NDA/NA(I) Exam 2014 Mathematics
Q. 1 Let x be the set of all citizens of India . Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct?
A. The relation is an equivalence relation on x
B. The relation is symmetric but neither reflexive nor transitive
C. The relation is reflexive but neither symmetric nor transitive
D. None of above
Q. 2 Consider the following relation from A to B where A = {u, v, w, x, y, z} and B = {p, q, r, s}
1. {(u,p), (v,p) (w,p) (x,q), (y,q), (z,q)}
2. {(u,p), (v,q), (w,r), (z,s)}
3. {(u,s), (v,r), (w,q), (u,p), (v,q), (z,q)}
4. {(u,q), (v,p), (w,s), (x,r), (y,q), (z,s)}
Which of the above relation are not function?
A. 1 and 2
B. 1 and 4
C. 2 and 3
D. 3 and 4
Q. 3 If α and β are the roots of the equation ax² + bx + c = 0, where a ≠ 0, then (aα + b)(aβ + b) is equal to :
A. ab
B. bc
C. ca
D. abc
Q. 4 Let S denote set of all integers. Define a relation R on S as ‘aRb if ab ≥ where a, b ∈ S’. Then R is:
A. Reflexive but neither symmetric nor transitive relation
B. Reflexive, symmetric but not transitive relation
C. An equivalence relation
D. Symmetric but reflexive nor transitive relation
Q. 5 The roots of the equation 2a²x² – 2abx + b² = 0 when a < 0 and b > 0 are:
A. Sometimes complex
B. Always irrational
C. Always complex
D. Always real
Q. 6 What is the sum of the two numbers (11110)₂ and (1010)₂?
A. (101000)₂
B. (110000)₂
C. (100100)₂
D. (101100)₂
Q. 7 Let N denote the set of all non-negative integers and Z denote the set of all integers. The function f : Z → N given by f(x) = |x| is:
A. One – one but not onto
B. Onto but not one – one
C. Both one – one and onto
D. Neither one – one nor onto
Q. 8 If P and Q are two complex numbers, then the modulus of the quotient of P and Q is:
A. Greater than the quotient of their moduli
B. Less than the quotient of their moduli
C. Less than or equal to the quotient of their moduli
D. Equal to the quotient of their moduli
Q. 9 Let z = x + iy where x, y are real variables and i = √- 1. If |2z – 1| = |z – 2|, then the point z describes:
A. A circle
B. An ellipse
C. A hyperbola
D. A parabola
Q. 10 The sum of an infinite GP is x and the common ratio r is such that |r| < 1. If the first term of the GP is 2, then which one of the following is correct?
A. -1 < x < 1
B. -∞ < x < 1
C. 1 < x < ∞
D. None of the above
Q. 11 A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?
A. 2/5
B. 1/5
C. 1/10
D. None of the above
Q. 12 For two variables x and y, the two regression coefficients are bᵧₓ = -3/2 and bₓᵧ = -1/6. The correlation coefficient between x and y is:
A. -1/4
B. 1/4
C. -1/2
D. 1/2
Q. 13 The variance of numbers x₁, x₂, x₃……..xᵤ is V. Consider the following statements :
1. If every x₁ is increased by 2, the variance of the new set of numbers is V.
2. If the number x₁ is squared, the variance of the new set is V².
Which of the following statements is/are correct ?
A. 1 only
B. 2 only
C. both 1 and 2
D. Neither 1 and 2
Q. 14 What is the mean of the squares of the first 20 natural numbers?
A. 151.5
B. 143.5
C. 65
D. 72
Q. 15 p, q , r, s, t are five numbers such that the average of p, q and r is 5 and that of s and t is 10. What is the average of all five numbers?
A. 7.75
B. 7.5
C. 7
D. 5
Q. 16 The cumulative frequency of the largest observed value must always be:
A. Less than the total number of observations
B. Greater than the total number of observation
C. Equal to total number of observations
D. Equal to mid point of the last class interval
Q. 17 It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternatively, is:
A. 5/12
B. 5/36
C. 19/27
D. 5/27
Q. 18 Out of the 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is:
A. 25200
B. 22500
C. 10080
D. 5040
Q. 19 Let X denote the number of scores which exceed 4 in 18 tosses of a symmetrical die. Consider the following statements:
1. The arithmetic mean of X is 6.
2. The standard deviation of X is 2.
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. 20 How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to be start with A?
A. 6
B. 12
C. 24
D. None of the above
Q. 21 The sum of the series formed by the sequence 3, √3, ….. upto infinity is:
A. 3√3(√3 + 1)/2
B. 3√3(√3 – 1)/2
C. 3(√3 + 1)/2
D. 3(√3 – 1)/2
Q. 22 If |z + z̅| = |z – z̅|, then the locus of z is:
A. A part of straight lines
B. A lines
C. A set of four straight lines
D. A circles
Q. 23 The number 251 in decimal system is expressed in binary system by:
A. 11110111
B. 11111011
C. 11111101
D. 11111110
Q. 24 What is the argument of the complex number (1 + i)(2 + i)/(3 – i) where i = √-1?
A. 0
B. π/4
C. -π/4
D. π/2
Q. 25 Consider the following statements in respect of the matrix A given in figure
1. The matrix A is skew-symmetric.
2. The matrix A is symmetric.
3. The matrix A is invertible.
Which of the above statements is/are correct?
A. 1 only
B. 3 only
C. 1 and 3
D. 2 and 3
Q. 26 Consider two matrices A and B given in the figure. Which one of the following is correct?
A. B is the right inverse of A
B. B is the left inverse of A
C. B is the both sided inverse of A
D. None of the above
Q. 27 One of the roots of the matrix shown in figure
A. abc
B. a + b + c
C. -(a + b + c)
D. -abc
Q. 28 If A is any matrix , then the product AA is defined only when AA is defined only when A is a matrix of order m x n where:
A. m > n
B. m < n
C. m = n
D. m ≤ n
Q. 29 The determinant of an odd order skew symmetric matrix is always:
A. Zero
B. One
C. Negative
D. Depends on the matrix.
Q. 30 If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant:
A. Becomes zero
B. Remains the same
C. Changed its sign
D. Is doubled
Questions: 31 – 33
In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.
Q. 31 The number of students who had taken only Physics is:
A. 2
B. 3
C. 5
D. 6
Q. 32 The number of students who had taken only two subjects is:
A. 7
B. 8
C. 9
D. 10
Q. 33 Consider the following statements:
1. The number of students who had taken only one subject is equal to the number of students who had taken only two subjects.
2. The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects.
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: 34 – 36
In the expansion of (x³ – 1/x²)ⁿ where n is a positive integer, the sum of the coefficients of x⁵ and x¹⁰ is 0.
Q. 34 What is n equal to?
A. 5
B. 10
C. 15
D. None of the above
Q. 35 What is the value of the independent term?
A. 5005
B. 7200
C. -5005
D. -7200
Q. 36 What is the sum of the coefficients of the two middle terms?
A. 0
B. 1
C. -1
D. None of the above
Questions: 37 – 39
Given that C(n, r) : C(n, r + 1) = 1 : 2 and C(n, r + 1) : C(n, r + 2) = 2 : 3.
Q. 37 What is n equal to?
A. 11
B. 12
C. 13
D. 14
Q. 38 What is r equal to?
A. 2
B. 3
C. 4
D. 5
Q. 39 What is P(n, r) : C(n, r) equal to?
A. 6
B. 24
C. 120
D. 720
Q. 40 The complete solution of 3 tan²x = 1 is given by :
n ⋳ Z
A. x = nπ ± π/3
B. x = nπ ± π/3 only
C. x = nπ ± π/6
D. x = nπ ± π/3 only
Q. 41 What is the value of cos 36°?
A. (√5 – 1)/4
B. (√5 + 1)/4
C. √(10 + 2√5)/4
D. √(10 – 2√5)/4
Q. 42 Consider the following statements:
1. Value of sin θ oscillates between -1 and 1.
2. Value of cos θ oscillates between 0 and 1.
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. 43 If x and y are positive and xy > 1, then what is tan⁻¹ x + tan⁻¹ y equal to?
A. tan⁻¹ (x + y)/(1 – xy)
B. π + tan⁻¹ (x + y)/(1 – xy)
C. π – tan⁻¹ (x + y)/(1 – xy)
D. tan⁻¹ (x – y)/(1 + xy)
Q. 44 Consider the following statements:
1. n(sin² 67(1/2)° – sin²22(1/2)°) > 1 for all positive integers n ≥2.
2. If x is any positive real number, then nx > 1 for all positive integers n ≥ 2.
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. 45 Consider the following statements:
1. If 3θ is an acute angle such that sin 3θ = cos 2θ, then the measurement of θ in radian equals to π/10.
2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle.
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. 46 From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30° and 45°. The height of the aeroplane above the ground is:
A. 10√3 m
B. 10(√3 – 1) m
C. 10(√3 + 1) m
D. 20 m
Q. 47 Consider the following statements:
1. There exists no triangle ABC for which sin A + sin B = sin C.
2. If the angles of a triangle are in the ratio 1 : 2 : 3, then its sides will be in the ratio 1 : √3 : 2. 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. 48 Consider the following statements:
1. sin |x| + cos |x| is always positive.
2. sin(x²) + cos(x²) is always positive.
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. 49 What is (1 + sin A)/(1 – sin A) – (1 – sin A)/(1 + sin A) equal to?
A. sec A – tan A
B. 2 sec A . tan A
C. 4 sec A . tan A
D. 4 cosec A . cot A
Q. 50 What is (cot 224° – cot 134°)/(cot 226° + cot 316°) equal to?
A. -cosec 88°
B. -cosec 2°
C. -cosec 44°
D. -cosec 46°
Q. 51 Consider the following statements:
1. tan⁻¹ 1 + tan⁻¹ (0.5) = π/2
2. sin⁻¹ (1/3) + cos⁻¹ (1/3) = π/2
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. 52 If A + B + C = π, then what is cos(A + B) + cos C equal to?
A. 0
B. 2 cos C
C. cos C – sin C
D. 2 sin C
Q. 53 What is cos 20° + cos 100° + cos 140° equal to?
A. 2
B. 1
C. 1/2
D. 0
Q. 54 What is sin⁻¹ sin 3π/5 equal to?
A. 3π/5
B. 2π/5
C. π/5
D. None of the above
Q. 55 What is sin²(3π) + cos²(4π) + tan²(5π) equal to?
A. 0
B. 1
C. 2
D. 3
Q. 56 Consider the following points:
1. (0, 5)
2. (2, -1)
3. (3, -4)
Which of the above lie on the line 3x + y = 5 and at a distance √10 from (1, 2)?
A. 1 only
B. 2 only
C. 1 and 2 only
D. 1, 2 and 3
Q. 57 What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point?
A. 2x – y = 4
B. 2x – y + 4 = 0
C. 2x + y = 4
D. 2x + y + 4 = 0
Q. 58 What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes?
A. x + y = 7
B. 3x + 4y = 7
C. x – y = 1
D. None of the above
Q. 59 What is the equation of the line midway between the lines 3x – 4y + 12 = 0 and 3x – 4y = 6
A. 3x – 4y – 9 = 0
B. 3x – 4y + 9 = 0
C. 3x – 4y – 3 = 0
D. 3x – 4y + 3 = 0
Q. 60 What is the sum of the major and minor axes of the ellipse whose eccentricity is 4/5 and length of latus rectum is 14.4 unit?
A. 32 unit
B. 48 unit
C. 64 unit
D. None of the above
Questions: 61 – 63
A straight line passes through (1, -2, 3) and perpendicular to the plane 2x + 3y – z = 7.
Q. 61 What are the direction ratios of normal to plane?
A. ⟨2, 3, -1⟩
B. ⟨2, 3, 1⟩
C. ⟨-1, 2, 3⟩
D. None of the above
Q. 62 Where does the line meet the plane?
A. (2, 3, -1)
B. (1, 2, 3)
C. (2, 1, 3)
D. (3, 1, 2)
Q. 63 What is the image of the point (1, -2, 3) in the plane?
A. (2, -1, 5)
B. (-1, 2, -3)
C. (5, 4, 1)
D. None of the above
Questions: 64 – 65
Consider the spheres x² + y² + z² – 4y + 3 = 0 and x² + y² + z² + 2x + 4z – 4 = 0
Q. 64 What is the distance between the centres of the two spheres?
A. 5 units
B. 4 units
C. 3 units
D. 2 units
Q. 65 Consider the following statements:
1. The two spheres intersect each other.
2. The radius of first sphere is less than that of second sphere.
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: 66 – 68
The vertices of a triangle ABC are A(2, 3, 1), B(-2, 2, 0) and C(0, 1, -1)
Q. 66 What is the cosine of angle ABC?
A. 1/√3
B. 1/√2
C. 2/√6
D. None of the above
Q. 67 What is the area of the triangle?
A. 6√2 square unit
B. 3√2 square unit
C. 10√3 square unit
D. None of the above
Q. 68 What is the magnitude of the line joining mid points of the sides AC and BC?
A. 1/√2 unit
B. 1 unit
C. 3/√2 unit
D. 2 unit
Q. 69 Consider the vectors a̅ = î – 2ĵ + k̂ and b̅ = 4î – 4ĵ + 7k̂.
What is the scaler projection of a̅ on b̅?
A. 1
B. 19/9
C. 17/9
D. 23/9
Q. 70 Consider the vectors a̅ = î – 2ĵ + k̂ and b̅ = 4î – 4ĵ + 7k̂.
What is the vector perpendicular to both the vectors?
A. -10î – 3ĵ + 4k̂
B. -10î + 3ĵ + 4k̂
C. 10î – 3ĵ + 4k̂
D. None of the above
Q. 71 Let a vector r makes angles 60°, 30° with x and y-axes respectively.
What angle does r vector make with z – axis?
A. 30°
B. 60°
C. 90°
D. 120°
Q. 72 Let a vector r makes angles 60°, 30° with x and y-axes respectively.
What are the direction cosines of r vector ?
A. ⟨1/2, √3/2, 0⟩
B. ⟨1/2, -√3/2, 0⟩
C. ⟨1/√2, 1/√2, 0⟩
D. ⟨-1/2, √3/2, 0⟩
Q. 73 Let |a̅ | = 7, |b̅| = 11, |a̅ + b̅| = 10√3, where ̅ denotes to vector
What is |a̅ – b̅| equal to?
A. 2√2
B. 2√10
C. 5
D. 10
Q. 74 Let |a̅ | = 7, |b̅| = 11, |a̅ + b̅| = 10√3, where ̅ denotes to vector
What is the angle between (a̅ + b̅) and (a̅ – b̅) ?
A. π/2
B. π/3
C. π/6
D. None of the above
Q. 75 A line passes through the points (6, -7, -1) and (2, -3, 1). What are the direction ratios of the line?
A. ⟨4, -4, 2⟩
B. ⟨4, 4, 2⟩
C. ⟨-4, 4, 2⟩
D. ⟨2, 1, 1⟩
Q. 76 What is lim(x → 0) {(1 +x)ⁿ – 1}/x equal to?
A. 0
B. 1
C. n
D. n – 1
Q. 77 What is lim(x → 0) x/√(1 – cos x) equal to?
A. √2
B. -√2
C. -1/√2
D. Limit does not exist
Q. 78 What is the derivative of √(1 + cos x)/(1 – cos x)?
A. 1/2 sec² x/2
B. -1/2 cosec² x/2
C. -cosec² x/2
D. None of the above
Q. 79 What is the value of the equation given in figure ?
A. eπ/⁴ – 1
B. eπ/⁴ + 1
C. e – 1
D. e
Q. 80 What is the slope of the tangent to the curve y = sin⁻¹(sin²ˣ) at x = 0?
A. 0
B. 1
C. 2
D. None of the above
Q. 81 The solution of dy/dx = |x| is, where c is an arbitrary constant.
A. y = x|x|/2 + c
B. y = |x|/2 + c
C. y = x²/2 + c
D. y = x³/2 + c
Q. 82 What is the solution of dy/dx + 2y = 1 satisfying y(0) = 0?
A. y = (1 – e⁻²ˣ)/2
B. y = (1 + e⁻²ˣ)/2
C. y = 1 + eˣ
D. y = (1 + eˣ)/2
Q. 83 Consider the curve y = e²ˣ
What is the slope of the tangent to the curve at (0, 1)?
A. 0
B. 1
C. 2
D. 4
Q. 84 Consider the curve y = e²ˣ
Where does the tangent to the curve at (0, 1) meet the x – axis?
A. (1, 0)
B. (2, 0)
C. (-1/2, 0)
D. (1/2, 0)
Q. 85 Consider an ellipse x²/a² + y²/b² = 1.
What is the area of the greatest rectangle that can be inscribed in the ellipse?
A. ab
B. 2 ab
C. ab/2
D. √ab
Q. 86 Consider an ellipse x²/a² + y²/b² = 1.
What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?
A. ab(π – 1)
B. 2ab(π – 1)
C. ab(π – 1)
D. None of the above
Questions: 87 – 88
Consider the integrals as shown in figure
Q. 87 What is I₁ – I₂ equal to ?
A. 0
B. 2I₁
C. π
D. None of the above
Q. 88 what is I₁ equal to ?
A. π/24
B. π/18
C. π/12
D. π/6
Questions: 89 – 90
Consider the function f(x) = (1 – sin x)/(π – 2x)² where x ≠ π/2 and f(π/2) = λ
Q. 89 What is lim(x → π/2) equals to?
A. 1
B. 1/2
C. 1/4
D. 1/8
Q. 90 What is the value of if the function is continuous at x = π/2?
A. 1/8
B. 1/4
C. 1/2
D. 1
Q. 91 If f(9) = 9 and f′(9) = 4 then what is the value of the expression shown in figure
A. 36
B. 9
C. 4
D. None of the above
Q. 92 What is ∫(π/2 → -π/2) x sin x dx equal to?
A. 0
B. 2
C. -2
D. π
Q. 93 What is the general solution of the differential equation x dy – y dx = y² ?
(where c is an arbitrary constant)
A. x = cy
B. y² = cx
C. x + xy – cy = 0
D. None of the above
Q. 94 Consider the following statements :
1. The function f(x) = ∛x is continuous at all x except at x = 0
2. The function f(x) = [x] is continuous at x=2.99 where [.] is the bracket function
Which of the above statement is are correct ?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2
Q. 95 Consider the following statements :
1. The function f(i) = |i| is not differentiable at i = 0
2. the function f(i) = eⁱ is differentiable at i = 0
Which of the above statement is are correct ?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2
Q. 96 If z= f o f(x) where f(x) = x², then what is dz/dx equal to?
A. x³
B. 2x³
C. 4x³
D. 4x²
Q. 97 Consider the function f(x) = (x² – x + 1)/(x² + x + 1)
What is the maximum value of the function?
A. 1/2
B. 1/3
C. 2
D. 3
Q. 98 Consider the function f(x) = (x² – x + 1)/(x² + x + 1)
What is the minimum value of the function?
A. 1/2
B. 1/3
C. 2
D. 3
Questions: 99 – 101
Let f(x) be a function defined in 1 ≤ x < ∞ by f(x) given in figure (1).
Q. 99 Consider the following statements:
1. The function is continuous at every point in the interval [1, ∞).
2. The function is differentiable at x = 1.5.
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. 100 What is the differentiable coefficient of f(x) at x = 3?
A. 1
B. 2
C. -1
D. -3
Q. 101 Consider the following statements:
1. f(2 + 0) does not exist.
2. f(2 – 0) does not exist.
Which of the above statements is/are correct?
A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor
Q. 102 What is ∫(π/2 → 0) ln (tan x) dx equal to?
A. ln 2
B. -ln 2
C. 0
D. None of the above
Questions: 103 – 105
The general solution pf the differential equation (x² + x + 1)dy + (y² + y + 1)dx = 0 is (x + y + 1) = A(1 + Bx + Cy + Dxy) where B, C and D are constants and A is parameter.
Q. 103 What is B equal to?
A. -1
B. 1
C. 2
D. None of the above
Q. 104 What is C equal to?
A. 1
B. -1
C. 2
D. None of the above
Q. 105 What is D equal to?
A. -1
B. 1
C. -2
D. None of the above
Q. 106 Consider the following statements:
1. The functional f(x) = sin x decreases on the interval (0, π/2).
2. The function f(x) = cos x increases on the interval (0, π/2)
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 What is the number of arbitrary constants in the particular solution of differential equation of third order?
A. 0
B. 1
C. 2
D. 3
Q. 108 What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx?
A. y = cos x
B. y = sin x
C. y = sec x
D. y = cosec x
Q. 109 Consider the following statements in respect of the differential equation d²y/dx² + cos(dy/dx) = 0:
1. The degree of the differential equation is not defined.
2. The order of the differential equation is 2.
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 equation of parabola whose vertex is at (0, 0) and focus is at (0, -2)?
A. y² + 8x = 0
B. y2 – 8x = 0
C. x² + 8y = 0
D. x² – 8y = 0
Questions: 111 – 114
Number X is randomly selected from the set of odd numbers and Y is randomly
selected from the set of even numbers of the set {1, 2, 3, 4, 5, 6, 7}. Let Z = (X + Y).
Q. 111 What is P(Z = 5) equal to ?
A. 1/2
B. 1/3
C. 1/4
D. 1/6
Q. 112 What is P(Z = 10) equal to?
A. 0
B. 1/2
C. 1/3
D. 1/5
Q. 113 What is P(Z > 11) equal to ?
A. 0
B. 1/4
C. 1/6
D. 1/12
Q. 114 What is P(Z is the product of two prime numbers) equal to ?
A. 0
B. 1/2
C. 1/4
D. None of the above
Questions: 115 – 117
The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the frequency distribution given in figure
Q. 115 What is the mean of the distribution?
A. 3.76
B. 3.84
C. 3.96
D. 4.05
Q. 116 What is the median of the distribution?
A. 3.5
B. 4
C. 4.5
D. 5
Q. 117 What is the mode of the distribution?
A. 3
B. 4
C. 5
D. 6
Questions: 118 – 120
The mean and standard deviation of all 100 items are 50, 5 and that of 150 items are 40, 6 respectively.
Q. 118 What is the combined mean of the 250 items?
A. 43
B. 44
C. 45
D. 46
Q. 119 What is the combined standard deviation of all 250 items?
A. 7.1
B. 7.3
C. 7.5
D. 7.7
Q. 120 What is the variance of all the 250 items?
A. 50.6
B. 53.3
C. 55.6
D. 59.3
| Answer Sheet |
||||||||||
| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | B | C | C | B | C | A | B | D | A | C |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | C | C | A | B | C | C | B | A | C | C |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | A | A | B | D | A | B | C | C | A | C |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | A | C | B | C | C | A | D | C | B | C |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | B | B | B | A | A | C | C | D | C | B |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | B | A | D | B | B | C | C | A | D | C |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| Answer | A | D | C | C | C | A | B | C | B | A |
| Question | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| Answer | C | A | B | D | C | C | D | B | A | A |
| Question | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
| Answer | A | A | C | C | B | C | A | C | D | A |
| Question | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
| Answer | C | B | ABCD | B | B | C | D | B | B | D |
| Question | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 |
| Answer | A | C | A | B | C | D | D | C | C | C |
| Question | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 |
| Answer | D | A | D | C | A | B | B | B | C | C |