़काया) जाता है । फेंके जाने के बाद जब वह ठहरते हैं तो इस बात की प्रायिकता क्या है कि दूसरे पासे के फलक का मान पहले पासे के फलक के मान से अधिक है ?

(a) ¼

(b) ⅙

(d) 5/18

Q. 105. एक निष्पक्ष सिक्के को उछाला गया और साथ ही साथ एक अनभिनत पासे को फेंका गया । तो चित के साथ-साथ 2 या 4 या 6 प्राप्त करने की प्रायिकता क्या

(a) ½

(b) ⅓

(d) ⅙

Q. 106. यदि A, B, C तीन घटनाएँ हैं, तो इनमें से कम-से-कम दो घटनाओं के एक साथ घटने की प्रायिकता क्या है ?

(a) P(A ⋂ B) + P(B ⋂ C) + P(C ⋂ A)

(b) P(A ⋂ B) + P(B ⋂ C) + P(C ⋂ A) – P(A ⋂ B ⋂ C)

(d) P(A ⋂ B) + P(B ⋂ C) + P(C ⋂ A) – 3P(A ⋂ B ⋂ C)

Q. 107. यदि दो चर X और Y स्वतंत्र हैं, तो उनके बीच सहसंबंध गुणांक क्या है ?

(a) 1

(b) – 1

(d) उपर्युक्त में से कोई नहीं

Q. 108. दो स्वतंत्र घटनाएँ A और B इस प्रकार हैं कि P(A ⋃ B) = ⅔ और P(A ⋂ B) = ⅙ है । यदि P(B) < P(A) है, तो P(B) किसके बराबर है ?

(a) ¼

(b) ⅓

(d) ⅙

Q. 109. एक सौ (100) प्रेक्षणों का माध्य 50 है और उनका मानक विचलन 10 है । यदि प्रत्येक प्रेक्षण में से 5 घटा दिया जाता है और फिर उसे 4 से विभाजित कर दिया जाता है, तो नया माध्य और नया मानक विचलन क्रमश: क्या होंगे?

(a) 45,5

(b) 11-25, 1-25

(d) 12-5, 2.5

Q. 110. यदि दो निष्पक्ष पासों को फेंका जाता है, तब इस बात की सप्रतिबन्ध प्रायिकता क्या है कि पहले पासे पर 6 आए, जबकि यह दिया हुआ है कि पासों पर आए अंकों का योगफल 8 रहे ?

(a) ⅓

(b) ¼

(d) ⅙

Q. 111. दो सममित पासों को उछाला जाता है, प्रत्येक पासे के दो फलक लाल रंग से, दो काले रंग से, एक पीले रंग से और एक अन्य सफेद रंग से पेन्ट किए गए हैं । इस बात की प्रायिकता क्या है कि दोनों पर एक जैसा रंग आए ?

(a) 3/18

(b) 2/9

(d) ⅓

Q. 112. एक दराज में n जुर्राबें हैं, जिनमें से 3 जुर्राबें लाल रंग की हैं । यदि 2 जुर्राबें यादृच्छिक रूप से चुनी जाती हैं। और इस बात की प्रायिकता ½ है कि दोनों चुनी हुई जुर्राबें लाल रंग की हैं, तो n का मान क्या है ?

(a) 3

(b) 4

(d) 6

Q. 113. ताश के 52 पत्तों की एक गड्डी से दो पत्तों को यादृच्छिक रूप से चुना जाता है । इस बात की प्रायिकता क्या है कि वे दोनों पत्ते एक ही मूल्य के (एक जैसे) हों ?

(a) 1/17

(b) 3/17

(d) 7/17

Q. 114. एक पासे को आठ बार फेंका जाता है और उसमें 5 या 6 का आना सफलता माना जाता है । सफलताओं की ” कुल संख्या का माध्य और मानक विचलन क्रमशः होंगे

(a) 8/3, 16/9

(b) 8/3, 4/3

(d) 4/3, 16/9

Q. 115. दो घटनाएँ A और B इस प्रकार हैं कि A और B परस्पर अपवर्जी हैं । यदि P(A) = 0-5 और P(B) = 0.6 है, तो P(A | B) का मान क्या है ?

(a) 1/5

(b) 1/6

(d) 1/3

Q. 116. निम्नलिखित कथनों पर विचार कीजिए : –

1. मानों के एक समुच्चय का उनके समान्तर माध्य से विचलनों का बीजीय योगफल सदैव शून्य होता है

2. एक सममित बंटन के लिए समान्तर माध्य > माध्यिका > बहुलक (मोड)। उपर्युक्त कथनों में से कौन-सा/से सही है/हैं ?

(a) केवल 1

(b) केवल 2

(d) न तो 1, न ही 2

Q. 117. मान लीजिए x और Y के बीच सहसंबंध गुणांक 0-6 है । यादृच्छिक चर Z और W इस प्रकार परिभाषित है कि Z = x + 5 और W = Y/3 है । Z और W के बीच सहसंबंध गुणांक क्या है ?

(a) 0.1

(b) 02

(d) 0.6

Q. 118. यदि 1 और 20 के बीच के सभी धन पूर्णांकों को 3 से गुणा कर दिया जाता है, तो परिणामी श्रेणी का प्रसरण क्या है ?

(a) 99.75

(b) 199.75

(d) 399.25

Q. 119. इस बात की प्रायिकता क्या है कि किसी वृत्त का एक आंतरिक बिन्दु उसकी परिधि की अपेक्षा उसके केन्द्र के अधिक समीप हो ?

(a) ¼

(b) ½

(d) इसे निर्धारित नहीं किया जा सकता

Q. 120. यदि A और B दो घटनाएँ हैं, तब या तो घटना A या घटना B के घटित होने की प्रायिकता क्या है?

(a) P(A) + P(B)

(b) P(A ⋃ B)

(d) P(A) P(B)

NDA/NA(I) Exam 2019 General Ability Test Previous Year Paper

NDA/NA(I) Exam 2019 General Ability Test Previous Year Paper

PART – A

SPOTTING ERRORS

Directions : Each item in this section has a sentence with three underlined parts labelled (a), (b) and (c). Read each sentence to find out whether there is any error in any underlined part and indicate your response in the Answer Sheet against the corresponding letter i.e., (a) or (b) or (c). If you find no error, your response should be indicated as (d).

Q. 1.

(a) Opening his letters ,

(b) reading them carefully and sending for his clerk,

(d) No error.

Q. 2.

(a) He was my school-friend,

(b) but becoming a great man,

(d) No error.

Q. 3.

(a) Rabindranath Tagore

(b) a Nobel laureate and the author of the national anthem,

(d) No error.

Q. 4.

(a) The art of printing was introduced into England

(b) during the reign of Edward IV

(d) No error.

Q. 5.

(a) From thirty years

(b) he devoted himself to public affairs

(d) No error.

Q. 6

(a) If Ramesh will be promoted

(b ) he will get

(d) No error.

Q. 7.

(a) My brother goes

(b) to the office

(d) No error.

Q. 8.

(a) If you lend Mohan a pen

(b) he will lend it to someone else

(d) No error.

Q. 9.

(a) One of most widely spread

(b) bad habits

(d) No error.

Q. 10.

(a) A great part

(b) of Arabia

(d) No error.

SYNONYMS

Directions : Each item in this section consists of a sentence with an underlined word followed by four words or group of words. Select the option that is nearest in meaning to the underlined word/words and mark your response in your Answer Sheet accordingly.

Q. 11. Some people complain when they encounter a small misfortune in the course of their thoroughly happy life.

(a) run into

(b) run away

(d) run with

Q. 12. This world is full of miseries.

(a) indifferent love

(b) perfect happiness

(d) moderate sympathies

Q. 13. A glance at a beautiful object gives us delight.

(a) wisdom

(b) happiness

(d) peace

Q. 14. It is terrible for people to die of starvation

(a) starch

(b) staple

(d) hunger

Q. 15. The university has constituted a grievance redressal committee to look into the matter.

(a) depression

(b) complaint

(d) gratefulness

Q. 16. Rakesh delivered a slanderous speech.

(a) abusive

(b) praiseworthy

(d) inspiring

Q. 17. Suddenly, the sky was darkened by a gigantic bird.

(a). winged

(b) small

(d) enormous

Q. 18. To abolish poverty would be to destroy the soil upon which mankind produces the virtues conducive to higher civilization

(a) detest

(b) eradicate

(d) assimilate

Q. 19. The Arabs who are not in the cities live in the desert throughout the year, shifting from one oasis to another.

(a) sandbank

(b) mound

(d) spring

Q. 20. The various facets of life can be found reflected in a large city.

(a) several

(b) similar

(d) singular

ANTONYMS

Directions: Each item in this section consists of a sentence with an underlined word followed by four word. Select the option that is opposite in meaning to the underlined word/words and mark your response in your Answer Sheet accordingly.

Q. 21. Ramesh is a very dubious character.

(a) shady

(b) suspicious

(d) doubtful

Q. 22. Do not indulge in unmindful activities, please.

(a) vigilant

(b) careless

(d) fatuous

Q. 23. He is suffering from a curable disease.

(a) remediable

(b) treatable

(d) operable

Q. 24. He was born on a very auspicious day.

(a) propitious

(b) fortunate

(d) opportune

Q. 25. He has deeper hostility towards Mohan.

(a) animosity

(b) belligerence

(d) friendship

Q. 26. His life is rather monotonous.

(a) exciting

(b) dreary

(d) uneventful

Q. 27. Macbeth is a morally repulsive character.

(a) abominable

(b) attractive

(d) ugly

Q. 28. The serene beauty of Kashmir had a soothing effect on his mind.

(a) placid

(b) pleasing

(d) turbulent

IDIOMS AND PHRASES

Directions : Given below are some idioms/phrases followed by four alternative meanings to each. Choose the response (a), (b), (c) or (d) which is the most appropriate expression.

Q. 29. Life is transient in nature.

(a) brief

(b) momentary

(d) short-lived

Q. 30. Sohan is a vain person.

(a) modest

(b) arrogant

(d) proud

Q. 31. A dark horse

(a) a black coloured horse

(b) a person who wins a race or competition although no one expected him to

(d) an ignorant person

Q. 32. A show-stopper

(a) someone who stops the show

(b) someone who organizes the show

(d) a fashionable person

Q. 33. A jack of all trades

(a) someone who has many skills

(b) a confident and not very serious young man

(d) a great businessman

Q. 34. Fight tooth and nail

(a) to quarrel with someone

(b) to attack someone with a lot of force

to try hard to prevent something from happening

(d) to try very hard to achieve some thing

Q. 35. Fair and square

(a) in an honest way

(b) in a critical way

(d) in a foolish way

ORDERING OF SENTENCES

Directions : In this section each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and 86. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet.

Q. 36.

S1: We do not know what to do with our knowledge.

S6: In the course of time they may rule over us altogether.

P : For example, we are unable to manage our machines,

Q: We already find it diflicult to do without machines.

R: Machines should be fed properly and waited upon attentively; otherwise they refuse to work or cause destruction.

S : Science has given us superhuman powers, which we do not use properly.

The proper sequence should be

(a) SPRO

(b) PSQR

(d) SRPQ

Q. 37.

Sl: The British rule in India has brought about moral, material, cultural and spiritual ruination of this great country.

S6: We are not to kill anybody but it is our dharma to see that the curse of this Government is blotted out.

P: I regard this rule as a curse.

Q : Sedition has become my religion.

R: Ours is a non-violent battle.

S: I am out to destroy this system of Government.

The proper sequence should be

(a) SPRO

(b) PSOR

(d) SRPQ

ORDERING OF WORDS IN A SENTENCE

Directions : Each of the following items in this section consists of a sentence, the parts of which have been jumbled. These parts have been labelled P, Q, R and S. Given below each sentence are four sequences namely (a), (b), (c) and (d). You are required to rearrange the jumbled parts of the sentence and mark your response accordingly.

Q. 38. the urban local body elections (P) unidentified gunmen (Q) and injured another during (R) shot dead two workers (S)

(a) QSRP

(b) POSR

(d) RPS

Q. 39. both intense political and (P) this state has a history of (Q) of syncretic accomplishments (R) religious contestation and (S)

(a) SQPR

(b) POSR

(d) QPSR

Q. 40. the father also (P) in his quest for justice (P) by the system (P) feels let down

(a) SQPR

(b) PSRQ

(d) PQRS

COMPREHENSION

Directions : In this section you have a passage. After the passage, you will find some items based on the passage. First, read the passage and answer the items based on it. You are required to select your answers based on the contents of the passage and opinion of the author only.

Passage

I do not wish to suggest that because we were one nation we had no differences, but it is submitted that our leading men travelled throughout India either on foot or in bullock carts. They learned one another’s languages and there was no aloofness amongst them. What do you think could have been the intention of those farseeing ancestors of ours who established Setubandha (Rameshwar) in the South, Jagannath in the East and Hardwar in the North as places of pilgrimage? You will admit they were no fools. They knew that worship of God could have been performed just as well at home. They taught us that those whose hearts were aglow with righteousness had the Ganges in their own homes. But they saw that India was one undivided land so made by nature. They, therefore, argued that it must be one nation. Arguing thus, they established holy places in various parts of India, and fired the people with an idea of nationality in a manner unknown in other parts of the world. And we Indians are one as no two Englishmen are. Only you and I and others who consider ourselves civilized and superior persons imagine that we are many nations. It was after the advent of railways that we began to believe in distinctions, and you are at liberty now to say that it is through the railways that we are beginning to abolish those distinctions. An opium-eater may argue the advantage of opium-eating from the fact that he began to understand the evil of the opium habit after having eaten it. I would ask you to consider well what I had said on the railways.

Q. 41. According to the author, India

(a) has never been one nation

(b) has been an aggregate of several nations

(d) became a nation after the British came

Q. 42. Why did the great sages of India establish pilgrimages in the different corners of the country?

(a) Because they wanted to push people to travel to different places

(b) Because they could observe the underlying unity of the country as made by nature

(d) Because they wanted people to be religious everywhere

Q. 43. In the passage, the author’s attitude towards the railways is

(a) critical

(b) sympathetic

(d) apathetic

Q. 44. What does the author mean when he says that “whose hearts were aglow with righteousness had the Ganges in their own homes” ?

(a) One need not visit the Ganges to take holy bath

(b) The Ganges has been polluted, so one should bath at home

(d) The purity of heart is superior to observance of any ritual

Q. 45. The paragraph is written in a

(a) dialogic style

(b) prescriptive style

(d) analytical style

Q. 46. ________forests prevent erosion.

(a) Lean

(b) Dense

(d) Tidy

Q. 47. Three people were arrested and an illegal anns unit was ______by the police in a raid.

(a) revealed

(b) searched

(d) busted

Q. 48. A woman got into the car and _____________

(a) drove off

(b) broke down

(d) drove in

Q. 49. The lecture was not very interesting. In fact I __________ in the middle of it.

(a) showed off

(b) put off

(d) plugged off

Q. 50. The cops _______ murder by kin.

(a) suspect

(b) afford

(d) administer

Q. 51. निम्नलिखित कोशिकांगों में से किसमें न्यूक्लीक अम्ल नहीं पाया जाता है ?

(a) केन्द्रिक

(b) हरितलवक

(d) जीवद्रव्य कला

Q. 52. निम्नलिखित कोशिकांगों में से किसमें प्रोटीन कोडन वाला इसका अपना आनुवंशिक पदार्थ नहीं पाया जाता है ?

(a) राइबोसोम

(b) केन्द्रक

(d) हरितलवक

Q. 53. पादपों में संवहन ऊतक का एक घटक निम्नलिखित में से कौनसा नहीं है ?

(a) रेशा (फाइबर)

(b) वाहिनिका

(d) चालनी नलिका

Q. 54. निम्नलिखित में से किस एक जीव में संवहन ऊतक पाये जाते हैं ?

(a) क्लैडोफोरा

(b) पेनिसिलियम

(d) ऐनाबीना

Q. 55. निम्नलिखित में से कौनसा जीव, किसी पारितन्त्र में प्राथमिक उपभोक्ता वर्ग को निरूपित करता है ?

(a) इल्ली

(b) जंगली सेब का पेड़ (क्रेब एप्पल ट्री)

(d) गौरहिवा शिकरा (स्पैरोहॉक)

Q. 56. वृहत् ज्वार भाटा किसे संदर्भित करता है ?

(a) उच्च और निम्न ज्वार-भाटाओं के दौरान समुद्र तल में अधिकतम अन्तर

(b) उच्च और निम्न ज्वार-भाटाओं के दौरान समुद्र तल में निम्नतम अन्तर

(d) चन्द्रमा के गुरुत्वीय कर्षण की तुलना में सूर्य के गुरुत्वीय कर्षण का प्रतिकरण

Q. 57. परमाणुओं के बीच बंधों में निम्नलिखित में से कौनसी ऊर्जा संगृहित होती है ?

(a) नाभिकीय ऊर्जा

(b) रासायनिक ऊर्जा

(d) उष्मीय ऊर्जा

Q. 58. सूर्य से निकलने वाली प्रकाश ऊर्जा किसके द्वारा फैलायी जा सकती है ?

(a) वर्षा-बिन्दुओं की एक बौछार से

(b) एक समतल दर्पण से

(d) एक उत्तल लेंस और एक अवतल लेंस के संयोजन से

Q. 59. एक सेब के भूमि पर गिरने पर होने वाले ऊर्जा स्थानान्तरण का सही अनुक्रम है

(a) गुरुत्वीय स्थितिज ऊर्जा → वायु में ऊष्मीय ऊर्जा → गतिज ऊर्जा → भूमि और सेब में उष्मीय ऊर्जा → ध्वनि ऊर्जा

(b) गुरुत्वीय स्थितिज ऊर्जा → ध्वनि ऊर्जा → गतिज ऊर्जा → वायु में उष्मीय ऊर्जा → भूमि और सेब में उष्मीय ऊर्जा

(d) गुरुत्वीय स्थितिज ऊर्जा → गतिज ऊर्जा → ध्वनि ऊर्जा → वायु में उष्मीय ऊर्जा →भूमि और सेब में उष्मीय ऊर्जा

Q. 60. परमाणु ऊर्जा केन्द्रों (न्यूक्लीयर पॉवर स्टेशन) में ईंधन के रूप में निम्नलिखित में से कौनसा खनिज पदार्थ प्रयुक्त होता है ?

(a) बॉक्साइट

(b) स्फटिक (क्वार्ट्ज)

(d) पिचब्लेन्ड

Q. 61. निम्नलिखित में से कौनसा एक संश्लेषित अपमार्जक नहीं है?

(a) CH₃(CH₂)₁₀CH₂O SO₃^– Na⁺

(b) [CH₃(CH₂)₁₅-N-(CH₃)₃]⁺ Br^–

(d) CH₃(CH₃)₁₆COO(CH₂CH₂O)_n CH₂CH₂OH

Q. 62. निम्नलिखित में से कौनसा स्वच्छ ईंधन का एक उदाहरण है ?

(a) कोक

(b) प्रोपेन

(d) मोम

Q. 63. निम्नलिखित में से कौनसी धातु शीतल जल के साथ अभिक्रिया नहीं करती है ?

(a) कैल्सियम (Ca)

(b) पोटैशियम (K)

(d) सोडियम (Na)

Q. 64. निम्नलिखित में से किस युग्म में आयन समइलेक्ट्रॉनी हैं ?

(a) Mg²⁺, Ar

(b) Na⁺, O^2-

(d) K⁺, Ne

Q. 65. रंगलेपों (पेन्ट) में योजक के रूप में निम्नलिखित में से किसे प्रयुक्त किया जाता हैं ?

(a) टाइटेनियम डाइऑक्साइड

(b) नोवोलेक

(d) सिलिकोन

Q. 66. वायु संहति के संदर्भ में निम्नलिखित में से कौनसा एक सही नहीं है ?

(a) वायु संहति या तो उष्णकटिबंधीय या ध्रुवीय प्रदेश में बनता है

(b) वायु संहति महाद्वीपों पर और इसके महासागर पर विकसित होता है

(d) वायु संहति मौसम की स्थितियों को बदल देता है

Q. 67. राष्ट्रीय जल अकादमी, जो जल संसाधन में प्रशिक्षण तथा क्षमता निर्माण में उत्कृष्टता का केन्द्र है, कहाँ स्थित है ?

(a) नई दिल्ली

(b) कोलकाता

(d) चेन्नई

Q. 68. “कैम्पोस” तथा “लानोस”, उष्णकटिबंधीय सवाना घासस्थल आमतौर पर कहाँ पाये जाते

(a) आस्ट्रेलिया

(b) मध्य अफ्रीका

(d) पूर्वी एशिया

Q. 69. “अंगूरोत्पादन” निम्नलिखित आस्ट्रेलियाई शहरों में से किस एक की सामान्य विशेषता हैं ?

(a) एडिलेड

(b) डार्विन

(d) ब्रिस्बेन

Q. 70. उष्ण तथा सूखा पवन “शमाल” जो कि एक “स्थानीय” हवा है, कहाँ पाई जाती है ?

(a) पूर्वी एशिया

(b) अफ्रीका का पश्चिमी तट

(d) मेसोपोटामिया

Q. 71. “वर्षा का व्युत्क्रमण” किससे संबद्ध है ?

(a) पर्वतीय वर्षा

(b) संवहनी वर्षा

(d) चक्रवातीय वर्षा (शीतोष्ण)

Q. 72. ‘हिस्ट्री ऑफ ब्रिटिश इंडिया’ नामक पुस्तक का लेखक कौन था ?

(a) चार्ल्स ग्रांट

(b) जॉन स्टुअर्ट मिल

(d) विलियम जॉन्स

Q. 73. अगस्त 25, 1857 की आजमगढ़ उद्घोषणा ने निम्नलिखित में से किस विषय पर बल दिया था?

(a) हिन्दु-मुस्लिम विभाजन

(b) अंग्रेजी सरकार को समर्थन देना

(d) भारी जुमास (राजस्व मांग) का आरोपण/अधिरोपण

Q. 74. किस वाइसराय ने यह कहा कि “अगर गांधी न होता तो यह दुनिया वाकई बहुत खूबसूरत होती …..” ?

(a) लॉर्ड इरविन

(b) लॉर्ड वेवेल

(d) लॉर्ड विलिंगडन

Q. 75. किस भारतीय व्यवसायी ने गांधीजी के ‘सर्वनिष्ठ उद्देश्य’ की ओर कार्य करने में उनकी सहायता के लिए ‘लाभप्रद पूंजीवाद’ का समर्थन किया ?

(a) घनश्याम दास बिड़ला

(b) अम्बालाल साराभाई

(d) टी. टी. के. कृष्णामचारी

Q. 76. ‘इन मेमोरियम’ कलाकृति निम्नलिखित में से किस यूरोपीय चित्रकार की एक रचना है ?

(a) थॉमस जोंस बार्कर

(b) जोसेफ नोएल पैटन

(d) चार्ल्स डोआयली (D’oyly)

Q. 77. किसी विद्युतरोधी को निम्नलिखित में से कौन आवेशित कर सकता है ?

(a) धारा वैद्युत

(b) स्थिर वैद्युत

(d) गुरुत्वीय क्षेत्र

Q. 78. 20°C पर, जल में ध्वनि की चाल होती है लगभग

(a) 330 m/s

(b) 800 m/s

(d) 5000 m/s

Q. 79. लौह (आयरन) का गलनांक निम्न में से क्या हो सकता है ?

(a) 25°C

(b) 37°C

(d) 1500°C

Q. 80. कॉपर के एक तार की त्रिज्या r तथा लम्बाई l है। इसका प्रतिरोध R है। यदि कॉपर के किसी अन्य तार की त्रिज्या 2r तथा लम्बाई 1/2 हो, तो इस तार का प्रतिरोध होगा

(a) R

(b) 2R

(d) R/8

Q. 81. किसी नाभिकीय रिऐक्टर की कार्यविधि में प्रयुक्त मूल वैज्ञानिक सिद्धांत है

(a) नाभिकीय संलयन

(b) नियंत्रित नाभिकीय संलयन

(d) नियंत्रित नाभिकीय विखंडन

Q. 82. नीचे दी गयी अभिक्रिया के लिए निम्नलिखित में से कौनसा कथन सही नहीं है ?

Fe(ठोस)+CuSO, (जलीय)→FeSO (जलीय) +Cu(ठोस)

(a) लौह अपचायक है

(b) अभिक्रिया के पश्चात् विलयन का रंग हरा हो जाता है

(d) यह अभिक्रिया अपचयोपचय (रेडॉक्स) अभिक्रिया का एक उदाहरण है

Q. 83. निम्नलिखित में से कार्बनिक अम्ल कौनसा है ?

(a) हाइड्रोक्लोरिक अम्ल

(b) नाइट्रिक अम्ल

(d) सल्फ्यूरिक अम्ल

Q. 84. डाईनाइट्रोजन (N₂) और डाईऑक्सीजन (O₂) वायु के मुख्य अवयव हैं, परन्तु ये परस्पर अभिक्रिया कर नाइट्रोजन के ऑक्साइड नहीं बनाते हैं

क्योंकि –

(a) अभिक्रिया को प्रारम्भ करने के लिए उत्प्रेरक की आवश्यकता होती है।

(b) नाइट्रोजन के ऑक्साइड अस्थायी होते हैं

(d) अभिक्रिया होने के लिए वायु में N₂ और O₂की रससमीकरणमिति (स्टॉइकियोमीट्री) आदर्श नहीं है

Q. 85. प्रकाशवैद्युत प्रभाव की परिघटना की व्याख्या निम्नलिखित में से किसने की है ?

(a) मैक्स प्लांक

(b) अल्बर्ट आइन्सटीन

(d) अर्नेस्ट रदरफोर्ड

Q. 86.C₂H₂O₄-2H₂O में ऑक्सैलिक अम्ल का तुल्यांकी भार है

(a) 45

(b) 63

(d) 126

Q. 87. निम्नलिखित में से कौनसी एक नदी पश्चिम की ओर बहने वाली नदी नहीं है ?

(a) पेरियार

(b) भरतपूझा

(d) ताम्रपर्णी

Q. 88. निम्नलिखित में से किस एक नदी को पहले “वितस्ता” नाम से जाना जाता था ?

(a) तिस्ता

(b) झेलम

(d) भरतपूझा

Q. 89. शारदा नदी उत्तरप्रदेश के उत्तरी मैदानों में निर्गम होती है। मैदानों में प्रवेश करने से पहले, शारदा किस नाम से जानी जाती है ?

(a) सरस्वती

(b) भागीरथी

(d) पिंडर

Q. 90. “मिशन इंद्रधनुष” किससे संबंधित है ?

(a) बुलेट ट्रेन परियोजना

(b) कृषि विकास

(d) पूर्ण प्रतिरक्षण

Q. 91. पृथ्वी के घूर्णन का/के पर्यावरणीय प्रभाव निम्नलिखित में से कौन सा/से है/हैं ? .

1. दिवालोक तथा वायु ताप में दैनिक या आह्निक आवर्तन (सामंजस्य)

2. वायु तथा जल दोनों का प्रवाह पथ एक तिरछे दिशा में सुसंगत रूप से मुड़ जाता हैं

3. ज्वार-भाटा की गति

नीचे दिये गये कूट का प्रयोग कर सही उत्तर चुनिये :

(a) केवल 1 और 2

(b) केवल 1 और 3

(d) केवल 3

Q. 92. निम्नलिखित में से किस एक इतिहासकार ने भारत छोड़ो आन्दोलन को एक “स्वतः प्रवर्तित क्रांति” के रूप में वर्णित किया है ?

(a) गोर्डन जॉनसन

(b) डेविड अर्नोल्ड

(d) पीटर रॉब

निम्नलिखित 3 (तीन) प्रश्नांशों में दो कथन हैं, कथन I और कथन II इन दोनों कथनों का सावधानीपूर्वक परीक्षण कीजिए और नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए :

कूट:

(a) दोनों कथन अलग-अलग सही हैं और कथन II, कथन I का सही स्पष्टीकरण है

(b) दोनों कथन अलग-अलग सही हैं, किन्तु कथन II, कथन I का सही स्पष्टीकरण नहीं है

(d) कथन I गलत है, किन्तु कथन II सही है

Q. 93.

कथन I : अबुल फजल ने अकबर के शासनकाल से सम्बन्धित विचारों को सुगठित किया, निरूपित किया और उन्हें सुस्पष्ट बनाया ।

कथन II : अबुल फजल के गुणों ने अकबर को प्रभावित किया और अकबर ने अबुल फजल को अपनी नीतियों के लिए उपयुक्त परामर्शदाता और प्रवक्ता के रूप में पाया ।

Q. 94.

कथन I : अगस्त 1936 में अखिल भरतीय किसान सभा द्वारा पारित किसान घोषणापत्र में आमूल परिवर्तनवादी (उप्र) मांगें अन्तर्विष्ट थी।

कथन II : अखिल भारतीय किसान सभा कांग्रेस का एक भाग थी और इसने प्रान्तीय कांग्रेस समितियों से घनिष्ठ सम्बन्ध बना रखे थे ।

Q. 95.

कथन I : ब्रिटिश ने भारत पर एक आधुनिक नौकरशाही के माध्यम से शासन किया, इस नौकरशाही में भारतीय सिविल सेवा की प्रधानता थी जिसके सदस्य खुली प्रतियोगिता पर आधारित योग्यता (मेरिट) द्वारा भर्ती किये गये थे।

कथन II : भारतीय सिविल सेवा, भारतीयों की एकनिष्ठ (अनन्य) सहभागिता पर आधारित थी।

Q. 96. दो धात्विक तार A और B कॉपर के उपयोग से बने हैं । तार A की त्रिज्या r तथा लंबाई l है। तार A के परितः dc वोल्टता V प्रयुक्त करने पर शक्ति क्षय P होता है। तार B की त्रिज्या 2r तथा लंबाई 21 है और इस तार के परितः भी समान dc वोल्टता V प्रयुक्त करने पर शक्ति क्षय P₁ होता है । P तथा P₁ के बीच सही संबंध निम्नलिखित में से कौन सा है ?

(a) P = 2P₁

(b) P = P₁/2

(d) P = P₁

Q. 97. किसी परिनालिका के संबंध में निम्नलिखित कथनों पर विचार कीजिए :

1. परिनालिका में चुम्बकीय क्षेत्र की तीव्रता परिनालिका में प्रति इकाई लंबाई में फेरों की संख्या पर निर्भर करती है ।

2. परिनालिका में चुम्बकीय क्षेत्र की तीव्रता परिनालिका के तार में प्रवाहित धारा पर निर्भर करती है

3. परिनालिका में चुम्बकीय क्षेत्र की तीव्रता परिनालिंका के व्यास पर निर्भर करती है

उपर्युक्त में से कौन से कथन सही हैं ?

(a) 1, 2 और 3

(b) केवल 1 और 3

(d) केवल 1 और 2

Q. 98. प्रकाश वर्ष किसके मापन का मात्रक होता है ?

(a) बहुत लम्बी दूरियों का

(b) वर्षों में समय अंतराल का

(d) परमाणुओं के द्रव्यमान का

Q. 99. किसी दूरदर्शक के अभिदृश्यक लेन्स की फोकस दूरी 50 cm है । यदि दूरदर्शक का आवर्धन 25 है, तो नेत्रिका लेन्स की फोकस दूरी है

(a) 12-5 cm

(b) 5 cm

(d) 10 cm

Q. 100. निम्नलिखित में से कौनसा एक बल अकेंद्रीय तथा असंरक्षी है ?

(a) घर्षण बल

(b) वैद्युत बल

(d) यांत्रिक बल

Q. 101. आई वायु के संपर्क में आने पर, कॉपर की सतह पर एक हरी परत बन जाती है ।

निम्नलिखित में से किस यौगिक के बनने के कारण ऐसा होता है ?

(a) कॉपर कार्बोनेट

(b) कॉपर आक्साइड

(d) कॉपर नाइट्रेट

Q. 102. निम्नलिखित में से कौनसा पदार्थ हाइड्रोक्लोरिक अम्ल के जलीय विलयन के साथ अभिक्रिया करके कार्बन डाइऑक्साइड उत्पन्न नहीं करेगा ?

(a) चूना पत्थर (लाइमस्टोन)

(b) बिना बुझा चूना

(d) संगमरमर

Q. 103. निम्नलिखित में से कौनसा पदार्थ एक मिश्रण नहीं है ?

(a) बर्फ

(b) आइसक्रीम

(d) शहद

Q. 104. निम्नलिखित में से कौनसा लवण-क्रिस्टल वृद्धि का एक उदाहरण है?

(a) रासायनिक अपक्षय

(b) भौतिक अपक्षय

(d) जैव रासायनिक अपक्षय

Q. 105. निम्नलिखित में से कौनसा एक भारत के राज्यों में प्रमाणित कोयला-निचयों का घटते क्रम में सही अनुक्रम है ?

(a) झारखंड, छत्तीसगढ़, ओडिशा, पश्चिम बंगाल

(b) झारखंड, ओडिशा, छत्तीसगढ़, पश्चिम बंगाल

(d) ओडिशा, छत्तीसगढ़, पश्चिम बंगाल, झारखंड

Q. 106. रिक्टर पैमाना (रिक्टर स्केल) से संबंधित निम्नलिखित कथनों पर विचार कीजिए :

1. इसका आविष्कार चार्ल्स एफ. रिक्टर द्वारा 1935 में हुआ

2. यह एक एकल भूकंप के कारण निर्मुक्त ऊर्जा की मात्रा का वर्णन करता है

3. रिक्टर स्केल की कोई ऊपरी सीमा नहीं है

उपर्युक्त में से कौन सा/से कथन सही है/

(a) केवल 1

(b) केवल 1 और 2

(d) 1, 2 और 3

Q. 107. निम्नलिखित महासागर धाराओं में से कौनसी एक शीत महासागर धारा नहीं है ?

(a) कैनरी धारा

(b) कैलिफोर्निया धारा

(d) ओयाशियो धारा

Q. 108. महासागर की सतह पर किसी निश्चित स्थान पर दो क्रमिक ज्वारों के घटित होने में समय अन्तराल कितना होता है ?

(a) 12 घंटे

(b) 12 घंटे 26 मिनट

(d) 24 घंटे 52 मिनट

Q. 109. दन्तवल्क निम्नलिखित में से किस एक कैल्सियम यौगिक से बना होता है ?

(a) कैल्सियम कार्बोनेट

(b) कैल्सियम सल्फेट

(d) कैल्सियम फॉस्फेट

Q. 110. मान लीजिए कि समान घनत्व वाले दो ग्रहों, 1 और 2 की त्रिज्यायें क्रमश: R₁ तथा R₂ हैं जहाँ R₁ > R₂ है । इन ग्रहों की सतह पर गुरुत्वीय त्वरण किस प्रकार संबंधित हैं ?

(a) g₁>g₂

(b) g₁<g₂

(d) कुछ कहा नहीं जा सकता

Q. 111. सूर्योदय से पहले तथा सूर्यास्त के पश्चात् भी सूर्य अल्प समय के लिए दिखायी देता है। ऐसा होने का क्या कारण है ?

(a) पूर्ण आंतरिक परावर्तन

(b) वायुमंडलीय अपवर्तन

(d) विक्षेपण (परिक्षेपण)

Q. 112.

उपर दिये गये चित्र में तीन वस्तुओं A, B तथा C के लिए उनके समय (1) – अवस्थिति (x) ग्राफ दर्शाये गये हैं। किसी क्षण (t>0) पर वस्तु A, B तथा C की चालों क्रमश: V.V, तथा V. के मध्य सही संबंध निम्नलिखित में से कौनसा है ?

(a) V_A < V_B < V_C

(b) V_A>V_B>V_C

(d) V_A=V_B= V_C = 0

Q. 113. एक (1) डाइन (CGS पद्धति में बल का मात्रक) किसके बराबर है ?

(a) 10³ g cm/s²

(b) 10^-3 g cm/s²

(d) 10⁵ kg m/s²

Q. 114.

दिए गये वेग (1)- समय (t) ग्राफ में, त्वरित गति तथा मंदित (अवत्वरण) गति क्रमश: किन रेखा खंडों द्वारा दर्शायी गयी है ?

(a) CD और BC

(b) BC और AB

(d) AB और CD

Q. 115. किसी थर्मस फ्लास्क के संबंध में निम्नलिखित में से कौनसा कथन सही नहीं है ?

(a) फ्लास्क की दीवारें काँच की बनी होती हैं, जो ऊष्मा का हीन चालक होता है। फ्लास्क की दीवारों के मध्य निर्वात । होता है

(b) काँच की दीवारों की सतह चमकीली होती हैं

(c) आंतरिक दीवार की सतह ऊष्मा की अधिक मात्रा का विकिरण करती है तथा बाहरी दीवार की सतह आंतरिक दीवार से विकरित होने वाली ऊष्मा के कुछ भाग को अवशोषित करती है

(d) कॉर्क आधार ऊष्मा के हीन चालक होते

Q. 116. कृष्ण विवर (ब्लैक होल) क्या है ?

(a) एक विशाल कृष्ण तारा, जिसका इसकी सतह पर गुरुत्व के कारण त्वरण शून्य है

(b) एक तारा, जिसका इसकी सतह पर गुरुत्व के कारण त्वरण मध्यम (सामान्य) है

(d) एक तारा, जो अपने आप में टूट गया है और जिसका इसकी सतह पर गुरुत्व के कारण त्वरण शून्य है

Q. 117. फारेनहाइट और सेल्सियस के बीच रूपांतरण का सूत्र °F=X+ (1-8 × °C) है। इसमें घटक x कितना है ?

(a) 32

(b) 22

(d) 42

Q. 118. जब श्वेतप्रकाश का एक किरणपुंज कांच के एक प्रिज़्म से होकर गुजरता है, तो कौनसे रंग वाला किरणपुज अपने पथ से सबसे कम विचलित होता है ?

(a) नीला

(b) लाल

(d) बैंगनी

Q. 119. LIGO का क्या अर्थ है ?

(a) लेज़र इंटरफेरोमीटर ग्रेविटेशनल वेव ऑब्जरवेटरी

(b) लाइट इंटरफेरोमीटर ग्रेविटेशनल वेव आब्जरवेटरी

(d) लेज़र इंड्यूस्ड गैसियस ऑप्टिक्स

Q. 120. एक फ्यूज़ का तार कैसा होना चाहिए ?

(a) चालक और निम्न गलनांक वाला

(b) चालक और उच्च गलनांक वाला

(d) रोधी और निम्न गलनांक वाला

Q. 121. कामराजार पत्तन को 2001 में उष्मीय कोयले की मांग का प्रबंध करने के लिए अधिकृत (चालू) किया गया था। यह किस भारतीय राज्य के तट के पास स्थित है ?

(a) आन्ध्र प्रदेश

(b) ओडिशा

(d) कर्नाटक

Q. 122. भारत का निम्नलिखित में से कौनसा संघ राज्यक्षेत्र भौगोलिक क्षेत्र की दृष्टि से सबसे छोटा है ?

(a) दमन और दीव

(b) चंडीगढ़

(d) लक्षद्वीप

Q. 123. निम्नलिखित में से किसे ‘पोलर फ्रंट थ्योरी’ (ध्रुवीय वाताग्र सिद्धान्त) से अनिवार्य रूप से सम्बन्धित कहा जा सकता है ?

(a) प्रतिचक्रवात

(b) उष्णकटिबन्धीय चक्रवात

(d) अन्तः उष्णकटिबन्धीय अभिसरण

Q. 124. ब्रह्मपुत्र और सिन्धु नदियां पूर्ववर्ती नदियां हैं। एक पूर्ववर्ती जल निकास अपवाह की सही परिभाषा निम्नलिखित में से कौन सी हो सकती है ?

(a) जो हिमालय के प्रारंभिक ढलान का अनुसरण करता है

(b) जो हिमालयी श्रेणी (परास) के अस्तित्व में आने से पहले ही विद्यमान था

(d) जिसने हिमालय के शैल संस्तरों के नतिलंबों का अनुसरण किया था

Q. 125. सन 1931 में कांग्रेस के कराची संकल्पने निम्नलिखित में से किस एक विषय का समर्थन किया था

(a) राज्य, मुख्य उद्योगों और सेवाओं का स्वामित्व या उन पर नियंत्रण नहीं रखेगा

(b) राज्य, प्रमुख उद्योगों और सेवाओं को भारतीय व्यवसाय वर्गों को सौंप देगा

(d) राज्य, प्रमुख उद्योगों और सेवाओं का स्वामित्व या उन पर नियंत्रण रखेगा

Q. 126. शॉनब्रुन की संधि (1809) निम्नलिखित में से किस युद्ध के बाद हस्ताक्षरित की गयी थी ?

(a) ऑस्टरलिट्ज का युद्ध

(b) तिलसिट का युद्ध

(d) लिस्बन का युद्ध

Q. 127. न्यू मॉडल यूनियनों के विषय में निम्नलिखित में से कौन सा/से कथन सही है/हैं ?

1. न्यू मॉडल यूनियनें 1850 के दशक में गठित की गयीं थी

2. न्यू मॉडल यूनियनें 1880 के दशक में गठित की गयीं थी .

3. न्यू मॉडल यूनियनें लेबर पार्टी के एक विचार को समाविष्ट करती थी

4. न्यू मॉडल यूनियनों ने 1920 के दशक में महिलाओं को बहिष्कृत कर दिया था

नीचे दिये गये कूट का प्रयोग कर सही उत्तर चुनिए :

(a) 1

(b) 2

(d) केवल 3

Q. 128. सन 1947 के टूमेन सिद्धांत (द टूमैन डॉक्ट्रिन) को निम्नलिखित में से किस उद्देश्य की प्राप्ति के लिए घोषित किया गया था ?

(a) USSR का परिरोधन

(b) USA में कृषि उत्पादन बढ़ाने के लिए

(d) UNO को सशक्त बनाने के लिए

Q. 129. निम्नलिखित में से कौन सा/से कथन सही है

1. सन 1948 में बर्मा को संयुक्त राष्ट्र में शामिल किया गया और उसके तत्काल बाद शीतयुद्ध में बर्मा ने USA का समर्थन किया

2. सन 1948 में बर्मा संयुक्त राष्ट्र से जुड़ गया पर उसने कोरियाई युद्ध में चीन को आक्रामक के रूप में दोषारोपित करने से इंकार कर दिया

नीचे दिये गये कूट का प्रयोग कर सही उत्तर चुनिए :

(a) केवल 1

(b) केवल 2

(d) न तो 1, न ही 2

Q. 130. निम्नलिखित में से किसने सन (1917) में रूसी जनता को “द अप्रैल थिसिस” प्रस्तुत किया ?

(a) स्टालिन

(b) ट्रॉट्स्की

(d) लेनिन

Q. 131. किसी निर्वाचन आयुक्त को किसकी संस्तुति पर पद से हटाया जा सकता है ?

(a) भारत का मुख्य न्यायमूर्ति

(b) मुख्य निर्वाचन आयुक्त

(d) संसद

Q. 132. राज्य सभा के विषय में निम्नलिखित में से कौनसा कथन सही नहीं है ?

(a) इसके सदस्यों का निर्वाचन किसी राज्य की विधान सभा के निर्वाचित सदस्यों द्वारा किया जाता है

(b) निर्वाचन, आनुपातिक प्रतिनिधित्व पद्धति के अनुसार एकल अंतरणीय वोट (मत) विधि द्वारा किया जाता है

(d) यह एक स्थायी निकाय है, किन्तु राष्ट्रपति द्वारा इसे पहले भी विघटित किया जा सकता है

Q. 133. भारत के संविधान के निम्नलिखित में से किस एक अनुच्छेद के अधीन मूल अधिकार की गारंटी केवल भारत के नागरिकों को उपलब्ध है ?

(a) अनुच्छेद 19

(b) अनुच्छेद 20

(d) अनुच्छेद 22

Q. 134. यान्डाबो की सन्धि कब हस्ताक्षरित की गयी थी?

(a) 1826

(b) 1825

(d) 1823

Q. 135. मनुस्मृति में “एक अविवाहिता और उसके प्रेमी के स्वैच्छिक मिलन” के परिणामस्वरूप विवाह किस प्रकार का माना जाता है ?

(a) आठवां प्रकार

(b) पांचवां प्रकार

(d) छठा प्रकार

Q. 136. भारत के एक भूतपूर्व प्रधानमंत्री की समाधि के निम्नलिखित विवरण पर विचार कीजिए :

केन्द्रीय समाधि चबूतरा काली पॉलिश वाले प्रेनाइट ठोस पत्थर के नौ चौकोर खण्डों से मिलकर बना है, जिसके केन्द्र में एक ‘दीया’ रखा गया है। संख्या नौ महत्त्वपूर्ण है और यह नवरसों, नवरात्रों और नवग्रहों को चित्रित करती है । तब नौ-चौकोर समाधि का स्थापन एक वृताकार कमल की आकृति के पैटर्न में है। नौ-चौकोर वाले चबूतरे तक पथों द्वारा, जो सफेद सम्मिश्र टाइलों से बने हैं ताकि फर्श गरम न हो, चार कार्डिनल दिशाओं से पहुंचा जा सकता है। इस समाधि को पहचानिए :

(a) शक्ति स्थल

(b) शांतिवन

(d) वीर भूमि

Q. 137. IMBEX एक संयुक्त अभ्यास है, जो नियमित रूप से भारत और एक अन्य देश की सेनाओं के बीच संचालित किया जाता है । वह अन्य देश कौनसा है ?

(a) मलेशिया

(b) मालदीव

(d) म्यांमार

Q. 138. वर्ष 2018 के लिए कथासाहित्य (उपन्यास) संवर्ग में निम्नलिखित में से किसे ‘द हिन्दू पुरस्कार’ से सम्मानित किया गया था ?

(a) नीलम सरन गौर

(b) एन कल्याण रमन

(d) अरूनव सिन्हा

Q. 139. भारत में GST के लागू होने के पश्चात राज्यों द्वारा सामना की गयी राजस्व में गिरावट की समस्या से निबटने के लिए तथा वसूली को बढ़ाने के लिये कदम सुझाने हेतु गठित सात सदस्यों वाली समिति के अध्यक्ष के रूप में निम्नलिखित में से किसे नियुक्त किया गया था ?

(a) हिमंता बिस्वा शर्मा

(b) थॉमस इसाक

(d) कैप्टन अभिमन्यु

Q. 140. 15वाँ प्रवासी भारतीय दिवस, 2019 कहाँ आयोजित किया गया था ?

(a) नई दिल्ली

(b) गांधी नगर

(d) वाराणसी

Q. 141. UNESCO द्वारा 2020 के लिये निम्नलिखित में से किस शहर को वास्तुशिल्प की विश्व राजधानी निर्धारित किया गया था ?

(a) टोक्यो

(b) जोहान्सबर्ग

(d) नई दिल्ली

Q. 142. वर्ष 2018 के लिये निम्नलिखित में से किसे ICC’s का उभरता हुआ खिलाड़ी नामित किया गया था ?

(a) ऋषभ पंत

(b) जोश हेजलवुड

(d) मुस्तफिजुर रहमान

Q. 143. भारत की पहली निजी क्षेत्रक होवित्जर बन्दूक बनाने वाली यूनिट (इकाई) कहाँ स्थित है ?

(a) जमशेदपुर

(b) कोलकाता

(d) ग्वालियर

Q. 144. भारत में द्वीपों के पुराने नामों तथा नये नामों के निम्नलिखित युग्मों में से कौन सा/से सही सुमेलित हैं ?

1. रॉस आइलेण्ड : शहीद द्वीप

2. नील आइलेण्ड : नेताजी सुभाष चन्द्र बोस द्वीप

3. हैवलॉक आइलेण्ड : स्वराज द्वीप

नीचे दिये गये कूट का प्रयोग कर सही उत्तर चुनिये :

(a) 1, 2 और 3

(b) केवल 2 और 3

(d) केवल 3

Q. 145. सन 2019 में भारत का सर्वोच्च शांतिकाल बीरता पुरस्कार ‘अशोक चक्र’, निम्नलिखित में से किसे मरणोपरांत प्रदान किया गया था ?

(a) ज्योति प्रकाश निराला

(b) नजीर अहमद वानी

(e) हंगपन दादा

(d) मोहन नाथ गोस्वामी

Q. 146. नामपद्धति की संहिता (कोड) के अनुसार, जीवविज्ञान संबंधी (जैव) एक नाम को लिखने का सही तरीका निम्नलिखित में से कौनसा है ?

(a) Amoeba Proteus

(b) Amoeba proteus

(d) Amoeba Proteus

Q. 147. इलैक्ट्रोकार्डियोग्राम के विषय में निम्नलिखित में से कौनसा कथन सही है ?

(a) यह कॉर्निया की वैद्युत सक्रियता का ग्राफीय चित्रण है

(b) यह वृक्क की गतिविधि का ग्राफीय चित्रण है

(d) यह हृदय की वैद्युत सक्रियता का ग्राफीय चित्रण है

Q. 148. पेनिसिलिन के विषय में निम्नलिखित में से कौनसा कथन सही है ?

(a) पेनिसिलिन प्रतिरोधी जीवाणु इस प्रतिजैविक को रसधानी में संग्रहित कर सकते हैं

(b) पेनिसिलिन प्रतिरोधी जीवाणु इस प्रतिजैविक को 8-लैक्टेमेज नामक एंजाइम द्वारा निम्नीकृत कर सकते हैं

(d) जीवाणुओं द्वारा पेनिसिलिन अवशोषित नहीं होता; इसलिए अधिकांश जीवाणु प्रतिरोधी हैं

Q. 149. स्तनधारियों की कोशिका के निम्नलिखित में से किस अंगक में जल-अपघटनीय एंजाइम प्रचुर मात्रा में होते हैं ?

(a) माइटोकॉन्ड्रिया

(b) राइबोसोम

(d) केन्द्रक (न्यूक्लिअस)

Q. 150. हैजा के विषय में निम्नलिखित में से कौनसा कथन सही है ?

(a) यह एक रोग है जिसके कारण याददाश्त में कमी हो जाती है ।

(b) यह पेशियों का एक रोग है जो शराब (एल्कोहॉल) का सेवन करने से होता है

(d) यह एक आनुवंशिक रोग है।

NDA/NA(I) Exam 2018 General Ability Test Previous Year Paper

NDA/NA(I) Exam 2018 General Ability Test

Questions: 1 – 10

Each item in this section consists of a sentence with a quotation marks followed by four words. Select the option that is nearest in meaning to the word in the quotation and mark your response in your answer sheet accordingly

Q. 1 I do not want you to lead a life of ‘sychophancy’ as you did during the foreign rule

A. admiration

B. love

C. appreciation

D. flattery

Q. 2 In India, it has become easy to ‘attack’ cultural artefacts these days

A. beckon

B. assault

C. belch

D. appreciate

Q. 3 A local court ‘granted’ bail to the criminal on thursday

A. confessed

B. donated

C. allowed

D. yielded

Q. 4 The judge told that he would analyze

A. liberate

B. surrender

C. transfer

D. pronounce

Q. 5 The growth and development of the peasant movement was ‘indissolubly’ linked with the national struggle for freedom

A. firmly

B. vaguely

C. individually

D. steadily

Q. 6 Weather conditions have been ‘improving’ over the past few weeks

A. mending

B. amending

C. becoming better

D. advancing

Q. 7 The confusion on the ‘interocutor’s’ face was gratifying

A. government officer

B. party worker

C. dialogist

D. revolutionary

Q. 8 He spends his money ‘lavishly’

A. hesitatingly

B. generously

C. foolishly

D. carefully

Q. 9 The government’s new policies will come into force from the next ‘fiscal’ year

A. calendar

B. academic

C. financial

D. leap

Q. 10 ‘Abundant’ food was available for the soldiers in the mess

A. little

B. plentiful

C. delicious

D. wholesome

Questions: 11 – 20

Each item in this section consists of a sentence with quotation marks followed by four words. Select the option that is opposite in meaning to the word in the quotation marks and mark your response in your answer sheet accordingly

Q. 11 The country’s economy must be ‘geared to’ wartime requirements

A. subordinated to

B. related to

C. adjusted to

D. unlinked to

Q. 12 Why does fire ‘attract’ insects?

A. discharge

B. destroy

C. repel

D. remove

Q. 13 The party was excellent, and I would like to thank all the people ‘concerned’

A. cared

B. attentive

C. dependable

D. uninvolved

Q. 14 He is very ‘serious’ by temperament

A. grave

B. trivial

C. sober

D. stupid

Q. 15 There are a few ‘miscellaneous’ items to discuss in this meeting

A. pure

B. mixed

C. homogenous

D. discordant

Q. 16 Due to the postal strike, the ‘outgoing’ mail got delayed

A. urgent

B. incoming

C. ordinary

D. speedy

Q. 17 He has a ‘fine’ ear for music

A. small

B. close

C. coarse

D. smooth

Q. 18 There is no ‘likeness’ between him and his brother

A. unlikeliness

B. unlikelihood

C. dissimilarity

D. disaffinity

Q. 19 Cultural ‘diversity’ in the working place is good for business

A. uniformity

B. conformity

C. identity

D. similarity

Q. 20 The company was ‘liquidated’ within five years

A. bankrupt

B. closed down

C. flourishing

D. privatised

Questions: 21 – 25

Each item in this section has a sentence with three words in quotation labelled (a),(b) and (c). Read each sentence to find out whether there is any error in any part under the quotations and indicate your response in the answer sheet against the corresponding letter i.e., (a),(b) or (c). If you find no error, your response should be indicated as (d)

Q. 21 ‘The political lost face in his constituency'(a)/ ‘when he broke the pre-election promises'(b)/ ‘he made to his people'(c)./ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 22 At the ‘request of the defence attorney,'(a)/ ‘the jury were called'(b)/ ‘and their individual verdicts were recorded'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 23 Frank Lloyd Wright ‘has been acclaimed'(a)/ ‘by colleagues'(b)/ ‘as greater of all modern architects'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 24 ‘In my younger days'(a)/ ‘I could run four miles'(b)/ ‘at a stretch'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Q. 25 ‘The owner'(a)/ ‘as well as his servants'(b)/ ‘ is honest'(c)/ ‘No error'(d)

A. (a)

B. (b)

C. (c)

D. (d)

Questions: 26 – 30

Given below are some idioms/phrases followed by four alternative meanings to each. Choose the response (a),(b),(c) or (d) which is the most appropriate expression

Q. 26 ‘Cry over spilt milk’

A. complaining about a loss in the past

B. too much inquisitive about something

C. when something is done badly to save money

D. dealing with a problem only in an emergency situation

Q. 27 ‘Cut the mustars’

A. prepare spices out of mustard seeds

B. to come up to expectations

C. making absurd expectations

D. very enthusiastic

Q. 28 ‘Devil’s advocate

A. a dangerous person

B. to present a counter argument

C. very argumentative person

D. creating an unpleasant situation

Q. 29 ‘Don’t count your chicken before the eggs have hatched’

A. if you are not good at something, better to avoid that

B. don’t make plans for something that might not happen

C. not to come up to expectations

D. don’t put all your resources in one possibility

Q. 30 ‘Give the benefit of doubt’

A. to be partial to someone

B. to be judgmental

C. regard someone as innocent until proven otherwise

D. say something exactly right

Questions: 31 – 35

In this section each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P,Q,R and S. Your are required to find the proper sequence of the four sentences and mark your response accordingly on the answer sheet

Q. 31 S1: The subsidiary Alliance system was extremely advantageous to the British

S6: They controlled the defence and the foreign relations of the protected ally

P: They could now maintain a large army at the cost of Indian states

Q: If any war occured in the territories

R: either of the British ally or of the Britishers

S: This enabled them to fight wars far away from their own territories

The proper sequence should be

A. P Q R S

B. P S Q R

C. Q R P S

D. S R P Q

Q. 32 S1: In reality, by signing a Subsidiary Alliance, an Indian state virtually signed away its independence

S6: In fact, the Indian ruler lost all vertiges of sovereignty in external matters

P: of maintaining diplomatic relations

Q: it lost the right of self defence

R: with its neighbors

S: and of selling its disputes

The proper sequence should be

A. P Q R S

B. R S P Q

C. Q P S R

D. Q S R P

Q. 33 S1: A mighty popular Revolt broke out in Northern and Central India in 1857

S6: Millions of peasants, artisans and soldiers fought heroically and wrote a glorious

chapter

P: Sepoys, or the Indian soldiers of the company’s army

Q: but soon engulfed wide regions and involved masses

R: and nearly swept awaay the British rule

S: it began with a mutiny of the

the proper sequence should be

A. R S P Q

B. P Q R S

C. S R P Q

D. Q R P S

Q. 34 S1: The Indian Civil Service gradually developed into one of the most efficient and powerful civil services in the world

S6: though these qualities obviously served British, and not Indian interests

P: and often participated in the making of policy

Q: independence, integrity and hard work

R: they developed certain traditions of

S: its members exercised vast power

The proper sequence should be

A. P Q R S

B. Q R S P

C. R S Q P

D. S P R Q

Q. 35 S1: The ruin of Indian handicrafts was reflected in the ruin of the towns and cities which were famous for their manufacturers

S6: centres were developed and laid waste

P: Dacca, Surat, Murshidabad and many other risinf industrial

Q: ravages of war and plunder, failed to

R: survive British conquest

S: Cities which had with stood the

The proper sequence should be

A. P Q R S

B. S Q R P

C. S R P Q

D. Q R S P

Questions: 36 – 40

In this section you have few short passages. After each passage, you will find some items based on the passage. First, read a passage and answer the items based on it. You are required to select your answers based on the contents of the passage and opinion of the author only.

Passage:

The rule of the road means that in order that the liberties of all may be preserved, the liberties of everybody must be curtailed. When the policeman, say, at a roadcrossing steps into the middle of the road and puts our his hand, he is the symbol not of tyranny but of liberty. You have submitted to a curtailment of private liberty in order that you may enjoy a social order which makes your liberty a reality. We have both liberties to preserve-our individual liberty and our social liberty. That is, we must have a judicious mixture of both. I shall not permit any authority to say that my child must go to this school or that, shall specialize in science and arts. These things are personal. But if I say that my child shall have no education at all, then society will firmly tell me that my child must have education whether I like it or not

Q. 36 According to the author, the “rule of the road” implies

A. the rule regulating the traffic on the road

B. the principle on which a road is constructed to ensure safe traffic

C. unrestricted freedom for all to lead a happy life

D. restricted individual freedom to ensure freedom for all

Q. 37 The author thinks that when a policeman signals you to stop on a road-crossing he is

A. behaving in a whimsical manner

B. interfering with your freedom to the road

C. protecting the liberty of all to use the road

D. mischievously creating hurdles in your way from some personal motive

Q. 38 The author is of view that we should

A. have absolute individual liberty without any restrictions imposed by the society

B. have everything controlled by the society without any kind of individual liberty

C. try to strike a sensible balance between our individual liberty and our social liberty

D. have more of social liberty than individual liberty

Q. 39 The author holds that

A. educating or not educating his child is a matter of personal liberty

B. educating or not educating his child is also a matter of social liberty

C. choosing the school for his child is a matter of social liberty

D. choosing the subject of study for his child is a matter of social liberty

Q. 40 The most suitable title of the passage would be

A. the policeman at a road crossing

B. the laws of the road

C. importance of liberty

D. education of children

Questions: 41 – 45

My most interesting visitor comes at night, when the lights are still burning—a tiny bat who prefers to fly in through the open door, and will use the window only if there is no alternative. His object in entering the house is to snap up the moths that cluster around the lamps. All the bats I have seen fly fairly high, keeping near the ceiling; but this particular bat flies in low, like a dive-bomber, zooming in and out of chair legs and under tables. Once, he passed straight between my legs. Has hits radar wrong, I wondered, or is her just plain crazy?

Q. 41 Consider the following statements:

1. The tiny bat flew in low like a dive-bomber

2. The tiny bat like all bats keeps near the ceiling

3. It has lost direction because its radar has gone wrong

4. It wants to entertain the author with its skill in flying

Which of the above statements may be assumed to be true from the information given in the passage?

A. 1 only

B. 1 and 3

C. 2 and 4

D. 3 and 4

Q. 42 The bat entered the room

A. because there was no alternative

B. to eat the moths round the lamps

C. as it had gone mad

D. as it preferred to fly in through the open door

Q. 43 After comparing the habits of the tiny bast with those of other bats, the author was

A. sure that this bat had lost its direction

B. not sure to find that it was an expert flier

C. surprised to find that it was an expert flier

D. unable to give the correct explanation for its behaviour

Q. 44 The author calls the tiny bat an “interesting visitor”. This means

A. the bat visits him at night

B. the bat is interested in the moths

C. this bat has peculiar qualities

D. this bat surprises him by zooming in and out like a dive-zoomer

Q. 45 What, according to you, can be the most suitable title for the passage?

A. someone visits me

B. night of mysteries

C. my nocturnal visitor

D. a funny visitor

Questions: 46 – 50

Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the answer sheet accordingly

Q. 46 The tired traveller ________________ on in the hope of finding some resting place

A. strolled

B. scurried

C. paraded

D. ploded

Q. 47 The car was damaged beyond repair in the ___________________ accident

A. outrageous

B. ghastly

C. nasty

D. heinous

Q. 48 They gave a _________ dinner to celebrate the occasion, which impressed every guest

A. austere

B. public

C. sumptuous

D. summary

Q. 49 Once the ________________ manuscript is received by the publishers, it is typed in double space

A. total

B. full

C. complete

D. filled

Q. 50 I am used to ___________________ in queues

A. stand

B. standing

C. stand up

D. standing still

Q. 51 Which of the following statements is correct?

A. any energy transfer that does not involve temperature difference in some way is not heat

B. any energy transfer always requires a temperature differences

C. On heating the length and volume of the object remain exactly the same

D. whenever there is a temperature difference, heat it the only way of energy transfer

Q. 52 If T is the time period of an oscillating pendulum, which one of the following statements is NOT correct?

A. the motion repeats after time T only once

B. T is the least time after which motion repeats itself

C. the motion repeats itself after nT, where n is a positive integer

D. T remains the same only for small angular displacement

Q. 53 If an object moves with constant velocity then which one of the following statements is NOT correct?

A. its motion is along a straight line

B. its speed changes with time

C. its acceleration is zero

D. its displacement increases linearly with time

Q. 54 An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v=u+at. The velocity(along y-axis) time(along xaxis) graph shall be a straight line

A. passing through origin

B. with x-intercept u

C. with y-intercept u

D. with slope u

Q. 55 What is the net force experienced by a bar magnet placed in a uniform magnetic field?

A. zero

B. depends upon length of the magnet

C. never zero

D. depends upon temperature

Q. 56 Which one of the following has maximum inertia?

A. an atom

B. a molecule

C. a one-rupee coin

D. a cricket ball

Q. 57 Which one of the following is the value of 1 kWh of energy converted into joules?

A. 1.8*10⁶J

B. 3.6*10⁶J

C. 6.0*10⁶J

D. 7.2*10⁶J

Q. 58 Which one of the following statements about gravitational force is NOT correct?

A. it is experienced by all bodies in the universe

B. it is a document force between celestial bodies

C. it is a negligible force for atoms

D. it is same for all pairs of bodies in our universe

Q. 59 Whether an object will float or sink in a liquid, depends on

A. mass of the object only

B. mass of the object and density of liquid only

C. differences in the densities of the object and liquid

D. mass and shape of the object only

Q. 60 Which one of the following devices is non-ohmic?

A. conducting copper coil

B. electric heating coil

C. semi conductor diode

D. rheostat

Q. 61 Which one of the following is the natural phenomenon based on which a simple periscope works?

A. reflection of light

B. refraction of light

C. dispersion of light

D. total internal reflection of light

Q. 62 Which one of the following frequency ranges is sensitive to human ear?

A. 0-200 Hz

B. 20-20,000 Hz

C. 200-20,000 Hz only

D. 2,000-20,000 Hz only

Q. 63 The accidental touch of Nettle leaves creates a burning sensation, which is due to inject of

A. hydrochloric acid

B. methanoic acid

C. citric acid

D. sulphuric acid

Q. 64 Which of the following properties is true for a tooth paste?

A. it is acidic

B. it is neutral

C. it is basic

D. it is made up of calcium phosphate, the material of tooth enamel

Q. 65 Which one of the following given the highest amount of hydrogen ions(H⁺)?

A. sodium hydroxide solution

B. milk of magnesia

C. lemon juice

D. gastric juice

Q. 66 Brine is an aqueous solution of

A. NaCl

B. NaOH

C. NaHCO₃

D. Na₂CO₃

Q. 67 Which one of the following is the chemical formula of washing soda?

A. NaHCO₃

B. Na₂CO₃.10H₂O

C. Na₂CO₃.5H₂O

D. NaOH

Q. 68 Which one of the following is NOT true for bleaching powder?

A. it is used as a reducing agent in chemical industries

B. it is used for bleaching wood pulp in paper factories

C. it is used for disinfecting drinking water

D. it is used for bleaching linen in textile industry

Q. 69 AIDS is caused by virus whose genetic material is

A. single stranded circular DNA

B. double stranded DNA

C. single stranded RNA

D. double stranded RNA

Q. 70 Which one of the following is an organelle that is NOT found in pro-karyotic cells?

A. cell wall

B. mitochondria

C. plasma membrane

D. ribosome

Q. 71 Which one of the following parts of body does NOT take part in the process of breathing?

A. Bronchi

B. Bowman’s capsule

C. Diaphragm

D. Trachea

Q. 72 Which one of the following statements about classification of plants is correct?

A. Thallophytes have well differentiated body design

B. Funaria is a fungus

C. All Pteridophytes are Phanerogams

D. Vascular system is not found among Bryophytes

Q. 73 Which one of the following is the correct sequence of hierarchy of classification of organisms from higher to lower?

A. Phylum-Class-Order-Family-Genus

B. Phylum-Class-Family-Order-Genus

C. Family-Order-Class-Species-Genus

D. Class-Family-Order-Species-Genus

Q. 74 Which one of the following statements about meristematic tissues in plants is correct?

A. these are dead tissues and form wood

B. they provide flexibillity to plant due to their thickened walls

C. these are present in the bark of a tree only

D. growth occurs in plants due to division of cells of these tissues

Q. 75 Which one of the following Union Territories has the highest female literacy rate?

A. Chandigarh

B. Lakshadweep

C. Andaman and Nicobar Islands

D. Puducherry

Q. 76 Consider the following statements about Roaring Forties:

1. They are strong Westerly winds found in the oceans of Southern Hemisphere

2. The strong east to west air currents are caused by the combination of air being displaced from the Equator towards the south pole and the earth’s rotation and abundance of landmasses to serve as wind breaks.

Which of the statement given above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

Q. 77 Consider the following statements:

1. The doldrums is a low pressure area around Equator where the prevailing winds are calm

2. Chinook is a hot and dry wind that blows in winter and therefore raises the temperature in a short time

which of the statements given above is/are correct?

A. 1

B. 2

C. both 1,2

D. neither i nor 2

Q. 78 Which one of the following is the driest desert of the world?

A. atacama

B. gobi

C. sahara

D. kalahari

Q. 79 Which of the following statements about latent heat heat for a given substance is/are correct?

1. It is fixed upon the temperature

2. It depends upon the temperature and volume

3. It is independent of temperature and volume

4. It depends on the temperature but independent of volume

select the correct answer using the code given below:

A. 2

B. 1,3

C. 4

D. 1,4

Q. 80 Which one of the following statements about the mass of a body is correct?

A. it changes from one place to another

B. it is same everywhere

C. it depends on its shape

D. it does not depend on its temperature

Q. 81 A ball balanced on a vertical rod is an example of

A. stable equilibrium

B. unstable equilibrium

C. neutral equilibrium

D. perfect equilibrium

Q. 82 Which of the following statements about a fluid at rest in a cup is/are correct

1. Pressure is same at all the points in the fluid

2. Pressure is exerted on the walls

3. Pressure exists everywhere in the fluid

select the correct answer using the code given below:

A. 1,2 only

B. 2,3 only

C. 1 only

D. 1,2,3

Q. 83 Which one of the following devices is used to measure atmospheric pressure?

A. ammeter

B. barometer

C. potentiometer

D. lactometer

Q. 84 Which one of the following is the number of water molecules that share with two formula unit CaSO₄ in plaster of Paris?

A. 1

B. 2

C. 5

D. 10

Q. 85 How is carbon black obtained?

A. by heating wood at high temperature in absence of air

B. by heating coal at high temperature in absence of air

C. by burning hydrocarbons in a limited supply of air

D. by heating coal at a high temperature in presence of air

Q. 86 Which of the following properties is NOT true for graphite?

A. hybridisation of each carbon atom is sp³

B. hybridisation of each carbon atom is sp²

C. electrons are delocalized over the whole sheet of atoms

D. each layer is composed of hexagonal rings

Q. 87 Which one of the following is the purest form of carbon?

A. charcoal

B. coke

C. fullerene

D. carbon black

Q. 88 The poisonous nature of carbon monoxide(CO) is due to

A. insolubility of water

B. ability to form a complex with haemoglobin

C. ability to reduce some metal oxides

D. property of having one sigma bond

Q. 89 Which one of the following elements is needed in the human body to transfer electrical signals by nerve cells?

A. lithium

B. sodium

C. rubidium

D. caesium

Q. 90 Who among the following first discovered cell?

A. robert brown

B. robert hooke

C. leeuwen hoek

D. rudolf virchow

Q. 91 Which one of the following group of organisms forms a food chain?

A. grass, human and fish

B. grass, goat and human

C. tree, tree cutter and tiger

D. goat,cow and human

Q. 92 Which one of the following types of tissues will have contractile proteins?

A. nervous tissue

B. muscle tissue

C. bone tissue

D. blood tissue

Q. 93 If by an unknown accident the acid secreting cells of the stomach wall of an individual are damaged, digestion of which one of the following biomolecule will be affected to a greater extent?

A. protein only

B. lipid

C. carbohydrate only

D. protein and carbohydrate

Q. 94 In which one of the following places, headquarters of a railway zone is located?

A. kanpur

B. lucknow

C. hajipur

D. new jalpaiguri

Q. 95 Which of the following statements about Indian academy of highway engineers is/are correct?

1. It is a registered society

2. It is a collaborative body of both central government and state governments

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1,2

D. neither 1 nor 2

Q. 96 Which one of the following is NOT a tributary of Indus river?

A. beas

B. ravi

C. chenah

D. tawi

Q. 97 Which one among the following is the largest tiger reserve of India in terms of area of the core/critical tiger habitat?

A. manas

B. pakke

C. nagarjunasagar srisailam

D. periyar

Q. 98 Which of the following is NOT a coastal depositional featute?

A. tombolo

B. sand bar

C. stack

D. spit

Q. 99 Which of the following is/are coastal erosional feature(s)

1. Notch

2. Sea Arch

3. Cliff

4. Hook

select the correct answer using the code given below:

A. 1,2,3

B. 2,3,4

C. 2,3

D. 1

Q. 100 Chemical weathering of rocks is much greater in a place with

A. cold and dry climate

B. hot and humid climate

C. hot and dry climate

D. cold and humid climate

Q. 101 Which of the following statements about specific heat of a body is/are correct?

1. It depends upon mass and shape of the body

2. It is independent of mass and shape of the body

3. It depends only upon the temperature of the body

select the correct answer using the code given below:

A. 1

B. 2,3

C. 1,3

D. 2

Q. 102 Which one of the following is an example of the force of gravity of the earth acting on a vibrating pendulum bob?

A. applied force

B. frictional force

C. restoring force

D. virtual force

Q. 103 Which one of the following statements about the refractive index of a material medium with respect to air is correct?

A. it can be either positive or negative

B. it can have only zero value

C. it is unity for all materials

D. it is always greater than one

Q. 104 Which one of the following statements about magnetic field lines is NOT correct?

A. they can emanate from a point

B. they do not cross each other

C. field lines between two poles cannot be precisely straight lines at the ends

D. there are no field lines within a bar magnet

Q. 105 Two convex lenses with power 2 dipotre are kept in contact with each other. The focal length of the combined lens system is

A. 0.10 m

B. 2 m

C. 4 m

D. 0.25 m

Q. 106 Which one of the following alkali metals has lowest melting point?

A. sodium

B. potassium

C. rubidium

D. caesium

Q. 107 Which one of the following metals is alloyed with sodium to transfer heat in a nuclear reactor?

A. potassium

B. calcium

C. magnesium

D. strontium

Q. 108 Which one of the following metals is used in the filament of photo-electric cells that convert light energy into electric energy?

A. tungsten

B. copper

C. rubidium

D. aluminium

Q. 109 Which of the following statements about Ring of Fire is/are correct?

1. It is a zone of convergence plate boundaries

2. It is an active seismic and volcanic zone

3. It is associated with deep trench

Select the correct answer using the code given below:

A. 1,2

B. 2,3

C. 1

D. 1,2,3

Q. 110 Which one of the following Himalayan vegetation species is found between the altitudes of 1800 to 2600 metres?

A. saal

B. chir

C. spruce

D. deodar

Q. 111 Which one of the following rivers is NOT a tributary of river Cauvery?

A. Hemavati

B. Arkavati

C. Indravati

D. Amravati

Q. 112 Which of the following conditions is/are essential for tea cultivation?

1. Tropical and sub-tropical climate

2. Heavy rainfall ranging from 150 cm to 250 cm

3. Soil should contain good amount of lime

select the correct answer using the code given below:

A. 1,2,3

B. 1,2

C. 2,3

D. 1

Q. 113 Bharatmala Project is related to

A. improving road connectivity

B. interlinking ports and railways

C. interlinking of rivers

D. interlinking major cities with gas pipelines

Q. 114 Which one of the following is a local wind that blows out from Siberia?

A. bora

B. purga

C. mistral

D. blizzard

Q. 115 Which one of the following centres is NOT known for iron and steel industry?

A. bhadravati

B. salem

C. vishakhapatnam

D. renukoot

Q. 116 Which one of the following are essential pre-requisites for establishment of a thermal power station?

1. availability of fossil fuels

2. proximity to a river, lake or sea

3. good transport network

4. proximity to an urban centre

select the correct answer using the code given below:

A. 1,2,3

B. 2,4

C. 2,3

D. 1,3

Q. 117 Which of the following statements about ‘Aadi Mahotsav’ held recently in New Delhi is/are correct?

1. The theme of the festival was ‘A celebration of the spirit of tribal culture, cuisine and commerce’

2. The festival was organized by the ministry of tourism, government of India

select the correct answer using the code given below:

A. 1

B. 2

C. both 1,2

D. neither 1 nor 2

Q. 118 Light year is a unit for measurement of

A. age of universe

B. very small time intervals

C. very high temperature

D. very large distance

Q. 119 Which of the following statements about electromagnetic waves, sound waves and water waves is/are correct?

1. they exhibit reflection

2. they carry energy

3. they exert pressure

4. they can travel in vacuum

select the correct answer using the code given below:

A. 1,2,3

B. 2,4

C. 1,3

D. 1

Q. 120 Thermal capacity of a body depends on the

A. mass of the body only

B. mass and shape of the body only

C. density of the body

D. mass, shape and temperature of the body

Q. 121 Who among the following first used the term ‘industrial revolution’ in english to describe the changes that occured in british industrial development between 1760 and 1820?

A. karl marx

B. georges michelet

C. arnold toynbee

D. friedrich engels

Q. 122 Which one of the following statements about the Olympe de Gouges(1748-1793) is correct?

A. she declared that although citizens should have equal rights, they are not entitled to the same honours by the state

B. she was supporter of the Jacobin government

C. she was jailed for treason by the National Assembly

D. she declared that the nation is the union of woman and man

Q. 123 Who among the following built a model steam engine in 1698 called “Miner’s Friend” to drain mines?

A. thomas savery

B. thomas newcomen

C. james watt

D. richard arkwright

Q. 124 Which one of the following statements about Renaissance Humanist culture is NOT true?

A. it slackened the control of religion over human life

B. it believed that human nature was many-sided

C. it was concerned with good manners

D. it criticized material wealth, power and glory

Q. 125 Who gifted the ‘Badshah Nama’ to King George in 1799?

A. abul fazl

B. abdul hamid lahori

C. nawab of awadh

D. william jones

Q. 126 What is the name of the award given to meritorious men in the Mughal Court in the form of a robe of honour that was once worn by the Emperor?

A. sarapa

B. patka

C. padma murassa

D. khilat

Q. 127 Who among the following social reformer started a society for the encouragement of a widow remarriage in 1866 in maharashtra?

A. bal gangadhar tilak

B. jyotirao phule

C. vishnushastri pandit

D. pandita ramabai

Q. 128 Name the first major voluntary association representing primarily Indian landlords interests that was set up in Calcutta in 1851?

A. british indian association

B. ladholder’s society

C. madras native association

D. bombay association

Q. 129 Who among the following introduced the permanent settlement of bengal in 1793?

A. lord cornwallis

B. lord ripon

C. robert clive

D. john adam

Q. 130 Name the rebel who fought against the British in the battle of Chinhat in the course of the 1857 revolt?

A. ahmadullah shah

B. shah mal

C. mangal pandey

D. kunwar singh

Q. 131 Who among the following are the two civil servants who assisted the constituent assembly in framing the constitution of india?

A. B.N.Rau and K.M.Munshi

B. S.N.Mukherjee and Alladi Krishna swamy Aiyar

C. B.N.Rau and S.N.Mukherjee

D. K.M.Munshi and Alladi Krishna swamy Aiyar

Q. 132 Which member of the constituent assembly proposed the resolution that the national flag of india be a “horizontal tricolour of saffron,white and dark green in equal proportion”, with a wheel in navy blue at the centre?

A. jawaharlal nehru

B. B.R.Ambedkar

C. rajendra prasad

D. sardar vallabhai patel

Q. 133 Which of the following is/are NOT historical biography/biographies?

1. Dipavamsa

2. Harshacharita

3. Vikramankadevacharita

4. Prithvirajavijaya

select the correct answer from the code given below:

A. 1

B. 2,3

C. 2,3,4

D. 1,2,3,4

Q. 134 Which of the following pairs are correctly matched from the figure

A. 1,2,3

B. 2,3

C. 1,2,3,4

D. 1,4

Q. 135 Which of the following clans are included in the Agnikula Rajputs?

1. Pratiharas

2. Chaulukyas

3. Paramaras

4. Chahamanas

select the correct answer from the code given below:

A. 1,3

B. 1,3,4

C. 1,2,3,4

D. 2,4

Q. 136 Who among the following was the author of Humayun Nama?

A. roshanara begum

B. Ruquaiya Sultan Begum

C. gulbadan begum

D. gauhara begum

Q. 137 Which one of the following about the parliament of India is NOT correct?

A. parliament consists of the president, the lok sabha and the rajya sabha

B. there are no nominated members in the lok sabha

C. the rajya sabha cannot be dissolved

D. some members of the rajya sabha are nominated bu the president

Q. 138 Which one of the following statements with regard to the Comptroller and auditor general(CAG) of india is NOT correct?

A. he is appointed by the president of india

B. he can be removed from the office in the same way as the judge of the supreme court of india

C. the CAG is eligible for further office under the government of india after he has

ceased to hold his office

D. the salary of the CAG is charged upon the consolidated fund of india

Q. 139 The superintendence, direction and control of elections of india is vested in

A. the supreme court of india

B. the parliament of india

C. the election commission of india

D. the chief election commissioner

Q. 140 Which of the following provision(s) of the constitution of india became effective from 26th november 1949?

1. elections

2. citizenship

3. emergency provisions

4. appointment of the judges

select the correct answer using the code given below:

A. 1

B. 1,2

C. 1,2,3

D. 2,4

Q. 141 Which of the following statements regarding construction of rohtang tunnel is NOT correct?

A. it is located at an altitude of 5,000 feet

B. it will provide all-year connectivity to Lahaul and Spiti valley

C. the tunnel is being built by the border roads organization

D. it will reduce the length of the leh-manali highway by approximately 50 km

Q. 142 Who among the following recently became the first woman pilot in Indian Navy?

A. astha segal

B. roopa A

C. sakthi maya S

D. shubhangi swaroop

Q. 143 Who among the following indians did NOT hold the title of Miss world?

A. reita faria

B. sushmita sen

C. diana hayden

D. yukta mookhey

Q. 144 Which one of the following countries has failed to qualify for the first time in 60 years for the FIFA world cup to be held in russia in the year 2018?

A. mexico

B. iran

C. saudi arabia

D. italy

Q. 145 The defence Technology and trade initiative(DTTI) is a forum for dialogue on defence partnership between india and

A. russia

B. USA

C. israel

D. france

Q. 146 As per the policy applicable in 2017, how much foreign direct investment (FDI) is permitted in the defence sector in India?

A. 49 percent through the automatic route

B. 26 per cent through the government route

C. 26 per cent through the automatic route and beyond that up to 49 per cent through

the government route

D. 75 per cent through the automatic route

Q. 147 Which one of the following countries did NOT participate in the 21st edition of exercise malabar?

A. USA

B. japan

C. India

D. australia

Q. 148 Justice Dalveer Bhandari of India was recently re-elected to the International Court of Justice after Christopher Greenwood pulled out before 12th round of voting. Christopher Greenwood was a nominee of

A. canada

B. russia

C. britain

D. USA

Q. 149 In order to review the income tax act, 1961 and to draft a new direct tax law in consconance with economic needs of the country, the government of india in november 2017 has constituted a task force. Who among the following is made the convenor of it?

A. shri arvind subramanian

B. shri arbind modi

C. shri amitabh kant

D. Dr. Bibek debroy

Q. 150 The 5th global conference on cyber space(GCCS) was held in new delhi in november, 2017.

Which of the following statements about GCCS is/are correct?

1. The 4th version of GCCS was held in London

2. The main theme of GCCS 2017 is ‘Cyber4All: A secure and inclusive cyberspace for sustainable development’.

3. ‘Bindu’ is the logo of GCCS 2017

select the correct answer using the code given below:

A. 1

B. 2

C. 2,3

D. 1,2,3

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	D	B	C	D	A	C	C	B	C	B
Question	11	12	13	14	15	16	17	18	19	20
Answer	D	C	D	B	C	B	C	C	A	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	C	D	C	B	D	A	B	C	B	C
Question	31	32	33	34	35	36	37	38	39	40
Answer	B	C	A	D	B	D	C	C	B	C
Question	41	42	43	44	45	46	47	48	49	50
Answer	A	B	C	C	C	D	B	C	C	B
Question	51	52	53	54	55	56	57	58	59	60
Answer	A	A	B	C	A	D	B	D	C	C
Question	61	62	63	64	65	66	67	68	69	70
Answer	A	B	B	C	D	A	B	A	C	B
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	D	A	D	B	A	C	A	D	B
Question	81	82	83	84	85	86	87	88	89	90
Answer	B	B	B	A	C	A	D	B	B	B
Question	91	92	93	94	95	96	97	98	99	100
Answer	B	B	A	C	C	D	C	C	A	B
Question	101	102	103	104	105	106	107	108	109	110
Answer	B	C	D	D	D	D	A	C	D	A
Question	111	112	113	114	115	116	117	118	119	120
Answer	C	B	A	B	D	A	A	D	A	A
Question	121	122	123	124	125	126	127	128	129	130
Answer	C	C	A	D	C	A	C	A	A	A
Question	131	132	133	134	135	136	137	138	139	140
Answer	C	C	C	C	C	C	B	C	C	B
Question	141	142	143	144	145	146	147	148	149	150
Answer	A	D	B	D	B	A	D	C	B	B

NDA/NA(II) Exam 2018 Mathematics Previous Year Paper

NDA/NA(II) Exam 2018 Mathematics

Q. 1 What is the value of log₇ log₇ {√7[√7(√7)]} equal to?

A. 3 log₂ 7

B. 1−3 log₂ 7

C. 1−3 log₇ 2

D. 7/8

Q. 2 If an infinite GP has the first term x and the sum 5, then which one of the following is correct ?

A. x < −10

B. −10 < x < 0

C. 0 < x < 10

D. x > 10

Q. 3 Consider the following expressions:

1. x + x² – 1/x

2. √[ax² + bx + x -c + (d/x) – (e/x²)]

3. 3x² − 5x + ab

4. 2/x² − ax + b³

5. 1/x − 2/x + 5

Which of the above are rational expressions?

A. 1, 4 and 5 only

B. 1, 3, 4 and 5 only

C. 2, 4 and 5 only

D. 1 and 2 only

Q. 4 A square matrix A is called orthogonal if

Note: where A′ is the transpose of A

A. A = A²

B. A′ = A⁻¹

C. A = A⁻¹

D. A = A′

Q. 5 If A, B and C are subsets of a Universal set, then which one of the following is not correct?

Note: where A′ is the complement of A

A. A ⋃ (B ∩ C) = (A ⋃ B) ∩ (A ⋃ C)

B. A′ ⋃ (A ⋃ B) = (B′ ∩ A)′ ⋃ A

C. A′ ⋃ (B ⋃ C) = (C′ ∩ B)′ ∩ A′

D. (A ∩ B) ⋃ C = (A ⋃ C) ⋂ (B ⋃ C)

Q. 6 Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

A. 2480

B. 2481

C. 2482

D. 2483

Q. 7 The sum of the series 3 – 1 + 1/3 – 1/9 + … is equal to

A. 20/9

B. 9/20

C. 9/4

D. 4/9

Questions: 8 – 9

A survey was conducted among 300 students. It was found that 125 students like to play cricket,145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.

Q. 8 How many students like to play all the three games?

A. 14

B. 21

C. 28

D. 35

Q. 9 How many students like to play exactly only one game?

A. 196

B. 228

C. 254

D. 268

Q. 10 If α and β(≠0) are the roots of the quadratic equation x²+αx-β=0, then the quadratic expression -x²+αx+β where x ⋲ R has

A. Least value -1/4

B. Least value -9/4

C. Greatest value 1/4

D. Greatest value 9/4

Q. 11 What is the coefficient of the middle term in the binomial expansion of (2 + 3x)⁴?

A. 6

B. 12

C. 108

D. 216

Q. 12 For a square matrix A, which of the following properties hold?

1. (A⁻¹)⁻¹ = A

2. det(A⁻¹) = 1/detA

3. (λA)⁻¹ = λA⁻¹ where λ is a scalar

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1,2 and 3

Q. 13 Which one of the following factors does the expansion of the determinant shown in figure contain?

A. x − 3

B. x − y

C. y − 3

D. x − 3y

Q. 14 What is the adjoint of the matrix? Choose the correct option.

A. (a)

B. (b)

C. (c)

D. (d)

Q. 15 What is the value of (-1+i√3/2)³ⁿ, where i=√-1 ?

A. 3

B. 2

C. 1

D. 0

Q. 16 There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

A. C (17, 11)

B. C (12, 8)

C. C (17, 5) X C (5, 3)

D. C (5, 3) X C (12, 8)

Q. 17 What is the value of log₉ 27 + log₈ 32 ?

A. 7/2

B. 19/6

C. 4

D. 7

Q. 18 If A and B are two invertible square matrices of same order, then what is (AB)⁻¹ equal to?

A. B⁻¹ A⁻¹

B. A⁻¹ B⁻¹

C. B⁻¹ A

D. A⁻¹ B

Q. 19 What is the solution of the of equation given if a+b+c=0 ?

A. x=a

B. x=[√3(a²+b²+c²)]/√2

C. x=[√2(a²+b²+c²)]/√3

D. x=0

Q. 20 What should be the value of x so that the matrix does not have an inverse?

A. 16

B. -16

C. 8

D. -8

Q. 21 The system of equations

2x + y – 3z = 5,

3x – 2y + 2z = 5 and

5x – 3y – z = 16

A. is inconsistent

B. is consistent, with a unique solution

C. is consistent, with infinitely many solutions

D. has its solution lying along x-axis in three-dimensional space

Q. 22 Which one of the following is correct in respect of the cube roots of unity?

A. They are collinear

B. They lie on a circle of radius √3

C. They form an equilateral triangle

D. None of the above

Q. 23 If u, v and w (all positive) are the pᵗʰ, qᵗʰ and rᵗʰ terms of a GP, then the determinant of the given matrix is?

A. 0

B. 1

C. (p-q)(q-r)(r-p)

D. ln u x ln v x ln w

Q. 24 Let the coefficient of the middle term of the binomial expansion of (1+x)²ⁿ be α and those of two middle terms of the binomial expansion of (1+x)²ⁿ⁻¹ be β and γ. Which one of the following relations is correct?

A. α > β + γ

B. α < β + γ

C. α = β + γ

D. α = βγ

Q. 25 Let A = {x ∈ R : – 1 ≤ x ≤ 1},

B = y ∈ R : – 1 ≤ y ≤ 1} and S be the

subset of A x B, defined by

S = [(x, y) ∈ A x B : x² + y² = 1]

Which one of the following is correct?

A. S is a one-one function from A into B

B. S is a many-one function from A into B

C. S is a bijective mapping from A into B

D. S is not a function

Q. 26 Let Tᵣ be the rth term of an AP for r=1, 2, 3, … . If for some distinct positive integers u and v we have Tᵤ=1/ᵥ and Tᵥ=1/ᵤ, then what is Tᵤᵥ equal to?

A. (uv)⁻¹

B. u⁻¹+v⁻¹

C. 1

D. 0

Q. 27 Suppose f(x) is such a quadratic expression that it is positive for all real x.

If g(x) = f(x) + f'(x) + f”(x), then for any real x

A. g(x) < 0

B. g(x) > 0

C. g(x) = 0

D. g(x) ≥ 0

Q. 28 Consider the following in respect of matrices A, B, and C of same order:

1. (A + B + C)’ = A’ + B’ + C’

2. (AB)’ = A’B’

3. (ABC) = C’B’A’

Where A’ is the transpose of the matrix A.

Which of the above is correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 29 The sum of the binary numbers (11011)₂, (10110110)₂ and (10011x0y)₂ is the binary number (101101101)₂. What are the values of x and y?

A. x = 1, y = 1

B. x = 1, y = 0

C. x = 0, y = 1

D. x = 0, y = 0

Q. 30 Let matrix B be the adjoint of a square matrix A, l be the identity matrix of same order as A. If k (≠0) is the determinant of the matrix A, then what is AB equal to?

A. l

B. kl

C. k²l

D. (1/k)l

Q. 31 If (0.2)ⁿ = 2 and log₁₀2 = 0.3010, then what is the value of n to the nearest tenth?

A. -10.0

B. -0.5

C. -0.4

D. -0.2

Q. 32 The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

A. 45360

B. 30240

C. 27216

D. 15120

Q. 33 What is the determinant of the matrix?

A. (x – y) (y – z) (z – x)

B. (x – y) (y – z)

C. (y – z) (z – x)

D. (z – x)² (x + y + z)

Q. 34 As given in the picture, if A, B and C are angles of a triangle then which one of the following is correct?

A. The triangle ABC is isosceles

B. The triangle ABC is equilateral

C. The triangle ABC is scalene

D. No conclusion can be drawn with regard to the nature of the triangle

Q. 35 Consider the following in respect of matrices A and B of same order:

1. A² – B² = (A + B)(A – B)

2. (A – I)(I + A) = O ⇔ A² = 1

where I is the identity matrix and O is the null matrix.

Which of the above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 36 What is 2 tanθ/1 + tan²θ equal to?

A. cos 2θ

B. tan 2θ

C. sin 2θ

D. cosec 2θ

Q. 37 If sec (θ – a), sec θ and sec (θ + a) are in AP, where cos a ≠ 1, then what is the value of sin²θ + cos a?

A. 0

B. 1

C. -1

D. 1/2

Q. 38 If A + B + C = 180°, then what is sin 2A – sin 2C equal to?

A. -4 sin A sin B sin C

B. -4 cos A sin B cos C

C. -4 cos A cos B sin C

D. -4 sin A cos B cos C

Q. 39 A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the

balloon is 48°. If the height of the balloon above the bridge is 122 m, then what is the length of the bridge?

A. 122 sin 48° m

B. 122 tan 42° m

C. 122 cos 48° m

D. 122 tan 48° m

Q. 40 A is an angle in the fourth quadrant. It satisfies the trigonometric equation 3 (3 – tan²A – cot A)² = 1. Which one of the following is the value of A?

A. 300°

B. 315°

C. 330°

D. 345°

Q. 41 The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π/6 and π/3 respectively. What is the height of the hill?

A. 2h

B. 3h/2

C. h

D. h/2

Q. 42 What is/are the solution(s) of the trigonometric equation cosec x + cot x = √3, where 0 < x < 2π ?

A. 5π/3 only

B. π/3 only

C. π only

D. π, π/3, 5π/3

Q. 43 If θ=π/8, then what is the value of

(2cosθ+1)¹⁰(2cos2θ-1)¹⁰(2cosθ-1)¹⁰(2cos4θ-1)¹⁰?

A. 0

B. 1

C. 2

D. 4

Q. 44 If cos α and cos β (0<α<β<π) are the roots of the quadratic equation 4x²-3=0, then what is the value of sec α and sec β?

A. -4/3

B. 4/3

C. 3/4

D. -3/4

Q. 45 Consider the following values of x:

1. 8

2. -4

3. 1/6

4. -1/4

Which of the above values of x is/are the solution(s) of the equation tan⁻¹(2x)+tan⁻¹(3x)=π/4 ?

A. 3 only

B. 2 and 3 only

C. 1 and 4 only

D. 4 only

Q. 46 If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is

A. 8, 2, 1/2, 1/8

B. 10, 2, 2/5, 2/25

C. 4, 2, 1, 1/2, 1/2²

D. 6, 3, 3/2, 3/4

Q. 47 If a, b, c are in AP or GP or HP, then a -b/b – c is equal to

A. b/a or 1 or b/c

B. c/a or c/b or 1

C. 1 or a/b or a/c

D. 1 or a/b or c/a

Q. 48 What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?

A. 2664

B. 3882

C. 4044

D. 4444

Q. 49 The ratio of roots of the equations ax²+bx+c=0 and px²+qx+r=0 are equal. If D₁ and D₂ are respective discriminants, then what is D₁/D₂ equal to?

A. a²/p²

B. b²/q²

C. c²/r²

D. None of the above

Q. 50 If A=sin²θ+cos⁴θ, then for all real θ, which one of the following is correct?

A. 1≤ A ≤ 2

B. 3/4 ≤ A ≤ 1

C. 13/16 ≤ A ≤ 1

D. 3/4 ≤ A ≤ 13/16

Q. 51 The equation of a circle whose end points of a diameter are (x₁,y₁) and (x₂,y₂) is

A. (x-x₁)(x-x₂)+(y-y₁)(y-y₂)=x²+y²

B. (x-x₁)²+(y-y₁)²=x₂y₂

C. x²+y²+2x₁x₂+2y₁y₂=0

D. (x-x₁)(x-x₂)+(y-y₁)(y-y₂)=0

Q. 52 The second degree equation x² + 4y² – 2x – 4y + 2 = 0 represents

A. A point

B. An ellipse of semi-major axis 1

C. An ellipse with eccentricity √3/2

D. None of the above

Q. 53 The angle between the two lines lx+my+n=0 and l’x+m’y+n’=0 is given by tan⁻¹θ. What is θ equal to?

A. |lm’-l’m/ll’-mm’|

B. |lm’+l’m/ll’+mm’|

C. |lm’-l’m/ll’+mm’|

D. |lm’+l’m/ll’+mm’|

Q. 54 Consider the following statements:

1. The distance between the lines y=mx+c₁ and y=mx+c₂ is |c₁-c₂|/[√1+m²]

2. The distance between the lines ax+by+c₁=0 and ax+by+c₂=0 is |c₁-c₂|/[√a²+b²]

3. The distance between the lines x=c₁ and x=c₂ is |c₁-c₂|

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 55 What is the equation of straight line passing through the point of intersection of the lines x/2 + y/3 = 1 and x/3 + y/2 = 1, and parallel to the line 4x + 5y – 6 = 0 ?

A. 20x + 25y – 54 = 0

B. 25x + 20y – 54 = 0

C. 4x + 5y – 54 = 0

D. 4x + 5y – 45 = 0

Q. 56 What is the distance of the point (2, 3, 4) from the plane 3x – 6y + 2z + 11 = 0?

A. 1 unit

B. 2 units

C. 3 units

D. 4 units

Q. 57 Coordinates of the points O, P ,Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram who two adjacent sides LK and LM are each of length √2. What are the values of m and n respectively?

A. 6, 2

B. 1, 3

C. 3, 1

D. None of the above

Q. 58 The line x-1/2 = y-2/3 = z-3/4 is given by

A. x+y+z=6, x+2y-3z=-4

B. x+2y-2z=-1, 4x+4y-5z-3=0

C. 3x+2y-3z=0, 3x-6y+3z=-2

D. 3x+2y-3z=-2, 3x-6y+3z=0

Q. 59 Consider the following statements:

1. The angle between the planes

2x-y+z=1 and x+y+2z=3 is π/3.

2. The distance between the planes

6x-3y+6z+2=0 and

2x-y+2z+4=0 is 10/9

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 60 Consider the following statements:

Statement I: If the line segment joining the points P(m, n) and Q(r, s) subtends an angle α at the origin, then cos α = ms-nr/[√(m²+n²)(r²+s²)]

Statement II: In any triangle ABC, it is true that a²=b²+c²-2bc cos A

Which one of the following is correct in respect of the above two statements?

A. Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I

B. Both Statement I and Statement II are true, but Statement II is not the correct

explanation of Statement I

C. Statement I is true, but Statement II is false

D. Statement I is false, but Statement II is true

Q. 61 What is the area of the triangle with vertices (x₁, 1/x₁), (x₂, 1/x₂), (x₃, 1/x₃)?

A. |(x₁-x₂)(x₂-x₃)(x₃-x₁)|

B. 0

C. |(x₁-x₂)(x₂-x₃)(x₃-x₁)/x₁x₂x₃|

D. |(x₁-x₂)(x₂-x₃)(x₃-x₁)/2x₁x₂x₃|

Q. 62 If y-axis touches the circle

x²+y²+gx+fy+e/4=0, then the normal at this point intersects the circle at the point

A. (-g/2, -f/2)

B. (-g, -f/2)

C. (-g/2, f)

D. (-g, -f)

Q. 63 Let |a̅|≠0, |b̅|≠0

(a̅+b̅).(a̅+b̅)=|a̅|²+|b̅|²

holds if and only if

Note: a̅ and b̅ represent vector sign

A. a̅ and b̅ are perpendicular

B. a̅ and b̅ are parallel

C. a̅ and b̅ are inclined at an angle of 45°

D. a̅ and b̅ are anti-parallel

Q. 64 if r̅=xî+yĵ+zk̂, then what is r̅.(î+ĵ+k̂) equal to?

Note: r̅ represents the vector sign.

A. x

B. x+y

C. -(x+y+z)

D. (x+y+z)

Q. 65 A unit vector perpendicular to each of the vectors 2î-ĵ+k̂ and 3î-4ĵ-k̂ is

A. (1/√3)î+(1/√3)ĵ-(1/√3)k̂

B. (1/√2)î+(1/2)ĵ-(1/2)k̂

C. (1/√3)î-(1/√3)ĵ-(1/√3)k̂

D. (1/√3)î+(1/√3)ĵ+(1/√3)k̂

Q. 66 if |a̅|=3, |b̅|=4, and |a̅-b̅|=5, then what is the value of |a̅+b̅|?

Note: a̅, b̅ represent the vector sign.

A. 8

B. 6

C. 5√2

D. 5

Q. 67 Let a̅, b̅ and c̅ be three mutually perpendicular vectors each of unit magnitude. If A̅=a̅+b̅+c̅, B̅=a̅-b̅+c̅ and C̅=a̅-b̅-c̅, then which one of the following is correct?

Note: A̅, B̅, C̅, a̅, b̅ and c̅ represent the vector sign.

A. |A̅|>|B̅|>|C̅|

B. |A̅|=|B̅|≠|C̅|

C. |A̅|=|B̅|=|C̅|

D. |A̅|≠|B̅|≠|C̅|

Q. 68 What is (a̅-b̅)×(a̅+b̅) equal to?

Note: a̅ and b̅ represent the vector sign.

A. 0̅

B. a̅×b̅

C. 2(a̅×b̅)

D. |a̅|²-|b̅|²

Q. 69 A spacecraft located at î+2ĵ+3k̂ is subjected to a force λk̂ by firing a rocket. The spacecraft is subjected to a moment of magnitude

A. λ

B. √3λ

C. √5λ

D. None of the above

Q. 70 In a triangle ABC, if taken in order, consider the given statements.

How many of the statements given in the image are correct

A. One

B. Two

C. Three

D. Four

Q. 71 Let the slope of the curve y=cos⁻¹(sin x) be tan θ. Then the value of θ in the interval (0, π) is

A. π/6

B. 3π/4

C. π/4

D. π/2

Q. 72 If f(x)=(√x-1)/x-4 defines a function on ℝ, then what is its domain?

A. (-∞, 4)⋃(4, ∞)

B. [4, ∞)

C. (1, 4)⋃(4, ∞)

D. [1, 4)⋃(4, ∞)

Q. 73 Which one of the following is correct in respect of the function?

A. It is not continuous at x=0

B. It is continuous at every x

C. It is not continuous at x=π

D. It is continuous at x=0

Q. 74 For the function f(x) = |x-3|, which one of the following is not correct ?

A. The function is not continuous at x = -3

B. The function is continuous at x = 3

C. The function is differentiable at x = 0

D. The function is differentiable at x = -3

Q. 75 If the function f(x)=2x-sin⁻¹x/2x+tan⁻¹x is continuous at each point in its domain, then what is the value of f(0) ?

A. -1/3

B. 1/3

C. 2/3

D. 2

Q. 76 If f(x)=(√25-x²), then what is the given matrix equal to?

A. -1/√24

B. 1/√24

C. -1/4√3

D. 1/4√3

Q. 77 If y=tan⁻¹(5-2tan√x/2+5tan√x), then what is dy/dx equal to?

A. -1/2√x

B. 1

C. -1

D. 1/2√x

Q. 78 Which one of the following is correct in respect of the function f(x)=x sin x + cos x + ½ cos²x?

A. It is increasing in the interval (0, π/2)

B. It remains constant in the interval (0, π/2)

C. It is decreasing in the interval (0, π/2)

D. It is decreasing in the interval (π/4, π/2)

Q. 79 What is the given matrix equal to?

A. √2

B. 2√2

C. 1/√2

D. -1/2√2

Q. 80 A function f : A→R is defined by the equation f(x)=x²-4x+5 where A=(1, 4). What is the range of the function?

A. (2, 5)

B. (1, 5)

C. [1, 5)

D. [1, 5]

Q. 81 What is the given matrix equal to, where [.] is the greatest integer function?

A. b-a

B. a-b

C. 0

D. 2(b-a)

Q. 82 What is the given matrix equal to?

A. 2

B. 3

C. 4

D. 9

Q. 83 What is ∫ sin³ x cos x dx equal to?

Note: where c is the constant of integration.

A. cos⁴x+c

B. sin⁴x+c

C. [(1-sin²x)²/4] + c

D. [(1-cos²x)²/4] + c

Q. 84 What is the given matrix equal to?

A. ln|tan x|+c

B. ln|sec x|+c

C. tan x+c

D. eᵗᵃⁿ ˣ+c

Q. 85 What is the given matrix equal to?

A. 0

B. -π/4

C. -π/2

D. π/2

Q. 86 In which one of the following intervals is the function f(x)=x²-5x+6 decreasing?

A. (∼∞, 2]

B. [3, ∞)

C. (∼∞, ∞)

D. (2, 3)

Q. 87 The differential equation of the family of curves y=p cos (ax)+ q sin (ax), where p, q are arbitrary constants is

A. (d²y/dx²) – a²y = 0

B. (d²y/dx²) – ay = 0

C. (d²y/dx²) + ay = 0

D. (d²y/dx²) + a²y = 0

Q. 88 The equation of the curve passing through the point (-1, -2) which satisfies dy/dx=-x²-1/x³, is

A. 17x²y-6x²+3x⁵-2=0

B. 6x²y+17x²+2x⁵-3=0

C. 6xy-2x²+17x⁵+3=0

D. 17x²y+6xy-3x⁵+5=0

Q. 89 What is the order of the differential equation whose solution is y=a cos x + b sin x + ce⁻ⁿ + d, where a, b, c and d are arbitrary constants?

A. 1

B. 2

C. 3

D. 4

Q. 90 What is the solution of the differential equation ln(dy/dx)=ax+by?

Note: where c is an arbitrary constant

A. aeᵃˣ + beᵇʸ = c

B. (1/a)eᵃˣ +(1/b)eᵇʸ = c

C. aeᵃˣ + be⁻ᵇʸ = c

D. (1/a)eᵃˣ + (1/b)e⁻ᵇʸ = c

Q. 91 If u=eⁱ ⁿ sin bx and v=eⁱ ⁿ cos bx, then what is u(du/dx)+v(dv/dx) equal to?

A. a e²ⁱ ⁿ

B. (a²+b²)eⁱ ⁿ

C. ab e²ⁱ ⁿ

D. (a+b)eⁱ ⁿ

Q. 92 If y=sin(ln x), then which one of the following is correct?

A. (d²y/dx²) + y = 0

B. d²y/dx²=0

C. x²(d²y/dx²)+x(dy/dx)=0

D. x²(d²y/dx²)-x(dy/dx)=0

Q. 93 A flower-bed in the form of a sector has been fenced by a wire of 40 m length. If the flowerbed has the greatest possible area, then what is the radius of the sector?

A. 25 m

B. 20 m

C. 10 m

D. 5 m

Q. 94 What is the minimum value of [x(x-1)+1]¹⁄³, where 0≤x≤1 ?

A. (3/4)¹⁄³

B. 1

C. 1/2

D. (3/8)¹⁄³

Q. 95 If y=|sin x||ˣ|, then what is the value of dy/dx at x=-π/6 ?

A. [2⁻π/⁶ (6 ln 2 – √3π)] / 6

B. [2π/⁶ (6 ln 2 + √3π)] / 6

C. [2⁻π/⁶ (6 ln 2 + √3π)] / 6

D. [2π/⁶ (6 ln 2 – √3π)] / 6

Q. 96 What is d√(1-sin2x)/dx equal to, where π/4

A. cos x + sin x

B. -(cos x+ sin x)

C. ±(cos x + sin x)

D. None of the above

Q. 97 What is ∫ dx/a²sin²x+b²cos²x equal to?

Note: where c is the constant of integration

A. c+1/ab tan⁻¹(a tan x/b)

B. c-1/ab tan⁻¹(b tan x/a)

C. c+1/ab tan⁻¹(b tan x/a)

D. None of the above

Q. 98 According to the matrix given, let f(x+y)=f(x)f(y) and f(x)=1+xg(x)φ(x). Then what is f'(x) equal to?

A. 1+abf(x)

B. 1+ab

C. ab

D. abf(x)

Q. 99 What is solution of the differential equation dx/dy=x+y+1/x+y-1 ?

Note: where c is an arbitrary constant.

A. y-x+4ln(x+y)=c

B. y+x+2ln(x+y)=c

C. y-x+ln(x+y)=c

D. y+x+2ln(x+y)=c

Q. 100 What is the matrix given equal to?

A. -1/2

B. -1/3

C. -2

D. -3

Q. 101 If two dices are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is

A. 1/6

B. 4/11

C. 3/11

D. 2/11

Q. 102 The correlation coefficient computed from a set of 30 observations is 0.8. Then the percentage of variation not explained by linear regression is

A. 80%

B. 20%

C. 64%

D. 36%

Q. 103 The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and that of the group of women is 21 years, then the percentage of men and women in the group is respectively

A. 20, 80

B. 40, 60

C. 60, 40

D. 80, 20

Q. 104 If sin β is the harmonic mean of sin α and cos α, and sin θ is the arithmetic mean of sin α and cos α, then which of the following is/are correct?

1. √2 sin (α+π/4)sinβ = sin 2α

2. √2 sin θ = cos (α-π/4)

Select the correct answer using the code below:

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 105 Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = 1.5 P(A) and P(C) = 0.5 P(B), then P(A) is equal to

A. 3/4

B. 4/13

C. 2/3

D. 1/2

Q. 106 In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?

A. 5/39

B. 14/39

C. 20/39

D. 34/39

Q. 107 8 coins are tossed simultaneously. The probability of getting at least 6 heads is

A. 7/64

B. 57/64

C. 37/256

D. 229/256

Q. 108 Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is

A. 13/32

B. 9/32

C. 3/32

D. 1/32

Q. 109 Consider the following statements:

1. If 10 is added to each entry on a list, then the average increases by 10.

2. If 10 is added to each entry on a list, then the standard deviation increases by 10.

3. If each entry on a list is doubled, then the average doubles.

Which of the above statements are correct?

A. 1, 2 and 3

B. 1 and 2 only

C. 1 and 3 only

D. 2 and 3 only

Q. 110 The variance of 25 observations is 4. If 2 is added to each observation, then the new variance of the resulting observations is

A. 2

B. 4

C. 6

D. 8

Q. 111 If xᵢ>0, yᵢ>0 (i=1, 2, 3 … n) are the values of two variables X and Y with geometric means P and Q respectively, then the geometric mean of X/Y is

A. P/Q

B. antilog (P/Q)

C. n(logP-logQ)

D. n(logP+logQ)

Q. 112 If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct?

1. P(A̅)+P(B̅)=2-2p-q

2. P(A̅∩B̅)=1-p-q

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 113 If the regression coefficient of Y on X is -6, and the correlation coefficient between X and Y is -1/2, then the regression coefficient of X on Y would be

A. 1/24

B. -1/24

C. -1/6

D. 1/6

Q. 114 The set of bivariate observations (x₁, y₁), (x₂, y₂) …, (xᵣ, yᵣ) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between x and y are

A. 0 and 1 only

B. 0 and -1 only

C. 0, 1 and -1

D. -1 and 1 only

Q. 115 Two integers x and y are chosen with replacement from the set {0, 1, 2, …, 10}. The probability that |x – y| > 5 is

A. 6/11

B. 35/121

C. 30/121

D. 25/121

Q. 116 An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the result as shown in the table. The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are

A. Rs 1860, 100

B. Rs. 1750, 100

C. Rs. 1800, 81

D. None of the above

Q. 117 Three dice having digits, 1, 2, 3, 4, 5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III respectively. What is the number of possible outcomes such that x > y > z ?

A. 14

B. 16

C. 18

D. 20

Q. 118 Which one of the following can be obtained from an ogive?

A. Mean

B. Median

C. Geometric mean

D. Mode

Q. 119 In any discrete series (when all values are not same), if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct ?

A. y ≥ x

B. y ≤ x

C. x = y

D. x < y

Q. 120 In which one of the following cases would you expect to get a negative correlation?

A. The ages of husbands and wives

B. Shoe size and intelligence

C. Insurance companies’ profits and the number of claims they have to pay

D. Amount of rainfall and yield of crop

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	C	A	D	C	B	C	A	C	D
Question	11	12	13	14	15	16	17	18	19	20
Answer	D	A	A	A	B	D	B	A	D	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	C	A	C	D	C	B	C	B	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	C	C	D	B	B	C	A	D	B	A
Question	41	42	43	44	45	46	47	48	49	50
Answer	B	B	B	A	A	C	C	A	B	C
Question	51	52	53	54	55	56	57	58	59	60
Answer	D	A	C	D	A	A	C	B	C	D
Question	61	62	63	64	65	66	67	68	69	70
Answer	D	B	A	D	C	D	C	C	C	A
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	D	A	A	B	A	A	A	C	C
Question	81	82	83	84	85	86	87	88	89	90
Answer	B	D	D	B	C	A	D	B	D	D
Question	91	92	93	94	95	96	97	98	99	100
Answer	A	C	C	A	A	B	A	D	C	D
Question	101	102	103	104	105	106	107	108	109	110
Answer	C	D	D	C	B	A	C	A	C	B
Question	111	112	113	114	115	116	117	118	119	120
Answer	A	C	B	C	D	D	D	B	D	C

NDA/NA(II) Exam 2017 Mathematics Previous Year Paper

NDA/NA(II) Exam 2017 Mathematics

Q. 1 If x + log₁₀ (1 + 2ˣ) = x log₁₀ 5 + log₁₀ 6, then x is equal to

A. 2, -3

B. 2 only

C. 1

D. 3

Q. 2 The remainder and the quotient of the binary division (101110)₂ / (110)₂ are respectively

A. (111)₂ and (100)₂

B. (100)₂ and (111)₂

C. (101)₂ and (101)₂

D. (100)₂ and (100)₂

Q. 3 The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 – y columns. Both AB and BA exists. What are the values of x and y respectively?

A. 8 and 3

B. 3 and 4

C. 3 and 8

D. 8 and 8

Q. 4 If Sₙ = nP + n(n – 1)Q/2, where Sₙ denotes the sum of the first n terms of an AP, then the common difference is

A. P + Q

B. 2P + 3Q

C. 2Q

D. Q

Q. 5 The roots of the equation (q – r)x² + (r – p)x + (p – q) = 0 are

A. (r – p)/(q – r), 1/2

B. (p – q)/(q – r), 1

C. (q – r)/(p – q), 1

D. (r – p)/(p – q), 1/2

Q. 6 If E is the universal set and A = B U C, then the set E – (E – (E – (E – (E – A)))) is same as the set

A. B’ U C’

B. B U C

C. B’ ∩ C’

D. B ∩ C

Q. 7 If A = {x: x is a multiple of 2}, B = {x: x is a multiple of 5} and C = {x: x is a multiple of 10}, then A ∩ (B ∩ C) is equal to

A. A

B. B

C. C

D. {x: x is a multiple of 100}

Q. 8 If α and β are roots of the equation 1 + x + x² = 0, then the given matrix product is equal to

A. a

B. b

C. c

D. d

Q. 9 If lal denotes the absolute value of an integer, then which of the following are correct?

1. labl = lal lbl

2. la + bl <= lal + lbl

3. la – bl >=l lal – lbl l

Select the correct answer using the code given below.

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 10 How many different permutations can be made out of the letters of the word

‘PERMUTATION’?

A. 19958400

B. 19954800

C. 19952400

D. 39916800

Q. 11 Answer the questions given in the image.

A. a

B. b

C. c

D. d

Q. 12 The sum of all real roots of the equation lx – 3l² + lx – 3l – 2 = 0 is

A. 2

B. 3

C. 4

D. 6

Q. 13 It is given that the roots of the equation x² – 4x – log₃ P = 0 are real. For this, the minimum value of P is

A. 1/27

B. 1/64

C. 1/81

D. 1

Q. 14 If A is a square matrix, then the value of adj Aᵀ – (adj A)ᵀ is equal to

A. A

B. 2lAl I, where I is the identity matrix

C. null matrix whose order is same as that of A

D. unit matrix whose order is same as that of A

Q. 15 The value of the product 6¹/² x 6¹/⁴ x 6¹/⁸ x 6¹/¹⁶ x … up to infinite terms is

A. 6

B. 36

C. 216

D. 512

Q. 16 The value of the given determinant for all values of θ is

A. 1

B. cos θ

C. sin θ

D. cos 2θ

Q. 17 The number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is

A. 202

B. 101

C. 51

D. 50

Q. 18 In the expansion of (1 + x)⁵⁰, the sum of the coefficients of odd powers of x is

A. 2²⁶

B. 2⁴⁹

C. 2⁵⁰

D. 2⁵¹

Q. 19 If a, b, c are real non-zero numbers, then the inverse of the matrix A is

A. a

B. b

C. c

D. d

Q. 20 A person is to count 4500 notes. Let aₙ denote the number of notes he counts in the nth minute. If a1 = a2 = a3 = … = a10 = 150, and a10, a11, a12, …. are in AP with the common difference -2, then the time taken by him to count all the notes is

A. 24 minutes

B. 34 minutes

C. 125 minutes

D. 135 minutes

Q. 21 The smallest positive integer n for which given equation is correct is

A. 1

B. 4

C. 8

D. 16

Q. 22 If we define the relation R on the set N x N as (a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N x N, then the relation is

A. symmetric only

B. symmetric and transitive only

C. equivalence relation

D. reflexive only

Q. 23 If y = x + x² + x³ + … up to infinte terms, where x < 1, then which one of the following is correct?

A. x = y / (1 + y)

B. x = y / (1 – y)

C. x = (1 + y) / y

D. x = (1 – y) / y

Q. 24 If α and β are the roots of the equation 3x² + 2x + 1 = 0, then the equation whose roots are α + β⁻¹ and β + α⁻¹ is

A. 3x² + 8x + 16 = 0

B. 3x² – 8x – 16 = 0

C. 3x² + 8x – 16 = 0

D. x² + 8x + 16 = 0

Q. 25 The value of 1/log₃ e + 1/log₃ e² + 1/log₃ e⁴ + … upto infinite terms is

A. logₑ 9

B. 0

C. 1

D. logₑ 3

Q. 26 A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

A. 24 x 8! x 8!

B. (8!)³

C. 210 x 8! x 8!

D. 16!

Q. 27 The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k² has no solution if k equals

A. 0

B. 1

C. -1

D. -2

Q. 28 If 1.3 + 2.3² + 3.3³ + …. + n.3ⁿ = [(2n – 1)3ᵃ + b] / 4, then a and b are respectively

A. n, 2

B. n, 3

C. n + 1, 2

D. n + 1, 3

Q. 29 In △PQR, ∠R = π/2; If tan (P/2) and tan (Q/2) are the roots of the equation ax² + bx + c = 0, then which on of the following is correct?

A. a = b + c

B. b = c + a

C. c = a + b

D. b = c

Q. 30 If lz – 4/zl = 2, thn the maximum value of lzl is equal to

A. 1 + √3

B. 1 + √5

C. 1 – √5

D. √5 – 1

Q. 31 The angle of elevation of a stationary cloud from a point 25 m above a lake is 15° and the angle of depression of its image in the lake is 45°. The height of the cloud above the lake level is

A. 25 m

B. 25√3 m

C. 50 m

D. 50√3 m

Q. 32 The value of tan 9° – tan 27° – tan 63° + tan 81° is equal to

A. -1

B. 0

C. 1

D. 4

Q. 33 The value of √3 cosec 20° – sec 20° is equal to

A. 4

B. 2

C. 1

D. -4

Q. 34 Angle α is divided into two parts A and B such that A – B = x and tan A : tan B = p : q. The value of sin x is equal to

A. (p + q) sin α / (p – q)

B. p sin α / (p + q)

C. p sin α / (p – q)

D. (p – q) sin α / (p + q)

Q. 35 The value of sin⁻¹ (3/5) + tan⁻¹ (1/7) is equal to

A. 0

B. π/4

C. π/3

D. π/2

Q. 36 The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30° and 45°. If hₜ is the height of the tower and hₚ is the height of the pole, then which of the following are correct?

1. 2hₜhₚ/(3 + √3) = hₚ²

2. hₜ – hₚ / (√3 + 1) = hₚ/2

3. 2(hₚ + hₜ)/hₚ = 4 + √3

Select the correct answer using the code given below.

A. 1 and 3 only

B. 2 and 3 only

C. 1 and 2 only

D. 1, 2 and 3

Q. 37 In a triangle ABC, a – 2b + c = 0. The value of cot(A/2) cot(C/2) is

A. 9/2

B. 3

C. 3/2

D. 1

Q. 38 √(1 + sin A) = – (sin A/2 + cos A/2) is true if

A. 3π/2 < A < 5π/2 only

B. π/2 < A < 3π/2 only

C. 3π/2 < A < 7π/2

D. 0 < A < 3π/2

Q. 39 In triangle ABC, if (sin² A + sin² B + sin² C) / (cos² A + cos² B + cos² C) = 2 then the triangle is

A. right angled

B. equilateral

C. isosceles

D. obtuse angled

Q. 40 The principal value of sin⁻¹ x lies in the interval

A. (-π/2, π/2)

B. [-π/2, π/2]

C. [0, π/2]

D. [0, π]

Q. 41 The points (a, b), (0, 0), (-a, -b) and (ab, b²) are

A. the vertices of a paralellogram

B. the vertices of a rectangle

C. the vertices of a square

D. colinear

Q. 42 The length of the normal from origin to the plane x + 2y – 2z = 9 is equal to

A. 2 units

B. 3 units

C. 4 units

D. 5 units

Q. 43 If α, β, and γ are the angles which the vector OP (O being the origin) makes with the positive direction of the coordinate axis, then which of the following are correct?

1. cos² α + cos² β = sin² γ

2. sin² α + sin² β = cos² γ

3. sin² α + sin² β + sin² γ = 2

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 44 The angle between the lines x + y – 3 = 0 and x – y + 3 = 0 is α and the acute angle between the lines x – √3y + 2√3 = 0 and √3x – y + 1 = 0 is β. Which one of the following s correct?

A. α = β

B. α > β

C. α < β

D. α = 2β

Q. 45 Let ⃗α = î + 2ĵ – k̂, ⃗β = 2î + ĵ + 3k̂ and ⃗γ = 2î + ĵ + 6k̂ be three vectors. If ⃗α and ⃗β are both perpendicular to the vector ⃗δ and ⃗δ . ⃗γ = 10, then what is the magnitude of ⃗δ?

A. √3 units

B. 2√3 units

C. √3/2 units

D. 1/√3 units

Q. 46 If â and b̂ are two unit vectors, then the vector (â + b̂) x (â x b̂) is parallel to

A. (â – b̂)

B. (â + b̂)

C. (2â – b̂)

D. (2â + b̂)

Q. 47 A force ⃗F = î + 3ĵ + 2k̂ acts on a particle to displace it from the point A(î + 2ĵ – 3k̂) to the point B(3î – ĵ + 5k̂). The work done by the force will be

A. 5 units

B. 7 units

C. 9 units

D. 10 units

Q. 48 For any vector ⃗α, l ⃗α x î l² + l ⃗α x ĵ l² + l ⃗α x k̂ l² is equal to

A. l ⃗α l²

B. 2 l ⃗α l²

C. 3 l ⃗α l²

D. 4 l ⃗α l²

Q. 49 A man running around a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

A. 18π square meters

B. 15π square meters

C. 12π square meters

D. 8π square meters

Q. 50 The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4 is

A. 5/√13 units

B. 3/√17 units

C. √17 units

D. √17/2 units

Q. 51 If the vectors aî + ĵ + k̂, î + bĵ + k̂, î + ĵ + ck̂ (a, b, c ≠ 1) are coplaner, then the value of 1/(1 – a) + 1/(1 – b) + 1/(1 – c) is equal to

A. 0

B. 1

C. a + b + c

D. abc

Q. 52 The point of intersection of the line joining the points (-3, 4, -8) and (5, -6, 4) with the XYplane is

A. (7/3, -8/3, 0)

B. (-7/3, -8/3, 0)

C. (-7/3, 8/3, 0)

D. (7/3, 8/3, 0)

Q. 53 If the angle between the lines whose direction ratios are <2, -1, 2> and is π/4, then the smaller value of x is

A. 52

B. 4

C. 2

D. 1

Q. 54 The position of the point (1, 2) relative to the ellipse 2x² + 7y² = 20 is

A. outside the ellipse

B. inside the ellipse but not at the focus

C. on the ellipse

D. at the focus

Q. 55 The equation of a straight line which cuts off an intercept of 5 units on the negative direction of the y-axis and makes an angle 120⁰ with the positive direction of the x-axis is

A. y + √3x + 5 = 0

B. y – √3x + 5 = 0

C. y + √3x – 5 = 0

D. y – √3x – 5 = 0

Q. 56 The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is

A. 21x + 46y – 180 = 0

B. 21x – 46y + 96 = 0

C. 46x + 21y -155 = 0

D. 46x – 21y – 29 = 0

Q. 57 The equation of the ellipse whose center is at the origin, the major axis is along the x-axis with eccentricity 3/4 and latus rectum 4 units is

A. x²/1024 + 7y²/64 = 1

B. 49x²/1024 + 7y²/64 = 1

C. 8x²/1024 + 49y²/64 = 1

D. x²/1024 + y²/64 = 1

Q. 58 The equation of the circle which passes through the points (1, 0), (0, -6) and (3, 4) is

A. 4x² + 4y² + 142x + 47y + 140 = 0

B. 4x² + 4y² – 142x – 47y + 138 = 0

C. 4x² + 4y² – 142x + 47y + 138 = 0

D. 4x² + 4y² + 150x – 49y + 138 = 0

Q. 59 A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is

A. x/a + y/b + z/c = 1

B. a/x + b/y + c/z = 1

C. a/x + b/y + c/z = 2

D. x/a + y/b + z/c = 2

Q. 60 The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7 and perpendicular to the plane x – 5y + 3z = 5 is given by

A. x + 2y + 3z – 6 = 0

B. x + 2y + 3z + 6 = 0

C. 3x + 4y + 5z – 8 = 0

D. 3x + 4y + 5z + 8 = 0

Q. 61 The inverse of the function y = 5ˡⁿ ˣ is

A. x = y¹/ˡⁿ ⁵, y > 0

B. x = yˡⁿ ⁵, y > 0

C. x = y¹/ˡⁿ ⁵, y < 0

D. x = 5 ln y, y > 0

Q. 62 Which one is correct in respect of the given function?

A. f(x) is continuous at x = 0 but not differentiable at x = 0

B. f(x) is continuous as well as differentiable at x = 0

C. f(x) is discontinuous at x = 0

D. None of the above

Q. 63 Answer as per instructions given in the image.

A. – y²tan x / (1 – y ln(cos x))

B. y²tan x / (1 + y ln(cos x))

C. y²tan x / (1 – y ln(sin x))

D. y²sin x / (1 + y ln(sin x))

Q. 64 Consider the following:

1. x + x² is continuous at x = 0.

2. x + cos 1/x is discontinuous at x = 0.

3. x² + cos 1/x is continuous at x = 0.

Which of the above are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 65 Consider the following statements:

1. dy/dx at a point on the curve gives the slope of the tangent at that point.

2. If a(t) denotes acceleration of a particle, then ∫a(t) dt + c gives a velocity of the particle.

3. If s(t) gives a displacement of a particle at a time t, then ds/dt gives its acceleration at that instant.

Which of the above statement(s) is/are correct?

A. 1 and 2 only

B. 2 only

C. 1 only

D. 1, 2 and 3

Q. 66 If y = sec⁻¹ [(x + 1)/(x – 1)] + sin⁻¹ [(x – 1)/(x + 1)], then dy/dx is equal to

A. 0

B. 1

C. (x – 1)/(x + 1)

D. (x + 1)/(x – 1)

Q. 67 What is ∫ tan⁻¹ (sec x + tan x) dx equal to?

A. πx/4 + x²/4 + c

B. πx/2 + x²/4 + c

C. πx/4 + πx²/4 + c

D. πx/4 – x²/4 + c

Q. 68 Which one of the following is correct in respect of the derivative of the function, i.e. f'(x)?

A. f'(x) = 2x for 0<x≤1

B. f'(x) = -2x for 0<x≤1

C. f'(x) = -2x for 0<x<1

D. f'(x) = 0 for 0<x<∞

Q. 69 Which one of the following is correct in respect of the function f(x) = x(x – 1)(x + 1)?

A. The local maximum value is larger than local minimum value.

B. The local maximum value is smaller than local minimum value.

C. The function has no local maximum.

D. The function has no local minimum.

Q. 70 Consider the following statements:

1. A derivative of f(x) may not exist at some point.

2. A derivative of f(x) may exist finitely at some point.

3. A derivative of f(x) may be infinite (geometrically) at some point.

Which of the above statement(s) are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 71 The maximum value of (ln x)/x is

A. e

B. 1/e

C. 2/e

D. 1

Q. 72 The function f(x) = lxl – x³ is

A. odd

B. even

C. both even and odd

D. neither even nor odd

Q. 73 Answer as per instructions given in the image.

A. l₁ ≠ l₂

B. d/dx(l₃) = l₂

C. ∫ l₃ dx = l₂

D. l₃ = l₂

Q. 74 The general solution of dy/dx = (ax + h)/(by + k) represents a circle only when

A. a = b = 0

B. a = -b ≠ 0

C. a = b ≠ 0, h = k

D. a = b ≠ 0

Q. 75 Answer as per instructions given in the image.

A. l = 1, m = 1

B. l = 2/π, m = ∞

C. l = 2/π, m = 0

D. l = 1, m = ∞

Q. 76 Answer as per instructions given in the image.

A. 8

B. 4

C. 2

D. 0

Q. 77 The area bounded by the curve lxl + lyl = 1 is

A. 1 square unit

B. 2√2 square units

C. 2 square units

D. 2√3 square units

Q. 78 If x is any real number, then x²/(1 + x⁴) belongs to which one of the following intervals?

A. (0, 1)

B. (0, 1/2]

C. (0, 1/2)

D. [0, 1]

Q. 79 The left hand derivative of f(x) = [x] sin (πx) at x = k; where k is an integer and [x] is the greatest integer function; is

A. (-1)ᵏ (k – 1)π

B. (-1)ᵏ⁻¹ (k – 1)π

C. (-1)ᵏ (kπ)

D. (-1)ᵏ⁻¹ (kπ)

Q. 80 If f(x) = x/2 – 1, then on the interval [0, π] which one of the following is correct?

A. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both continuous

B. tan [f(x)], where [.] is the greatest integer function, and f⁻¹(x) are both continuous

C. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both discontinuous

D. tan [f(x)], where [.] is the greatest integer function, is discontinuous but 1/f(x) is

continuous

Q. 81 Answer as per instructions given in the image.

A. 3 and 2

B. 2 and 2

C. 2 and 3

D. 1 and 3

Q. 82 If y = cos⁻¹ (2x/(1 + x²)), then dy/dx is equal to

A. -2/(1 + x²) for all lxl < 1

B. -2/(1 + x²) for all lxl > 1

C. 2/(1 + x²) for all lxl < 1

D. None of the above

Q. 83 The set of all points, where the function f(x) = √(1 – e⁻ˣ²) is differentiable is

A. (0, ∞)

B. (-∞, ∞)

C. (-∞, 0) U (0, ∞)

D. (-1, ∞)

Q. 84 Match List – I with List – II and select the correct answer using the code given.

A. A – 2, B – 3, C – 1, D – 4

B. A – 2, B – 3, C – 4, D – 1

C. A – 3, B – 2, C – 1, D – 4

D. A – 3, B – 2, C – 4, D – 1

Q. 85 If f(x) = x(√x – √(x – 1)), then f(x) is

A. continuous but not differentiable at x = 0

B. differentiable at x = 0

C. not continuous at x = 0

D. None of the above

Q. 86 Which one of the given graphs represent the function f(x) = x/x’, x ≠ 0?

A. a

B. b

C. c

D. d

Q. 87 Answer as per instructions given in the image.

A. 251

B. 250

C. 1

D. 0

Q. 88 Answer as per instructions given in the image.

A. x (ln x)⁻¹ + c

B. x (ln x)⁻² + c

C. x (ln x) + c

D. x (ln x)² + c

Q. 89 A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is

A. 1

B. 2

C. 3

D. 4

Q. 90 The value of given function is

A. π/4

B. π/2

C. π/2√2

D. π/√2

Q. 91 Let g be the greatest integer function. Then the function f(x) = (g(x)² – g(x)) is discontinuous at

A. all integers

B. all integers except 0 and 1

C. all integers except 0

D. all integers except 1

Q. 92 The differential equation of minimum order by eliminating the arbitraty constants A and C in the equation y = A [sin (x + C) + cos (x + C)] is

A. y” + (sin x + cos x)y’ = 1

B. y” = (sin x + cos x)y’

C. y” = (y’)² + sin x cos x

D. y” + y = 0

Q. 93 Consider the following statements:

Statement I – x > sin x for all x > 0

Statement II – f(x) = x – sin x is an increasing function for all x > 0

Which one of the following is correct in respect of the above statements?

A. Both I and II are true and II is the correct explanation of I

B. Both I and II are true and II is not the correct explanation of I

C. I is true but II is false

D. I is false but II is true

Q. 94 Answer as per instructions given in the image.

A. y = x/(∅(x) + c)

B. y = ∅(x)/x + c

C. y = (∅(x) + c) / x

D. y = ∅(x) / (x + c)

Q. 95 If f(x) = (4x + x⁴) / (1 + 4x³) and g(x) = ln [(1 + x)/(1 – x)], then what is the value of f ∘ g [(e – 1)/(e + 1)] equal to?

A. 2

B. 1

C. 0

D. 1/2

Q. 96 Answer as per the instructions given in the image.

A. (α – β)(β γ)(α – γ)

B. (α – β)(β γ)(γ – α)

C. (α – β)(β γ)(γ – α)(α + β + γ)

D. 0

Q. 97 Answer as per the instructions given in the image.

A. a

B. b

C. c

D. d

Q. 98 Answer as per the instructions given in the image.

A. A² = -2A

B. A² = -4A

C. A² = -3A

D. A² = 4A

Q. 99 Geometrically Re (z² – i) = 2, where i = √-1 and Re is the real part, represents

A. Circle

B. Ellipse

C. Rectangular Hyperbola

D. Parabola

Q. 100 Answer as per instructions given in the image.

A. 0

B. 1

C. pa + qb + rc

D. pa + qb + rc + a + b + c

Q. 101 A committee of two people is selected from two men and two women. The probability that the committee will have exactly one woman is

A. 1/6

B. 2/3

C. 1/3

D. 1/2

Q. 102 Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

A. 1/3

B. 2/3

C. 4/9

D. 5/9

Q. 103 Let the sample space consist of non-negative integers up to 50, X denotes the numbers which are multiples of 3 and Y denote odd numbers. Which of the following is/are correct?

1. P(X) = 8/25

2. P(Y) = 1/2

Select the correct answer using the code given below.

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 104 For two events A and B, let P(A) = 1/2, P (A U B) = 2/3 and P (A ∩ B) = 1/6. What is P(A̅ ∩ B) equal to?

A. 1/6

B. 1/4

C. 1/3

D. 1/2

Q. 105 Consider the following statements:

1. The coefficient of variation depends on the unit of measurement fo the variable.

2. A range is a measure of dispersion.

3. Mean deviation is least when measured about the median.

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 106 Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0 respectively. Then which one of the following is the arithmetic mean of the smallest five observations in the data?

A. 0

B. 8

C. 16

D. 24

Q. 107 Which one of the following can be considered as an appropriate pair of values of the regression coefficient of y on x and regression coefficient of x on y?

A. (1, 1)

B. (-1, 1)

C. (-1/2, 2)

D. (1/3, 10/3)

Q. 108 Let A and B be two events with P(A) = 1/3, P(B) = 1/6 and P(A ∩ B) = 1/12. What is P(BlA̅) equal to?

A. 1/5

B. 1/7

C. 1/8

D. 1/10

Q. 109 In a binomial distribution, the mean is 2/3 and the variance is 5/9. What is the probability that X = 2?

A. 5/36

B. 25/36

C. 25/216

D. 25/54

Q. 110 The probability that a ship safely reaches a port is 1/3. The probability that out of 5 ships, at least 4 ships would arrive safely is

A. 1/243

B. 10/243

C. 11/243

D. 13/243

Q. 111 What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?

A. 33/144

B. 17/72

C. 1/144

D. 2/9

Q. 112 It is given that X̅ = 10, Y̅ = 90, σₓ = 3, σᵧ = 12 and rₓᵧ = 0.8. The regression equation of X on Y is

A. Y = 3.2X + 58

B. X = 3.2Y + 58

C. X = -8 + 0.2Y

D. Y = -8 + 0.2X

Q. 113 If P(B) = 3/4, P (A ∩ B ∩ C̅) = 1/3 and P (A̅ ∩ B ∩ C̅) = 1/3, then what is P (B ∩ C) equal to?

A. 1/12

B. 3/4

C. 1/15

D. 1/9

Q. 114 In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the given ratios?

A. 1 : 1

B. 10 : 9

C. 100 : 91

D. 5 : 4

Q. 115 If a variable takes values 0, 1, 2, 3, ……., n with frequencies 1, C(n, 1), C(n, 2), C(n, 3),……, C(n, n) respectively, then the arithmetic mean is

A. 2n

B. n + 1

C. n

D. n/2

Q. 116 In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 – p. The probability of answering a question correctly is 1/m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

A. mp / (1 + mp)

B. mp / (1 + (m – 1)p)

C. (m – 1)p / (1 + (m – 1)p)

D. (m – 1)p / (1 + mp)

Q. 117 If x₁ and x₂ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

A. x₁ + x₂ > 2√(x₁x₂)

B. √x₁ + √x₂ > √2

C. l√x₁ – √x₂l > √2

D. x₁ + x₂ < 2√((x₁x₂) + 1)

Q. 118 Consider the following statements:

1. Variance is unaffected by the change of origin and change of scale.

2. A coefficient of variance is independent of the unit of observations.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 119 Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?

A. 0.5

B. 0.4

C. 0.3

D. 0

Q. 120 The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

A. 0.36

B. 0.2

C. 0.6

D. 0.9

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	A	C	B	D	C	C	B	D	A
Question	11	12	13	14	15	16	17	18	19	20
Answer	A	D	C	C	A	B	C	B	A	B
Question	21	22	23	24	25	26	27	28	29	30
Answer	B	C	A	A	A	C	D	D	C	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	B	D	A	B	B	C	B	C	A	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	D	B	C	B	B	A	C	B	B	D
Question	51	52	53	54	55	56	57	58	59	60
Answer	B	A	B	A	A	B	B	C	C	A
Question	61	62	63	64	65	66	67	68	69	70
Answer	A	C	A	A	A	A	A	C	A	D
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	D	B	B	C	A	C	B	A	B
Question	81	82	83	84	85	86	87	88	89	90
Answer	B	A	C	B	A	C	A	A	B	D
Question	91	92	93	94	95	96	97	98	99	100
Answer	D	D	A	D	B	B	B	B	C	A
Question	101	102	103	104	105	106	107	108	109	110
Answer	B	C	D	A	B	D	A	C	C	C
Question	111	112	113	114	115	116	117	118	119	120
Answer	B	C	A	B	D	B	C	B	C	C

NDA/NA(I) Exam 2018 Mathematics Previous Year Paper

NDA/NA(I) Exam 2018 Mathematics

Q. 1 If n ∈ N, then 121ⁿ – 25ⁿ + 1900ⁿ – (-4)ⁿ is divisible by which one of the following ?

A. 1904

B. 2000

C. 2002

D. 2006

Q. 2 If n = (2017)!, then what is 1/log₂n + 1/log₃n + 1/log₄n + … + 1/log₂₀₁₇n equals to

A. 0

B. 1

C. n/2

D. n

Q. 3 In the expansion of (1 + x)⁴³, if the coefficients of (2r + 1)th and (r + 2)th terms are equal, then what is the value of r(r ≠ 1)?

A. 5

B. 14

C. 21

D. 22

Q. 4 What is the principal argument of (-1 -i), where i = √-1?

A. π/4

B. -π/4

C. -3π/4

D. 3π/4

Q. 5 Let α and β be real numbers and z be a complex number. If z² + αz + β = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that

A. β ∈ ( -1, 0)

B. |β| = 1

C. β ∈ (1, ∞)

D. β ∈ (0, 1)

Q. 6 Let A and B be subsets of X and C = (A ∩ B’) ∪ (A’ ∩ B), where A’ and B’ are complements of A and B respectively in X. What is C equals to?

A. (A ∪ B’) – (A ∩ B’)

B. (A’ ∪ B) – (A’ ∩ B)

C. (A ∪ B) – (A ∩ B)

D. (A’ ∪ B’) – (A’ ∩ B’)

Q. 7 How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed?

A. 3⁵

B. 5³

C. 120

D. 60

Q. 8 The number of non-zero integral solutions of the equation |1 – 2i|^x = 5^x is

A. Zero (No solution)

B. One

C. Two

D. Three

Q. 9 If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to

A. 3 : 5

B. 2 : 9

C. 9 : 1

D. 5 : 3

Q. 10 If the coefficient of a^m and a^n in the expansion of (1 + a)^m+n are α and β, then which one of the following is correct?

A. α = 2β

B. α = β

C. 2α = β

D. α = (m + n)β

Q. 11 If x + log₁₅(1 + 3^x) = x log₁₅5 + log₁₅ 12, where x is an integer, then what is x equal to?

A. -3

B. 2

C. 1

D. 3

Q. 12 How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits?

A. 24

B. 36

C. 44

D. 64

Questions: 13 – 14

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.

Q. 13 What is the number of students who are good in either Hindi or Mathematics but not in English?

A. 99

B. 107

C. 125

D. 150

Q. 14 What is the number of students who are good in Hindi and Mathematics but not in English?

A. 18

B. 12

C. 10

D. 8

Q. 15 If If α and β are different complex numbers with |α| = 1, then what is |α – β|/|1 – αβ̅| equals to?

A. |β̅|

B. 2

C. 1

D. 0

Q. 16 The equation |1 – x| + x² = 5 has

A. a rational root and an irrational root

B. two rational roots

C. two irrational roots

D. no real roots

Q. 17 The binary number expression of the decimal number 31 is

A. 1111

B. 10111

C. 11011

D. 11111

Q. 18 What is i¹⁰⁰⁰ + i¹⁰⁰¹ + i¹⁰⁰² + i¹⁰⁰³ equal to (where i = √-1) ?

A. 0

B. i

C. -1

D. 1

Q. 19 What is 1/log₂N + 1/log₃N + 1/log₄N + … + 1/log₁₀₀N equal to (N ≠ 1)?

A. 1/log₁₀₀₁N

B. 1/log₉₉₁N

C. 99/log₁₀₀₁N

D. 99/log₉₉₁N

Q. 20 The modulus-amplitude form of √3 + i, where i = √-1 is

A. 2(cosπ/3 + i sinπ/3)

B. 2(cosπ/6 + i sinπ/6)

C. 2(cosπ/3 + i sinπ/3)

D. 2(cosπ/6 + i sinπ/6)

Q. 21 What is the number of non-zero terms in the expansion of (1 + 2√3 x)¹¹ + (1 – 2√3x)¹¹(after simplification)?

A. 4

B. 5

C. 6

D. 11

Q. 22 What is the greatest integer among the following by which the number 5⁵ + 7⁵ is divisible?

A. 6

B. 8

C. 11

D. 12

Q. 23 If x = 1 – y + y² – y³ + ….. up to finite terms, where |y| < 1, then which one of the following is correct?

A. x = 1/(1 + y)

B. x = 1/(1 – y)

C. x = y/(1 + y)

D. x = y/(1 – y)

Q. 24 What is the inverse of the matrix (among (a), (b), (c), (d)) given in figure?

A. (a)

B. (b)

C. (c)

D. (d)

Q. 25 If A is a 2 x 3 matrix and AB is a 2 x 5 matrix then B must be a

A. 3 x 5 matrix

B. 5 x 3 matrix

C. 3 x 2 matrix

D. 5 x 2 matrix

Q. 26 A is a matrix given in figure and A² – kA – I₂ = 0, where I₂ is the 2 x 2 identity matrix, then what is the value of k?

A. 4

B. -4

C. 8

D. -8

Q. 27 What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?

A. 185

B. 175

C. 115

D. 105

Q. 28 What is C(n, r) + 2C(n, r – 1) + C(n, r – 2) equal to?

A. C(n + 1, r)

B. C(n – 1, r + 1)

C. C(n, r + 1)

D. C(n + 2, r)

Q. 29 Let [x] denote the greatest integer function. What is the number of solutions of the equation x² – 4x + [x] = 0 inthe interval [0, 2] ?

A. Zero (No solution)

B. One

C. Two

D. Three

Q. 30 A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?

A. 40

B. 45

C. 50

D. 55

Q. 31 What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder?

A. 1565

B. 1585

C. 1635

D. 1655

Q. 32 If 0 < a < 1, the value of log₁₀a is negative. This is justified by

A. Negative power of 10 is less than 1

B. Negative power of 10 is between 0 and 1

C. Negative power of 10 is positive

D. Negative power of 10 is negative

Q. 33 The third term of a GP is 3. What is the product of the first five terms?

A. 216

B. 226

C. 243

D. Cannot be determined due to insufficient data

Q. 34 If x, 3/2, z are in AP; x, 3, z are in GP; then which one of the following will be in HP?

A. x, 6, z

B. x, 4, z

C. x, 2, z

D. x, 1, z

Q. 35 What is the value of the sum given in the figure:

A. i

B. 2i

C. -2i

D. 1 + i

Q. 36 If sin x = 1/√5, sin y = 1/√10 where 0 < x < π/2, 0 < y < π/2, 0 < y < π/2, then what is (x + y) equal to?

A. π

B. π/2

C. π/4

D. 0

Q. 37 What is (sin 5x – sin 3x)/(cos 5x + cos 3x) equal to?

A. sin x

B. cos x

C. tan x

D. cot x

Q. 38 What is sin 105° + cos 105° equal to?

A. sin 50°

B. cos 50°

C. 1/√2

D. 0

Q. 39 In a triangle ABC if a = 2, b = 3 and sinA = 2/3 what is angle B equal to?

A. π/4

B. π/2

C. π/3

D. π/6

Q. 40 What is the principal value of sin⁻¹(sin2π/3)?

A. π/4

B. π/2

C. π/3

D. 2π/3

Q. 41 If x, x- y and x + z are the angles of a triangle (not an equilateral triangle) such that tan (x – y), tan x and tan (x + y) are in GP, then what is x equal to?

A. π/4

B. π/3

C. π/6

D. π/2

Q. 42 ABC is a triangle inscribed in a circle with centre O. Let α = ∠BAC, where 45° < α < 90°. Let β = ∠BOC. Which one of the following is correct?

A. cos β = (1 – tan²α)/(1 + tan²α)

B. cos β = (1 + tan²α)/(1 – tan²α)

C. cos β = 2tanα/(1 + tan²α)

D. sin β = 2sin²α

Q. 43 If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2√3m along the ground, then what is the angle that the sun makes with the ground?

A. 60°

B. 45°

C. 30°

D. 15°

Q. 44 What is tan⁻¹(1/4) + tan⁻¹(3/5) equal to

A. 0

B. π/4

C. π/3

D. π/2

Q. 45 A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β. What is the height of the centre of the balloon (neglecting the height of the observer)?

A. r sin β/sin(α/2)

B. r sin β/sin(α/4)

C. r sin(β/2)/sinα

D. r sin α/ sin(β/2)

Q. 46 If [sin(x + y)]/[sin(x – y) = (a + b)/(a – b), then what is tan x/tan y equal to?

A. a/b

B. b/a

C. (a + b)/(a – b)

D. (a – b)/(a + b)

Q. 47 If sinα + sinβ = 0 = cosα + cosβ, where 0 < β < α < 2π, then which one of the following is correct?

A. α = π – β

B. α = π + β

C. α = 2π – β

D. 2α = π + 2β

Q. 48 Suppose cos A is given. If only one value of cos(A/2) is possible, then A must be

A. An odd multiple of 90°

B. A multiple of 90°

C. An odd multiple of 180°

D. A multiple of 180°

Q. 49 If cosα + cosβ + cosγ = 0, where 0 < α ≤ π/2, 0 < β ≤π/2, 0 < γ ≤ π/2, then what is the value of sinα + sinβ + sinγ?

A. 0

B. 3

C. 5√2/2

D. 3√2/2

Q. 50 The maximum value of sin(x + π/5) + cos(x + π/5), where x ∈ (0, π/2), is attained at

A. π/20

B. π/15

C. π/10

D. π/2

Q. 51 What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3?

A. 12√17/5

B. 13√17/5

C. √17/5

D. 6√17/5

Q. 52 What is the angle between the straight lines (m² – mn)y = (mn + n²)x + n³ and (mn + m²)y = (mn – n²)x + m³, where m > n?

A. tan⁻¹(2mn)/(m² + n²)

B. tan⁻¹(4m²n²)/(m⁴ – n⁴)

C. tan⁻¹(4m²n²)/(m⁴ + n⁴)

D. 45°

Q. 53 What is the equation of the straight line cutting off an intercept 2 from the negative direction of y-axis and inclined at 30° with the positive direction of x-axis?

A. x – 2√3y – 3√2 = 0

B. x + 2√3y – 3√2 = 0

C. x + √3y – 2√3 = 0

D. x – √3y – 2√3 = 0

Q. 54 What is the equation of the line passing through the point of intersection of the lines x + 2y – 3 = 0 and 2x – y + 5 = 0 and parallel to he line y – x + 10 = 0?

A. 7x – 7y + 18 – 0

B. 5x – 7y + 18 = 0

C. 5x – 5y + 18 = 0

D. x – y + 5 = 0

Q. 55 Consider the following statements:

1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p² = c²/(a² + b²).

2. The length p of the perpendicular from the origin to the line x/a + y/b = 1 satisfies the relation 1/p² = 1/a² + 1/b².

3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1/p² = (1 + m² + c²)/c².

A. 1, 2 and 3

B. 1 only

C. 1 and 2 only

D. 2 only

Q. 56 What is the equation of the ellipse whose vertices are (±5, 0) and foci are at (±4, 0)?

A. x²/25 + y²/9 = 1

B. x²/16 + y²/9 = 1

C. x²/25 + y²/16 = 1

D. x²/9 + y²/25 = 1

Q. 57 What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive y-axis equal to twice its intercept on the positive x-axis?

A. 2x + y = 5

B. 2x + y = 7

C. x + 2y = 7

D. 2x – y = 1

Q. 58 Let the coordinates of the points A, B, C be (1, 8, 4), (0, -11, 4) and (2, -3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC?

A. (3, 4, -2)

B. (4, -2, 5)

C. (4, 5, -2)

D. (2, 4, 5)

Q. 59 What is the equation of the plane passing through the points (-2, 6, -6), (-3, 10, -9) and (-5, 0, -6)?

A. 2x – y – 2z = 2

B. 2x + y + 3z = 3

C. x + y + z = 6

D. x – y – z = 3

Q. 60 A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC?

A. x² + y² + z² = r²

B. x² + y² + z² = 4r²

C. 9(x² + y² + z²) = 4r²

D. 3(x² + y² + z²) = 2r²

Q. 61 The coordinates of the vertices P, Q and R of a triangle PQR are (1, -1, 1), (3, -2, 2) and (0, 2, 6) respectively. If ∠RQP = θ, then what is ∠PQR equal to?

A. 30° + θ

B. 45° – θ

C. 60° – θ

D. 90° – θ

Q. 62 The perpendiculars that fall from any point of the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x – 3y = 2 are

A. 12 and 4 respectively

B. 11 and 5 respectively

C. Equal to each other

D. Not equal to each other

Q. 63 The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2 is

A. Either x + y = 4 or 9x + y = 12

B. Either x + y = 5 or 4x + 9y = 30

C. Either x + y = 4 or x + 9y = 12

D. Either x + y = 5 or 9x + 4y = 30

Q. 64 What is he distance between the straight lines 3x + 4y = 9 and 6x + 8y = 15?

A. 3/2

B. 3/10

C. 6

D. 5

Q. 65 What is the equation to the sphere whose centre is at (-2, 3, 4) and radius is 6 units?

A. x² + y² + z² + 4x – 6y – 8z = 7

B. x² + y² + z² + 6x – 4y – 8z = 7

C. x² + y² + z² + 4x – 6y – 8z = 7

D. x² + y² + z² + 4x + 6y + 8z = 7

Q. 66 If a̅ and b̅ are vectors such that | a̅ | = 2, | b̅ | = 7 and a̅ x b̅ = 3î + 2ĵ + 6k̂, then what is the acute angle between a̅ and b̅? ( ̅ denotes vector )

A. 30°

B. 45°

C. 60°

D. 90°

Q. 67 Let p̅ and q̅ be the position vectors of the points P and Q respectively with respect to origin O. The points R and S divide PQ internally and externally respectively in the ratio 2 : 3. If O̅R̅ and O̅S̅ are perpendicular, them which one of the following is correct? ( ̅ denotes vector )

A. 9p² = 4q²

B. 4p² = 9q²

C. 9p = 4q

D. 4p = 9q

Q. 68 What is the moment about the point î + 2ĵ – k̂ of a force represented by 3î + k̂ acting through the point 2î – ĵ + 3k̂?

A. -3î + 11ĵ + 9k̂

B. 3î + 2ĵ + 9k̂

C. 3î + 4ĵ + 9k̂

D. î + ĵ + k̂

Q. 69 If a⁻ + 2b⁻ + 3c⁻ = 0⁻ and a⁻ x b⁻ + b⁻ x c⁻ + c⁻ x a⁻ = λ(b⁻ x c⁻), then what is the value of λ?

A. 2

B. 3

C. 4

D. 6

Q. 70 If the vectors k̅ and A̅ are parallel to each other, then what is kk̅ x A̅ equal? ( ̅ denotes vector )

A. k²A̅

B. 0̅

C. -k²A̅

D. A̅

Q. 71 Which one of the following is correct in respect of the function f : R → R⁺ defined as f(x) = |x + 1|?

A. f(x²) = [f(x)]²

B. f(|x|) = |f(x)|

C. f9x + y) = f(x) + f(y)

D. None of the above

Q. 72 Suppose f : R → R is defined by f(x) = x²/(1 + x²). What is the range of the function?

A. [0, 1)

B. [0, 1]

C. (0, 1]

D. (0, 1)

Q. 73 If f(x) = |x| + |x – 1|, then which one of the following is correct?

A. f(x) is continuous at x = 0 and x = 1

B. f(x) is continuous at x = 0 but not at x = 1

C. f(x) is continuous at x = 1 but not at x = 0

D. f(x) is neither continuous at x = 0 nor at x = 1

Q. 74 Consider the function given in figure. What is f'(0) equal to ?

A. 0

B. 1

C. -1

D. It does not exist

Q. 75 What is the area of the region bounded by the parabolas y² = 6(x – 1) and y² = 3x?

A. √6/3

B. 2√6/3

C. 4√6/3

D. 5√6/3

Questions: 76 – 78

Three sides of a trapezium are each equal to 6 cm. Let α ∈ (0, π/2) be the angle between a pair of adjacent sides.

Q. 76 If the area of the trapezium is the maximum possible, then what is α equals to?

A. π/6

B. π/4

C. π/3

D. 2π/5

Q. 77 If the area of the trapezium is maximum, what is the length of the fourth side?

A. 8 cm

B. 9 cm

C. 10 cm

D. 12 cm

Q. 78 What is the maximum area of the trapezium?

A. 36√3 cm²

B. 30√3 cm²

C. 27√3 cm²

D. 24√3 cm²

Q. 79 What is the value of the given equation (given in the figure)?

A. (e^π + 1)/2

B. (e^π – 1)/2

C. e^π + 1

D. (e^π + 1)/4

Q. 80 If f(x) = (x² – 9)/(x² – 2x – 3), x ≠ 3 is continuous at x = 3, then which one of the following is correct?

A. f(3) = 0

B. f(3) = 1.5

C. f(3) = 3

D. f(3) = -1.5

Q. 81 What is the value of the equation given in the figure?

A. (e + 1)/4

B. (e² + 1)/4

C. (e – 1)/4

D. (e² – 1)/4

Q. 82 What is the value of the equation given in the figure (where [.] is the greatest integer function)?

A. √2 – 1

B. 1 – √2

C. 2(√2 – 1)

D. √3 – 1

Q. 83 What is the maximum value of 16 sin θ – 12 sin²θ?

A. 3/4

B. 4/3

C. 16/3

D. 4

Q. 84 If f : R → S defined by

f(x) = 4 sin x – 3 cos x + 1 is onto, then what is S equal to?

A. [-5, 5]

B. (-5, 5)

C. (-4, 6)

D. [-4, 6]

Q. 85 For f to be a function, what is the domain of f, if f(x) = 1/(√|x| – x) ?

A. (-∞, 0)

B. (0, ∞)

C. (-∞, ∞)

D. (-∞, 0]

Q. 86 What is the solution of the differential equation x dy – y dx = 0 ?

A. xy = c

B. y = cx

C. x + y = c

D. x – y = c

Q. 87 What is the derivative of the function

f(x) = e^tan x + ln(sec x) – e^ln x at x = π/4?

A. e/2

B. e

C. 2e

D. 4e

Q. 88 Which one of the following differential equations has a periodic solution? (where μ > 0)

A. d²x/dt² + μx = 0

B. d²x/dt² – μx = 0

C. x(dx/dt) + μt = 0

D. dx/dt + μxt = 0

Q. 89 What is the period of the function f(x) = sin x?

A. π/4

B. π/2

C. π

D. 2π

Q. 90 What is the value of the equation given in figure?

A. ln(2^x – 1) + C

B. ln(1 – 2^-x)/ln 2 + C

C. ln(2^-x – 1)/2 ln 2 + C

D. ln(1 + 2^-x)ln 2 + C

Q. 91 The order and degree of the differential equation y² = 4a(x – a), where ’a’ is an arbitrary constant, are respectively

A. 1, 2

B. 2, 1

C. 2, 2

D. 1, 1

Q. 92 What is the value of the equation given in figure?

A. 1/√2 + ln(1/√2)

B. 1/√2

C. 0

D. √2

Q. 93 What are the values of a and b according to the two equations given in the figure?

A. -1, 1

B. 1, 1

C. 0, 0

D. 2, -2

Q. 94 What is the value of the equation given in the figure?

A. 1/110

B. 1/132

C. 1/148

D. 1/240

Q. 95 What is lim(x→0) tanx/sin 2x equal to?

A. 1/2

B. 1

C. 2

D. Limit does not exist

Q. 96 What is lim(h→0) [(√2x + 3h) – (√2x)]/2h equal to?

A. 1/2√2x

B. 3/√2x

C. 3/2√2x

D. 3/4√2x

Q. 97 If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?

A. f'(x) is an even function

B. f'(x) is an odd function

C. f'(x) may be an even or odd function depending on the type of function

D. f'(x) is a constant function

Q. 98 If y = e^x^2 sin 2x, what is dy/dx at x = π equal to?

A. (1 + π)e^π^2

B. 2πe^π^2

C. 2e^π^2

D. e^π^2

Q. 99 What is the solution of (1 + 2x)dy – (1 – 2y)dx = 0?

A. x – y – 2xy = c

B. y – x – 2xy = c

C. y + x – 2xy = c

D. x + y + 2xy = c

Q. 100 What are the order and degree, respectively, of the differential equation

(d³y/dx³)² = y⁴ + (dy/dx)⁵ ?

A. 4, 5

B. 2, 3

C. 3, 2

D. 5, 4

Q. 101 In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?

A. 80/243

B. 40/243

C. 20/243

D. 10/243

Q. 102 Consider the following statements:

1. P(A̅ U B) = P(A̅) + P(B) – P(A̅ ∩ B)

2. P(A ∩ B̅) = P(B) – P(A ∩ B)

3. P(A ∩ B) = P(B) P(A|B)

Which of the above statements are correct?

A. 1 and 2 only

B. 1 and 3 only

C. 2 and 3 only

D. 1, 2 and 3

Q. 103 If the correlation coefficient between x and y is 0.6, covariance is 27 and variance of y is 25, then what is the variance of x?

A. 9/5

B. 81/25

C. 9

D. 81

Q. 104 The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?

A. 0.6

B. 0.7

C. 0.8

D. 0.9

Q. 105 Let x̅ be the mean of x₁, x₂, x₃, ….., xn. If xi = a + cyi for some constants a and c, then what will be the mean of y₁, y₂, y₃, ….., yn?

A. a + cx̅

B. a – (1/c)x̅

C. (1/c)x̅ – a

D. (x̅ – a)/c

Q. 106 Consider the following statements:

1. If the correlation coefficient rₓᵧ = 0, then the two lines of regression are parallel to each other.

2. If the correlation coefficient rₓᵧ = +1, then the two lines of regression are perpendicular to each other.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 107 If 4x – 5y + 33 = 0 and 20x – 9y = 1-7 are two lines of regression, then what are the values of x̅ and y̅ respectively

A. 12 and 18

B. 18 and 12

C. 13 and 17

D. 17 and 13

Q. 108 Consider the following statements:

1. Mean is independent of change in scale and change in origin.

2. Variance is independent of change in scale but not in origin.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 109 Consider the following statements:

1. The sum of deviations from mean is always zero

2. The sum of absolute deviations is minimum when taken around median.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 110 What is the median of the numbers

4.6, 0, 9.3, -4.8, 7.6, 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2?

A. 3.8

B. 4.9

C. 5.7

D. 6.0

Q. 111 In a test in Mathematics, 20% of the students obtained “first class”. If the data are represented by a Pie-Chart, what is the central angle corresponding to “first class”?

A. 20°

B. 36°

C. 72°

D. 144°

Q. 112 The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values?

A. 10

B. 20

C. 40

D. 70

Q. 113 A train overs the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. What is the average speed of the train?

A. 35 km/hr

B. 37.5 km/hr

C. 39.5 km/hr

D. 40 km/hr

Q. 114 Two fair dice are rolled. What is the probability of getting a sum of 7?

A. 1/36

B. 1/6

C. 7/12

D. 5/12

Q. 115 If A and B are two events such that 2P(A) = 3P(B), WHERE 0 < P(A) < P(B) < 1, then which one of the following is incorrect?

A. P(A∣B) < P(B∣A) < P(A∩B)

B. P(A∩B) < P (B∣A) < P (A∣B)

C. P(B∣A) < P(A∣B) < P(A∩B)

D. P(A∩B) < P(A∣B) < P(B∣A)

Q. 116 A box has ten chits numbered 0, 1, 2, 3, ….., 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is “9” ?

A. 1/10

B. 1/9

C. 1/90

D. None of the above

Q. 117 One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?

A. 3/8

B. 49/80

C. 8/13

D. 1/2

Q. 118 Consider the following in respect of two events A and B:

1. P(A occurs but nit B) = P(A) – P(B) if B ⊂ A

2. P(A alone or B alone occurs) = P(A) + P(B) – P(A ∩ B)

3. P(A ∪ B) = P(A) + P(B) if A and B are mutually exclusive

Which of the above is/are correct?

A. 1 only

B. 1 and 3 only

C. 2 and 3 only

D. 1 and 2 only

Q. 119 A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?

A. 5/14

B. 1/21

C. 3/14

D. 8/21

Q. 120 The standard deviation σ of the first N natural numbers can be obtained using which one of the following formula?

A. σ = (N² – 1)/12

B. σ = √(N² – 1)/12

C. σ = √(N – 1)/12

D. σ = √(N² – 1)/6N

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	A	C	A	A	A	B	D	A	C	D
Question	11	12	13	14	15	16	17	18	19	20
Answer	A	C	C	C	B	C	A	A	B	B
Question	21	22	23	24	25	26	27	28	29	30
Answer	A	C	C	A	D	C	B	D	B	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	A	D	C	D	B	A	B	A	D	D
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	A	C	A	B	A	A	A	B	B
Question	51	52	53	54	55	56	57	58	59	60
Answer	D	A	A	A	B	B	A	A	A	A
Question	61	62	63	64	65	66	67	68	69	70
Answer	B	C	C	D	C	D	B	B	A	B
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	B	D	A	B	D	C	C	C	C
Question	81	82	83	84	85	86	87	88	89	90
Answer	D	A	A	A	D	D	A	C	A	B
Question	91	92	93	94	95	96	97	98	99	100
Answer	A	C	A	D	C	B	C	C	A	B
Question	101	102	103	104	105	106	107	108	109	110
Answer	D	B	A	C	A	B	B	B	C	A
Question	111	112	113	114	115	116	117	118	119	120
Answer	A	C	D	A	C	A	B	C	D	C