NDA/NA(II) Exam 2016 Mathematics
Q. 1 Let S be a set of all distinct numbers of the form P/Q , where p, q ∈ { 1, 2, 3, 4, 5, 6 }. What is the cardinality of the set S?
A. 21
B. 23
C. 32
D. 36
Q. 2 If c > 0 and 4a + c < 2b, then ax² – bx + c = 0 has a root in which one of the following intervals?
A. (0, 2)
B. (2, 3)
C. (3, 4)
D. (–2, 0)
Q. 3 If A = {x ∈ R : x² + 6x – 7 < 0} and B = {x ∈R : x² +9x +14 > 0} , then which of the following is/are correct?
1. A ∩ B {X∈ R : –2 < x < 1}
2. A \ B = {x ∈R : –7 < x < –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. 4 If A is a square matrix of order 3 and det A= 5, then what is det[(2A)⁻¹] equal to?
A. 1/10
B. 2/5
C. 8/5
D. 1/40
Q. 5 What is ω¹⁰⁰ + ω²⁰⁰ + ω³⁰⁰ equal to, where w is the cube root of unity?
A. 1
B. 3ω
C. 3ω²
D. 0
Q. 6 If Re((z-1)/(z+1))= 0 where 2 = x + iy is a complex number, then which one of the following is correct?
A. z = 1+ i
B. |z| = 2
C. z = 1 – i
D. | z| = 1
Q. 7 Is equal to?
A. a
B. b
C. c
D. d
Q. 8 Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n?
A. 3
B. 4
C. 5
D. 6
Q. 9 what is the imaginary part of z equal to?
A. 0
B. 1/2
C. √3/2
D. 1
Q. 10 If both of the roots of the equation x² – 2kx + k² – 4 = 0 lies between -3 and 5 then which of the following is correct?
A. -2 < k < 2
B. -5 < k < 3
C. -3 < k < 5
D. -1 < k < 3
Q. 11 What is the number of distinct solutions of the equation z²+ IzI = 0 (where z is a complex number)
A. 1
B. 2
C. 3
D. 5
Q. 12 How many geometric progressions is/are possible containing 27, 8 and 12 are three of its/ their terms?
A. 1
B. 2
C. 4
D. infinitely many
Q. 13 Let R be a relation from A= {1,2,3,4} to B={1,3,5} such that R={(a,b): a < b, where aεA and b ε B }. What is RoR⁻¹ equal to ?
A. {(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)}
B. {(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)}
C. {(3,3),(3,5),(5,3),(5,5)}
D. {(3,3)(3,4)(4,5)}
Q. 14 A five digit number divisible by 3 is to be formed using the digits 0,1,2,3 and 4 without repetition of digits. what is the number of ways this can be done?
A. 96
B. 48
C. 32
D. no number can be formed
Q. 15 Equation(in figure) is equal to?
A. ⁵²C₄
B. ⁵¹C₅
C. ⁵³C₄
D. ⁵²C₅
Questions: 16 – 18
Consider the following for the next three items that follow:
Let a,x,y,z,b in AP, where x+y+z=15. let a,p,q,r,b `be in HP , where p⁻¹+q⁻¹+r⁻¹ = 5/3
Q. 16 what is the value of ab?
A. 10
B. 9
C. 8
D. 6
Q. 17 what is the value of xyz?
A. 120
B. 105
C. 90
D. cannot be determined
Q. 18 what is the value of pqr?
A. 35/243
B. 81/35
C. 243/35
D. cannot be determined
Questions: 19 – 20
Consider the following for the next two items that follow:
The sixth term of an AP is 2 and its common difference is greater than 1.
Q. 19 What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest?
A. 8/5
B. 9/5
C. 2
D. 11/5
Q. 20 What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest?
A. -4
B. -6
C. -8
D. -10
Questions: 21 – 22
Consider the following for the next two items that follows:
Q. 21 What is the value of c?
A. -1
B. 34
C. 35
D. 50
Q. 22 what is the value of a + b + c + d?
A. 62
B. 63
C. 65
D. 68
Questions: 23 – 24
Consider the following for the next two items that follows:
The interior angles of a polygon of n sides are in AP. The smallest angle is 120⁰ and the common difference is 5⁰
Q. 23 how many possible values can n have?
A. one
B. two
C. three
D. infinitely many
Q. 24 what is the largest interior angle of the polygon?
A. 160⁰ only
B. 195⁰ only
C. either 160⁰ or 195⁰
D. neither 160⁰ nor 195⁰
Q. 25 then, what is the value of the determinant of m cos θ – n sin θ ?
A. -1
B. 0
C. 1
D. 2
Q. 26 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. 27 Which of the following correct in respect of the system of equations x + y+ z =8 , x – y + 2z =6 and 3x – y + 5z =k?
1. They have no solution, if k =15
2. They have infinitely many solutions, if k = 20
3. They have unique solution, if k = 25
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. 28 which of the following is / are correct?
1. AB(A⁻¹B⁻¹) is a unit matrix.
2. (AB)⁻¹ = A⁻¹ ⁻B¹
Select the correct answer usin the code given below:
A. 1 only
B. 2 only
C. both 1 and 2
D. neither 1 nor 2
Q. 29 which of the following is correct?
A. ln y is the GM of ln x, ln x, ln x and ln z
B. ln y is the AM of ln x, ln x, ln x and ln z
C. ln y is the HM of ln x, ln x, ln x and ln z
D. ln y is the AM of ln x, ln x , ln x and ln z
Q. 30 If the number 235 in decimal system is converted into binary then what is the resulting number?
A. (11110011)₂
B. (11101011)₂
C. (11110101)₂
D. (11011011)₂
Questions: 31 – 32
Consider the following for the next two items that follow :
let α and β be the roots of the equation x²-(1-2a²)x+(1-2a²)= 0
Q. 31 under what condition does the above equation have real roots?
A. a² < 1/ 2
B. a² < 1/2
C. a²≤ 1/2
D. a²≥ 1/2
Q. 32 under what conditions is 1/α² + 1/ β² < 1?
A. a² < 1/2
B. a² > 1/2
C. a² > 1
D. a² ε (1/3, 1/2 ) only
Q. 33 What is √[(1+ω²)/(1+ω)] equal to, where ω is the cube root of unity?
A. 1
B. ω
C. ω²
D. iω, where i = √-1
Q. 34 In an examination 70% students passed in physics, 80% students passed in chemistry , 75% students passed in mathematics and 85% students passed in biology , and x% students failed in all the four subjects. what is the minimum value of x?
A. 10
B. 12
C. 15
D. none of the above
Questions: 35 – 36
consider the following for the next two items that follow
for the system of linear equations 2x+ 3y + 5z = 9, 7x + 3y -2z = 8 and 2x + 3y + λz
= μ
Q. 35 under what condition does the above system of equations have infinitely many solutions?
A. λ=5 and μ≠ 9
B. λ=5 and μ = 9
C. λ= 9 and μ = 5
D. λ=9 and μ ≠ 5
Q. 36 under what conditions does the above system of equations have unique solutions?
A. λ=5 and μ = 9
B. λ≠5 and μ = 7 only
C. λ≠9 and μ has any real value
D. λ has any real value and μ ≠ 9
Q. 37 what is the number of odd integers between 1000 and 9999 with no digit repeated?
A. 2100
B. 2120
C. 2240
D. 3331
Q. 38 What is the greatest value of the positive integer n satisfying the condition 1 + 1/2 + 1/4 + 1/8 +…+ 1/2ⁿ⁻¹ < 2- 1/1000 ?
A. 8
B. 9
C. 10
D. 11
Questions: 39 – 40
consider the following for the next two items that follow:
2x²+3x- α =0 has roots -2 and β while the equation x² – 3mx + 2m² = 0 has both
roots positive where α > 0 and β > 0
Q. 39 what is the value of α?
A. 1/2
B. 1
C. 2
D. 4
Q. 40 If β,2,2m are in GP , then what is the value of β√m ?
A. 1
B. 2
C. 4
D. 6
Q. 41 sin A + 2 sin 2A + sin 3A is equal to which of the following?
1. 4 sin 2A cos² (A/2)
2. 2 sin 2A(sin A/2 + cos A/2)²
3. 8 sin A cos A cos² (A/2)
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. 42 If x = sin 70⁰ . sin 50⁰ and y = cos 60⁰ . cos 80⁰, then what is xy equal to ?
A. 1/16
B. 1/8
C. 1/4
D. 1/2
Q. 43 If sin θ₁ + sin θ₂ + sin θ₃ + sin θ₄ = 4, then what is the value of cos θ₁ + cos θ₂ + cos θ₃ + cos θ₄ ?
A. 0
B. 1
C. 2
D. 4
Q. 44 What is the value of (1+ cos π /8)(1+ cos 3π /8)(1+ cos 5π/8)(1+ cos 7π /8) ?
A. 1/2
B. 1/2 + 1/2√2
C. 1/2 – 1/2√2
D. 1/8
Q. 45 if x cos θ + y sin θ = z, then what is the value of (x sin θ – y cos θ)² ?
A. x² + y² – z²
B. x ² – y² – z²
C. x² – y² + z²
D. x² + y² + z²
Q. 46 What is the value of cos (2 cos⁻¹ 0.8)?
A. 0.81
B. 0.56
C. 0.48
D. 0.28
Q. 47 The top hill when observed from the top and bottom of a building of a height h is at angles of elevation p and q respectively. What is the height of the hill?
A. (h cot q)/(cot q – cot p)
B. (h cot p)/(cot p-cot q)
C. (2h tan p)/(tan p – tan q)
D. (2h tan q)/(tan q-tan p)
Q. 48 If sin 18⁰ =(√5 -1)/4 what is the value of sin 81⁰?
A. [√(3+√5)+√(5-√5)]/4
B. [√(3+√5)+√(5+√5)]/4
C. [√(3-√5)+√(5-√5)]/4
D. [√(3+√5)-√(5-√5)]/4
Q. 49 A moving boat is observed from the top of a cliff at 150m height. The angle of depression of the boat changes from 60⁰ to 45⁰ in 2 minutes. What is the speed of the boat in meters per hour?
A. 4500/√3
B. [4500(√3-1)]/√3
C. 4500√3
D. [4500(√3+1)]/√3
Q. 50 What is (1-tan 2 ⁰ cot 62⁰) / (tan 152⁰ – cot 88⁰) equal to
A. √3
B. -√3
C. √2 – 1
D. 1-√2
Q. 51 An equilateral triangle has one vertex at (0,0) and another at (3,√3). what are the coordinates of the third vertex?
A. (0,2√3) only
B. (3,-√3) only
C. (0,2√3) or (3,-√3)
D. neither (0,2√3) nor (3,-√3)
Q. 52 what is the equation of the right bisector of the line segment joining (1,1) and (2,3) ?
A. 2x+4y-11=0
B. 2x-4y-5=0
C. 2x-4y-11=0
D. x-y+1=0
Q. 53 what is the radius of the circle passing through the point (2,4) and having centre at the intersection of the lines x-y = 4 and 2x+3y + 7 =0
A. 3 units
B. 5 units
C. 3√3 units
D. 5√2 units
Q. 54 What is the equation of the hyperbola having latus rectum and electricity 8 and 3/√5 respectively?
A. x²/25 – y²/20 = 1
B. x²/40 – y²/20 =1
C. x²/40 – y²/30 =1
D. x²/30 – y²/25 = 1
Q. 55 if the point (a,a) lies between the lines Ix+yI = 2, then which of the following is correct?
A. IaI < 2
B. IaI < √2
C. IaI < 1
D. IaI < 1/ √2
Q. 56 What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10 ?
A. 4x + 3y + 2 = 0
B. 4x – y + 2 = 0
C. 4x – 3y – 2 = 0
D. 4x – 3y + 2 = 0
Q. 57 If (a, b) is at unit distance from the line 8x + 6y + 1 =0 then which of the following conditions are correct?
1. 3a – 4b – 4 = 0
2. 8a + 6b + 11= 0
3. 8a + 6b – 9 = 0
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. 58 If the ellipse 9x² + 16y² =144 intercepts the line 3x + 4y = 12 then what is the length of the chord so formed?
A. 5 units
B. 6 units
C. 8 units
D. 10 units
Q. 59 A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (-3, 5). what is the foot of the perpendicular drawn from the point (3,3) on this line?
A. (1,3)
B. (2,0)
C. (0,2)
D. (1,1)
Q. 60 What is the eccentricity of rectangular hyperbola?
A. √2
B. √3
C. √5
D. √6
Questions: 61 – 62
Consider the following for the next two items that follows:
let Q be the image of the point P (-2,1,-5) in the plane 3x – 2y + 1=0
Q. 61 consider the following:
1. The coordinates of Q are (4, -3, -1)
2. PQ is of length more than 8 units
3. The point (1,-1, 3) is the midpoint of the line segment PQ and lies on the given plane
which of the above statemnets are correct?
A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3
Q. 62 Consider the following:
1. The direction ratios of the line segment PQ are <3, -2, 2>.
2. The sum of the squares of direction cosines of the line segment PQ is unity.
which of the above statements is/are correct?
A. 1 only
B. 2 only
C. both 1 and 2
D. neither 1 nor 2
Questions: 63 – 64
consider the following for the next two items that follows:
A line L passes through the point P (5,-6,7) and in parallel to the planes x+y+z=1 and 2x-y-2z = 3
Q. 63 what are the direction ratios of the line of intersection of the given planes?
A. <1,4,3>
B. <-1,-4,3>
C. <1,-4,3>
D. <1,-4,-3>
Q. 64 What is the equation of the line L?
A. (x-5)/-1 = (y+6)/4 = z-7/-3
B. (x+5)/-1 = (y-6)/4 = (z+7)/-3
C. (x-5)/-1 = (y+6)/-4 = (z-7)/3
D. (x-5)/-1 = (y+6)/-4 = (z-7)/-3
Questions: 65 – 66
Consider the following for the next two items that follows:
Q. 65 What is equal to vector c ?
A. a
B. b
C. c
D. d
Q. 66 Which of the following equations are correct?
A. a
B. b
C. c
D. d
Questions: 67 – 68
Consider the following for the next two items for that follow:
Q. 67 which of the following is the correct option?
A. a
B. b
C. c
D. d
Q. 68 which of the following is the correct options?
A. a
B. b
C. c
D. d
Q. 69 which of the following is correct?
A. a
B. b
C. c
D. d
Q. 70 which of the following is correct?
A. a
B. b
C. c
D. d
Q. 71 What is the domain of the function f(x) = 1/√(I x I – x) ?
A. (-∞,0)
B. (0,∞)
C. 0< x < 1
D. x > 1
Q. 72 consider the following in respect of the function f(x). which of the following is correct?
A. 1 only
B. 3 only
C. 2 and 3 only
D. 1 and 3 only
Q. 73 Let f: A → ℝ where A = ℝ∖(0) is such that f(x) = x + ∣x∣ / x. On which one of the following set is f(x) continuous?
A. A
B. B = (x ∈ ℝ: x ≥0 )
C. C = (x ∈ ℝ: x ≤0 )
D. D = ℝ
Q. 74 Which one of the following statements is correct in respect of the function f(x) = x³ sin x ?
A. it has local maximum at x = 0
B. it has local maximum at x = 0
C. it has neither maximum nor minimum at x = 0
D. it has maximum value 1
Q. 75 What is the area bounded by the curves I y I = 1- x² ?
A. 4/3 square units
B. 8/3 square units
C. 4 square units
D. 16/3 square units
Questions: 76 – 77
Consider the following function for the next two items that follows
Q. 76 which of the following statements is/are correct?
1. f(x) is increasing in the interval {-1,2}
2. f(x) is decreasing in the interval (2,3}
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. 77 which of the following statements are correct?
1. f(x) is continuous at x = 2
2. f(x) attains greatest value at x = 2
3. f(x) is differentiable at x = 2
select the correct answer using code given below
A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3
Questions: 78 – 80
consider the following for the next three items that follow:
let f(x) = {I x I – I x-1I}²
Q. 78 what if f'(x) equal to when x > 1 ?
A. 0
B. 2x-1
C. 4x-2
D. 8x-4
Q. 79 what is f'(x) equal to when 0 < x < 1 ?
A. 0
B. 2x-1
C. 4x-2
D. 8x-4
Q. 80 which of the following equations is/are correct?
1. f(-2) = f(5)
2. f”(-2) + f”(0.5) + f”(3) = 4
select the correct answer by using the code given below
A. 1 only
B. 2 only
C. both 1 and 2
D. neither 1 nor 2
Questions: 81 – 83
consider the following for the next three items that follow:
let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R
Q. 81 which of the following statements is correct?
A. bot f(x) and g(x) are continuous at x = 0
B. f(x) is continuous at x = 0 , but g(x) is not continuous at x = 0
C. g(x) is continuous at x = 0 but f(x) is not continuous at x = 0
D. both f(x) and g(x) are discontinuous at x = 0
Q. 82 which one of the following statements is correct?
A. a
B. b
C. c
D. d
Q. 83 which of the following statements are correct?
1. (fof)(x) = f(x)
2. (gog)(x) = g(x) only when x = 0
3. (go(fog))(x) can take only three values.
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 nd 3
Questions: 84 – 85
Consider the following for the next two items that follow
Q. 84 which one of the following statements is correct?
A. f(x) is a strictly decreasing function in (0,x)
B. f(x) is a strictly increasing function in (0,x)
C. f(x) is neither increasing nor decreasing function in (0,x)
D. f(x) is not decreasing function in (0,x)
Q. 85 which of the following statements is/are correct?
1. f(x) is right continuous at x = 0
2. f(x) is discontinuous at x = 1
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
Questions: 86 – 87
Consider the following for the next two items that follow:
consider the parabola y = x² + 7x + 2 and the straight line y = 3x-3
Q. 86 what are the coordinates of the point on the parabola which is closet to the
straight line?
A. (0,2)
B. (-2,-8)
C. (-7,2)
D. (1,10)
Q. 87 what is the shortest distance from the above point on the parabola to the line?
A. √10/2
B. √10/5
C. 1/√10
D. √5/4
Questions: 88 – 90
Consider the following for the next three items that follow:
Q. 88 which of the following statements is/are correct?
1. g(x) is differentiable at x =0
2. g(x) is differentiable at x = 2
select the correct answer
A. 1 only
B. 2 only
C. both 1 and 2
D. neither 1 nor 2
Q. 89 what is the value of the differential coefficient of g(x) at x = -2 ?
A. -1
B. 0
C. 1
D. 2
Q. 90 which of the following statements are correct ?
1. g(x) is continuous at x=0
2. g(x) is continuous at x = 2
3 g(x) is continuous at x = -1
select the correct answer:
A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3
Q. 91 choose the correct option
A. 2 f(1)
B. 0
C. 2f(-1)
D. 4f(1)
Q. 92 What is ∫[(x⁴-1)/x²√(x⁴+x²+1)] dx equal to?
A. √(x⁴+x²+1)/x + c
B. √(x⁴-1/x²+1)/x + c
C. √(x⁴+1/x²+1)/x + c
D. √(x⁴-x²+1)/x + c
Q. 93 What are the degree and order respectively of the differential equation satisfying the equation
A. 1,1
B. 1,2
C. 2,1
D. 2,2
Q. 94 what is the curve which passes through the point (1,1) and whose slope is 2y/x ?
A. circle
B. parabola
C. ellipse
D. hyperbola
Q. 95 if x dy = y dx + y² dy , y>0 and y(1) = 1, then what is y(-3) equal to?
A. 3 only
B. -1 only
C. both -1 and 3
D. neither -1 nor 3
Q. 96 what is the order of the differential equation dx/dy + ∫ y dx = x³ ?
A. 1
B. 2
C. 3
D. cannot be determined
Q. 97 which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?
A. (y-x dy/dx)² = 1-(dy/dx)²
B. (y+x dy/dx)² = 1+(dy/dx)²
C. (y-x dy/dx)² = 1+(dy/dx)²
D. (y+x dy/dx)² = 1-(dy/dx)²
Q. 98 Function in figure is equal to
A. ( x + sec x) eˢᶦⁿ ˣ + c
B. ( x – sec x) eˢᶦⁿ ˣ + c
C. ( x + tan x) eˢᶦⁿ ˣ + c
D. ( x – tan x) eˢᶦⁿ ˣ + c
Q. 99 If function (in figure) then what is the value of the k?
A. 1/4
B. 1/2
C. 1
D. 2
Q. 100 what is the value equal to the given equation?
A. -232/5
B. -116/5
C. 116/5
D. 232/5
Q. 101 A special dice with number 1,-1,2,-2,0 and 3 is thrown thrice. what is the probability that the sum of the numbers occurring on the upper face is zero?
A. 1/72
B. 1/8
C. 7/72
D. 25/216
Q. 102 There is a 25% chance that it rains on any particular day. What i the probability that there is at least one rainy day within a period of 7 days?
A. 1-(1/4)²
B. (1/4)⁷
C. (3/4)⁷
D. 1-(3/4)⁷
Q. 103 A salesman has a 70% chance to sell a product to any customer. the behaviour of successive customers is independent. If two customers A and B enter, what is the
probability that the salesman will sell the product to consumer A or B?
A. 0.98
B. 0.91
C. 0.70
D. 0.49
Q. 104 A student appears for tests I,II and III. The student is considered successful if he passes in tests I,II or I,III or all of the three. The probabilities of the student passing in tests I,II and III are m, n and 1/2 respectively. If the probability of the student to be successful is 1/2 then which one of the following is correct?
A. m(1+n) = 1
B. n(m+1) = 1
C. m=1
D. mn = 1
Q. 105 Three candidates solve a question. odds in favour of the correct answer 5:2, 4:3 and what is the probability that at least two of them solve the question correctly?
A. 209/343
B. 134/343
C. 149/343
D. 60/343
Q. 106 consider the following statements:
1. the mean and median are equal in symmetric distribution
2.the range is the difference between the maximum value and minimum value in the data
3. the sum of the areas of the rectangles in the histogram is equal to the total area
bounded by the frequency polygon and horizontal axis
choose the correct one from the below
A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3
Q. 107 The scores of 15 students in an examination were recorded as 10,5,8,16,18,20,8,10,16 mean, median and mode, an error is found. one of the values is wrongly written as 16 instead of 18. which of the following measures of central tendency will change?
A. mean and median
B. median and mode
C. mode only
D. mean and mode
Q. 108 for 10 observations on price(x) and supply(y) the following data was obtaines:
Σx=130,Σy=220,Σx² = 2288, Σy² = 5506
what is the line of regression of y on x?
A. y=0.91x + 8.74
B. y=1.02x + 8.74
C. y=1.02x – 7.02
D. y=0.91x – 7.02
Q. 109 from the data choose the correct option:
A. a
B. b
C. c
D. d
Q. 110 consider the following statements in respect of class intervals of grouped frequency distribution:
1. class intervals need not be mutually exclusive
2. class intervals should be exhaustive
3. class intervals need not be of equal width
choose correct statements
A. 1 and 2 only
B. 2 and 3only
C. 1 and 3 only
D. 1,2 and 3
Q. 111 A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 parents, what is the probability that at least one patient is cured by this medicine?
A. 1/1024
B. 243/1024
C. 1023/1024
D. 781/1024
Q. 112 choose the correct one according to the given data
A. 3/7
B. 3/4
C. 1/3
D. 4/7
Q. 113 A machine has three parts A,B and C, whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. what is the probability that the machine will not stop working?
A. 0.06
B. 0.16
C. 0.84
D. 0.94
Q. 114 Three independent events A₁, A₂, A₃ occur with probabilities P(Aᵢ) = 1/1+ i , i = 1, 2, 3. What is the probability that at least one of three events occurs.
A. 1/4
B. 2/3
C. 3/4
D. 1/24
Q. 115 Two varieties x and y are uncorrelated and have standard deviation σₓ and σᵧ respectively. What is the correlation coefficient between x+y and x – y?
A. a
B. b
C. c
D. d
Q. 116 what is the mean age of this group of people?
A. 41.0
B. 41.5
C. 42.0
D. 42.5
Q. 117 if the covariance between x and y is 30 variance of x is 25 and variance of y is 144 then what is the correlation coefficient?
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Q. 118 A coin is tossed three times. consider the following events:
A: no head appears
B: exactly one head appears
C: at least two heads appear
which one of the following is correct?
A. (A U B) ∩ (A U C) = B U C
B. (A ∩ B’) U (A ∩ C’) =B’ U C’
C. A ∩ (B’ U C’) = A U B U C
D. A ∩ (B’ U C’) = B’ ∩ C’
Q. 119 In a series of 3 one day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. if a win, loss or draw gives 2, 0 and 1 point respectively , then what is the probability that team A will score 5 points in the series?
A. 17/18
B. 11/12
C. 1/12
D. 1/18
Q. 120 let the random variable X follow B(6,p). If 16 P(X =4) = P(X=2), then what is the value of p?
A. 1/3
B. 1/4
C. 1/5
D. 1/6
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | A | A | C | D | D | D | D | C | A | D |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | C | D | C | D | A | B | B | C | A | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | C | B | A | A | C | D | A | A | B | B |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | D | A | B | C | B | C | C | D | C | B |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | C | A | A | D | A | D | B | A | B | B |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | C | A | D | A | C | D | B | A | D | A |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| Answer | D | C | C | A | A | D | B | C | B | C |
| Question | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| Answer | A | B | A | C | B | C | A | A | D | A |
| Question | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
| Answer | C | D | D | B | B | B | C | D | D | D |
| Question | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
| Answer | A | C | A | B | A | A | C | B | B | D |
| Question | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 |
| Answer | D | D | B | A | A | B | D | B | D | D |
| Question | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 |
| Answer | C | A | C | C | C | B | B | D | B | C |