128 + Interview Questions in NDA IN GENERAL AWARENESS Page 2 InterviewSolution

51.	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 × 8! × 8! B. (8!)3 C. 24 × 8! × 8! D. 16!
Answer» Correct option C. 24 × 8! × 8! Explanation: Four people can be arranged on 8 chairs in ⁸P₄ ways, similarly two people can be arranged on 8 chairs on other side in ⁸P₂ ways. Remaining 10 can be arranged in 10! Ways. Therefore no. of ways people can be seated = (8! × 8! × 10!)/(4! × 6!) = 210 × 8! × 8!

51.

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 × 8! × 8! B. (8!)3 C. 24 × 8! × 8! D. 16!

Answer»

Correct option C. 24 × 8! × 8!

Explanation:

Four people can be arranged on 8 chairs in ⁸P₄ ways, similarly two people can be arranged on 8 chairs on other side in ⁸P₂ ways. Remaining 10 can be arranged in 10! Ways.

Therefore no. of ways people can be seated

= (8! × 8! × 10!)/(4! × 6!)

= 210 × 8! × 8!

Discussion

52.	Three sides of a trapezium be the angle between a pair of adjacent sides.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
Answer» Correct option d. 12 cm Explanation: Fourth side = 6 + 6 = 12

52.

Three sides of a trapezium be the angle between a pair of adjacent sides.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

Answer»

Correct option d. 12 cm

Explanation:

Fourth side = 6 + 6 = 12

Discussion

53.	Three sides of a trapezium be the angle between a pair of adjacent sides.What is the maximum area of the trapezium? a. 36√3 cm2 b. 30√3 cm2 c. 27√3 cm2d. 24√3 cm2
Answer» Correct option c. 27√3 cm² Explanation: Maximum area = 9 x 3√3 = 27√3

53.

Three sides of a trapezium be the angle between a pair of adjacent sides.What is the maximum area of the trapezium? a. 36√3 cm2 b. 30√3 cm2 c. 27√3 cm2d. 24√3 cm2

Answer»

Correct option c. 27√3 cm²

Explanation:

Maximum area = 9 x 3√3 = 27√3

Discussion

54.	Consider the following statements: Statement I : x > sinx for all x > 0 Statement II: f(x) = x −sinx is an increasing function for all x > 0 Which one of the following is correct in respect of the above 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 and 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
Answer» Correct option A. Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I Explanation: Both statements are correct but 2 is not the correct explanation of 1.

54.

Consider the following statements: Statement I : x > sinx for all x > 0 Statement II: f(x) = x −sinx is an increasing function for all x > 0 Which one of the following is correct in respect of the above 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 and 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

Answer»

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

Explanation:

Both statements are correct but 2 is not the correct explanation of 1.

Discussion

55.	Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0
Answer» Correct option b. g(x) > 0 Explanation: Let f(x) = ax² + bx + c, a > 0, b² < 4ac (∵ f(x) > 0) Now, g(x) = ax² + bx + c + 2ax + b + 2a = ax²+ (b + 2a)x + 2a + b + c Now, (b + 2a)² - 4a(2a + b + c) = b² + 4ab + 4a² - 8a² - 4ab - 4ac = b² - 4ac - 8a² < 0 ⇒ g(x) > 0

55.

Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0

Answer»

Correct option b. g(x) > 0

Explanation:

Let f(x) = ax² + bx + c, a > 0, b² < 4ac

(∵ f(x) > 0)

Now, g(x) = ax² + bx + c + 2ax + b + 2a

= ax²+ (b + 2a)x + 2a + b + c

Now, (b + 2a)² - 4a(2a + b + c)

= b² + 4ab + 4a² - 8a² - 4ab - 4ac

= b² - 4ac - 8a² < 0 ⇒ g(x) > 0

Discussion

56.	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)
Answer» Correct option a. [0, 1) Explanation: y = f(x) = x²/(1 + x²) Cleary y ≥ 0, Again x² < 1 + x² So Range is [0, 1)

56.

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)

Answer»

Correct option a. [0, 1)

Explanation:

y = f(x) = x²/(1 + x²)

Cleary y ≥ 0, Again x² < 1 + x²

So Range is [0, 1)

Discussion

57.	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]
Answer» Correct option d. [–4, 6] Explanation: ∵ f(x) = 4 sec x – 3 cosx + 1 Minimum f = - √(4² + (-3)² + 1 = - 4 Maximum f = √(4² + (-3)² + 1 = 6 S = Range of f = [Minimum f, maximum f] = [–4, 6]

57.

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]

Answer»

Correct option d. [–4, 6]

Explanation:

∵ f(x) = 4 sec x – 3 cosx + 1

Minimum f = - √(4² + (-3)² + 1 = - 4

Maximum f = √(4² + (-3)² + 1 = 6

S = Range of f

= [Minimum f, maximum f] = [–4, 6]

Discussion

58.	In which one of the following intervals is the function f(x) = x2 – 5x + 6 decreasing? a. (- ∞, 2] b. [3, ∞] c. (- ∞, ∞) d. (2, 3)
Answer» Correct option a. (- ∞, 2] Explanation: f(x) = x² - 5x + 6 ⇒ f'(x) = 2x - 5 ⇒ f'(x) < 0 ⇒ 2x - 5 < 0 ⇒ x < 5/2

58.

In which one of the following intervals is the function f(x) = x2 – 5x + 6 decreasing? a. (- ∞, 2] b. [3, ∞] c. (- ∞, ∞) d. (2, 3)

Answer»

Correct option a. (- ∞, 2]

Explanation:

f(x) = x² - 5x + 6

⇒ f'(x) = 2x - 5

⇒ f'(x) < 0

⇒ 2x - 5 < 0

⇒ x < 5/2

Discussion

59.	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. z, 2, z d. x, 1, z
Answer» Correct option a. x, 6, z Explanation: x + z = 3, xz = 9 2xz/(x + z) = 18/3 = 6 ⇒ x, 6, z ∈ H.P

59.

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. z, 2, z d. x, 1, z

Answer»

Correct option a. x, 6, z

Explanation:

x + z = 3, xz = 9

2xz/(x + z) = 18/3 = 6 ⇒ x, 6, z ∈ H.P

Discussion

60.	The differential equation of the family of curves y = p cos (ax) + q sin (ax), where p, q are arbitrary constants, isa. d2y/dx2 - a2y = 0b. d2y/dx2 - ay = 0c. d2y/dx2 + ay = 0d. d2y/dx2 + a2y = 0
Answer» Correct option d. d²y/dx² + a²y = 0 Explanation: y = p cos ax + q sin ax ⇒ dy/dx = – p a sin ax + qa cos ax ⇒ d²y/dx² = – p a² cos ax – qa² sin ax = –a²y ⇒ d²y/dx² + a²y = 0

60.

The differential equation of the family of curves y = p cos (ax) + q sin (ax), where p, q are arbitrary constants, isa. d2y/dx2 - a2y = 0b. d2y/dx2 - ay = 0c. d2y/dx2 + ay = 0d. d2y/dx2 + a2y = 0

Answer»

Correct option d. d²y/dx² + a²y = 0

Explanation:

y = p cos ax + q sin ax

⇒ dy/dx = – p a sin ax + qa cos ax

⇒ d²y/dx² = – p a² cos ax – qa² sin ax = –a²y

⇒ d²y/dx² + a²y = 0

Discussion

61.	If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more isa. 1/6b. 4/11c. 3/11d. 2/11
Answer» Correct option c. 3/11 Explanation: n(S) = 36 A = {(1,5,) , (2,5), (3,5) (4,5) (5,5), (6,5), (5,1), (5,2), (5,3), (5,4), (5,6)} B = {(5,5), (6,4), (4,6) , (6,5), (5,6), (6,6)} A ∩ B = {5,6,), (6,5), (5,6)} P(B/A) = 3/11

61.

If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more isa. 1/6b. 4/11c. 3/11d. 2/11

Answer»

Correct option c. 3/11

Explanation:

n(S) = 36

A = {(1,5,) , (2,5), (3,5) (4,5) (5,5), (6,5), (5,1), (5,2), (5,3), (5,4), (5,6)}

B = {(5,5), (6,4), (4,6) , (6,5), (5,6), (6,6)}

A ∩ B = {5,6,), (6,5), (5,6)}

P(B/A) = 3/11

Discussion

62.	A survey was conducted among 300 students. If 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.How many students like to play exactly only one game? a. 196 b. 228 c. 254 d. 268
Answer» Correct option c. 254 Explanation: Exactly One = \|A\| + \|B\| + \|C\| - 2[\|A ∩ B\| + \|B ∩ C\| + \|A ∩ C\|] + 3\|A ∩ B ∩ C\| = 125 + 145 + 90 – 2[32 + 3 × 14] + 3 × 14 = 360 – 106 = 254

62.

A survey was conducted among 300 students. If 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.How many students like to play exactly only one game? a. 196 b. 228 c. 254 d. 268

Answer»

Correct option c. 254

Explanation:

Exactly One = |A| + |B| + |C| - 2[|A ∩ B| + |B ∩ C| + |A ∩ C|] + 3|A ∩ B ∩ C|

= 125 + 145 + 90 – 2[32 + 3 × 14] + 3 × 14

= 360 – 106 = 254

Discussion

63.	The smallest positive integer n for which (1 + i/1− i)n = 1, is A. 1 B. 4 C. 8 D. 16
Answer» Correct option B. 4 Explanation: ((1 + i)/(1 - i))ⁿ = ((1 + i)/(1 - i) x (1 - i)/(1 - i))ⁿ = (i)ⁿ = > n = 4

63.

The smallest positive integer n for which (1 + i/1− i)n = 1, is A. 1 B. 4 C. 8 D. 16

Answer»

Correct option B. 4

Explanation:

((1 + i)/(1 - i))ⁿ = ((1 + i)/(1 - i) x (1 - i)/(1 - i))ⁿ = (i)ⁿ = > n = 4

Discussion

64.	Let the sample space consist of non negative integers up to 50, x denote the numbers which are multiples of 3 and y denote the 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
Answer» Correct option D. Neither 1 nor 2 Explanation: X = 3,6,9…….48} = 16 Y = 1,3,5,…...49} = 25 Total integers = 51 (0 is also included) ∴ P(X) = 16/51, P(Y) = 25/51

64.

Let the sample space consist of non negative integers up to 50, x denote the numbers which are multiples of 3 and y denote the 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

Answer»

Correct option D. Neither 1 nor 2

Explanation:

X = 3,6,9…….48} = 16

Y = 1,3,5,…...49} = 25

Total integers = 51 (0 is also included)

∴ P(X) = 16/51, P(Y) = 25/51

Discussion

65.	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
Answer» Correct option B. 34 minutes Explanation: Total notes counted in first 10 minutes = 150 × 10 = 1500 Remaining notes = 3000 Further counting of notes form an A. P series with a = 150 , d = -2 S_n = 3000 = n/2[2a + (n - 1)d] ⇒ n = 34

65.

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

Answer»

Correct option B. 34 minutes

Explanation:

Total notes counted in first 10 minutes

= 150 × 10 = 1500

Remaining notes = 3000

Further counting of notes form an A. P

series with a = 150 , d = -2

S_n = 3000 = n/2[2a + (n - 1)d]

⇒ n = 34

Discussion

66.	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
Answer» Correct option B. 2 Explanation: For any open cylinder of surface area, when it has maximum volume, the height and radius of the base are equal. Therefore diameter of cylinder = Twice of its height So k will be equal to 2

66.

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

Answer»

Correct option B. 2

Explanation:

For any open cylinder of surface area, when it has maximum volume, the height and radius of the base are equal.

Therefore diameter of cylinder = Twice of its height So k will be equal to 2

Discussion

67.	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
Answer» Correct option B. differentiable at x = 0 Explanation: f(x) is continuous and differentiable also [As L.H.L = R.H.L = f(0) = 0 and L.H.D = R.H.D]

67.

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

Answer»

Correct option B. differentiable at x = 0

Explanation:

f(x) is continuous and differentiable also

[As L.H.L = R.H.L = f(0) = 0 and L.H.D = R.H.D]

Discussion

68.	The set of all points, where the function f(x) = √1− e − x2 is differentiable, is A. (0, ∞)B. (-∞, ∞)C. (-∞, ∞) ∪(0, ∞) D. (-1, ∞)
Answer» Correct option B. (-∞, ∞) Explanation: f'(x) = (xe^-x2)/(1 - e^-x2) which is defined for all x∈ R

68.

The set of all points, where the function f(x) = √1− e − x2 is differentiable, is A. (0, ∞)B. (-∞, ∞)C. (-∞, ∞) ∪(0, ∞) D. (-1, ∞)

Answer»

Correct option B. (-∞, ∞)

Explanation:

f'(x) = (xe^-x2)/(1 - e^-x2)

which is defined for all x∈ R

Discussion

69.	What is sin105° + cos105° equal to ? a. sin 50° b. cos 50° c. 1/√2 d. 0
Answer» Correct option c. 1/√2 Explanation: sin (90° + 15°) + cos105° = cos15° + cos105° = 2cos 60°.cos 45° = 2 x 1/2 x 1/√2 = 1/√2

69.

What is sin105° + cos105° equal to ? a. sin 50° b. cos 50° c. 1/√2 d. 0

Answer»

Correct option c. 1/√2

Explanation:

sin (90° + 15°) + cos105° = cos15° + cos105°

= 2cos 60°.cos 45°

= 2 x 1/2 x 1/√2 = 1/√2

Discussion

70.	What is the value of the sum∑(in + in + 1), for n ∈ [n = 2, 11] where i = √(-1)?a. i b. 2i c. –2i d. 1 + i
Answer» Correct option c. - 2i Explanation: Sum = i² + 2i³ + 2i⁴ + ..... + 2i¹⁰ + 2i¹¹ + i¹² = 2i¹¹ = 2i³ = –2i

70.

What is the value of the sum∑(in + in + 1), for n ∈ [n = 2, 11] where i = √(-1)?a. i b. 2i c. –2i d. 1 + i

Answer»

Correct option c. - 2i

Explanation:

Sum = i² + 2i³ + 2i⁴ + ..... + 2i¹⁰ + 2i¹¹ + i¹²

= 2i¹¹ = 2i³ = –2i

Discussion

71.	What is (sin5x - sin3x)/(cos5x + cos3x) equal to? a. sin x b. cos x c. tan x d. cot x
Answer» Correct option c. tan x Explanation: (sin5x - sin3x)/(cos5x + cos3x) = (2cos4x.sinx)/(2cos4x.cosx) = tanx

71.

What is (sin5x - sin3x)/(cos5x + cos3x) equal to? a. sin x b. cos x c. tan x d. cot x

Answer»

Correct option c. tan x

Explanation:

(sin5x - sin3x)/(cos5x + cos3x) = (2cos4x.sinx)/(2cos4x.cosx) = tanx

Discussion

72.	If sin x = 1/√5 , sin y = 1/√10 , where 0 < x < π/2, 0 < y < π/2, then what is (x + y) equal to? a. π b. π/2 c. π/4 d. 0
Answer» Correct option c. π/4 Explanation: sinx = 1/√5, siny = 1/√10 sin (x + y) = sinx . cosy + cosx siny cosx = √(1 - 1/5) = 2/√5, cosy = √(1 - 1/10) = √(9/10) = 3/√10 sin(x +y) = 1/√5 x 3/√10 + 2/√5 x 1/√10 = 5/√50 = 1/√2 ⇒ x + y = 45°

72.

If sin x = 1/√5 , sin y = 1/√10 , where 0 < x < π/2, 0 < y < π/2, then what is (x + y) equal to? a. π b. π/2 c. π/4 d. 0

Answer»

Correct option c. π/4

Explanation:

sinx = 1/√5, siny = 1/√10

sin (x + y) = sinx . cosy + cosx siny

cosx = √(1 - 1/5) = 2/√5, cosy = √(1 - 1/10) = √(9/10) = 3/√10

sin(x +y) = 1/√5 x 3/√10 + 2/√5 x 1/√10 = 5/√50 = 1/√2

⇒ x + y = 45°

Discussion

73.	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
Answer» Correct option C. 4/9 Explanation: Prime numbers are 2,3 and 5. P(prime no.) = P(even no.) P(prime no.) + P(odd no.) P(prime no.) = 2/3 x 1/3 + 1/3 x 2/3 = 4/9

73.

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

Answer»

Correct option C. 4/9

Explanation:

Prime numbers are 2,3 and 5.

P(prime no.) = P(even no.) P(prime no.) + P(odd no.) P(prime no.)

= 2/3 x 1/3 + 1/3 x 2/3 = 4/9

Discussion

74.	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 = 4 d. x2 + y2 + z2 + 4x + 6y + 8z = 4
Answer» Correct option a. x² + y² + z² + 4x –6y –8z = 7 Explanation: (x + 2)² + (y – 3)² + (z – 4)² = 6² ⇒ x² + y² + z² + 4x – 6y – 8z = 6²– 2² – 3² – 4² ⇒ x²+ y² + z² + 4x – 6y – 8z = 7

74.

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 = 4 d. x2 + y2 + z2 + 4x + 6y + 8z = 4

Answer»

Correct option a. x² + y² + z² + 4x –6y –8z = 7

Explanation:

(x + 2)² + (y – 3)² + (z – 4)² = 6²

⇒ x² + y² + z² + 4x – 6y – 8z = 6²– 2² – 3² – 4²

⇒ x²+ y² + z² + 4x – 6y – 8z = 7

Discussion

75.	What is (vector a - vector b) x (vector a + vector b) equal to?a. vector 0b. vector a x vector bc. 2(vector a x vector b)d. \|vector a\|2 - \|vector b\|2
Answer» Correct option c. 2(vector a x vector b) Explanation: (vector a - vector b) x (vector a + vector b) = vector a x vector a + vector a x vector b - vector b x vector a + vector b - vector b = 0 + vector a x vector b + vector a x vector b + 0 = 2(vector a x vector b)

75.

What is (vector a - vector b) x (vector a + vector b) equal to?a. vector 0b. vector a x vector bc. 2(vector a x vector b)d. |vector a|2 - |vector b|2

Answer»

Correct option c. 2(vector a x vector b)

Explanation:

(vector a - vector b) x (vector a + vector b)

= vector a x vector a + vector a x vector b - vector b x vector a + vector b - vector b

= 0 + vector a x vector b + vector a x vector b + 0

= 2(vector a x vector b)

Discussion

76.	If the vectors k and vector A are parallel to each other, then what is k vector k x vector A equal to? a. k2 vector A b. vector 0 c. - k2 vector A d.vector A
Answer» Correct option b. vector 0 Explanation: Cross product of parallel vectors = vector 0

76.

If the vectors k and vector A are parallel to each other, then what is k vector k x vector A equal to? a. k2 vector A b. vector 0 c. - k2 vector A d.vector A

Answer»

Correct option b. vector 0

Explanation:

Cross product of parallel vectors = vector 0

Discussion

77.	Let vector a, vector b and vector c be three mutually perpendicular vectors each of unit magnitude. If vector = vector a + vector b + vector c, vector B = vector a - vector b + vector c and vector C = vector a - vector b - vector c, then which one of the following is correct? a. \|vector A\| > \|vector B\| > \|vector C\|b.\|vector A\| = \|vector B\| ≠ \|vector C\|c. \|vector A\| = \|vector B\| = \|vector C\|d. \|vector A\| ≠ \|vector B\| ≠ \|vector C\|
Answer» Correct option c. \|vector A\| = \|vector B\| = \|vector C\| Explanation: for simplicity let us take vector a, vector b, vector c as i, j, k. Now magnitude of vector A, vector B and vector C will be √3.

77.

Let vector a, vector b and vector c be three mutually perpendicular vectors each of unit magnitude. If vector = vector a + vector b + vector c, vector B = vector a - vector b + vector c and vector C = vector a - vector b - vector c, then which one of the following is correct? a. |vector A| > |vector B| > |vector C|b.|vector A| = |vector B| ≠ |vector C|c. |vector A| = |vector B| = |vector C|d. |vector A| ≠ |vector B| ≠ |vector C|

Answer»

Correct option c. |vector A| = |vector B| = |vector C|

Explanation:

for simplicity let us take vector a, vector b, vector c as i, j, k.

Now magnitude of vector A, vector B and vector C will be √3.

Discussion

78.	If a and b are two unit vectors, then the vector (a + b) × (a × b) is parallel to A. (a − b) B. (a + b) C. (2a − b) D. (2a + b)
Answer» Correct option A. (a - b) Explanation: (a + b)× (a × b) = a ×(a × b) + a×(a × b) (a . b)a – (a .a)b + (b . b)a – (b.a)b a - b + a - b [a and b are unit vectors] = 2 (a - b) i.e., parallel to (a - b)

78.

If a and b are two unit vectors, then the vector (a + b) × (a × b) is parallel to A. (a − b) B. (a + b) C. (2a − b) D. (2a + b)

Answer»

Correct option A. (a - b)

Explanation:

(a + b)× (a × b) = a ×(a × b) + a×(a × b) (a . b)a – (a .a)b + (b . b)a – (b.a)b a - b + a - b [a and b are unit vectors]

= 2 (a - b)

i.e., parallel to (a - b)

Discussion

79.	If vector F = i + 3j+ 2k acts on a particle to displace it from the point A(i + 2j− 3k) to the point B(3i − j + 5k). The work done by the force will be A. 5 units B. 7 units C. 9 units D. 10 units
Answer» Correct option C. 9 units Explanation: The line joining the points vector A(i + 2j – 3k) and vector B(3i – j + 5k) is i.e., vector AB = 2i – 3j +8k Work done = vector (F.AB) = 1×2 + 3×(-3) + 2 × 8 = 9

79.

If vector F = i + 3j+ 2k acts on a particle to displace it from the point A(i + 2j− 3k) to the point B(3i − j + 5k). The work done by the force will be A. 5 units B. 7 units C. 9 units D. 10 units

Answer»

Correct option C. 9 units

Explanation:

The line joining the points vector A(i + 2j – 3k) and vector B(3i – j + 5k) is i.e., vector AB = 2i – 3j +8k Work done = vector (F.AB) = 1×2 + 3×(-3) + 2 × 8 = 9

Discussion

80.	If vector a and vector b are vectors such that \|vector a\| = 2, = \|vector b\| = 7 and vector(a x b) = 3i + 2j + 6k, then what is the acute angle between vector a and vector b ? a. 30° b. 45° c. 60° d. 90°
Answer» Correct option a. 30° Explanation: sinθ = vector(\|a x b\|)/(\|vector a\|\|vector b\|) = 7/2 x 7 = 1/2 ⇒ θ = 30°

80.

If vector a and vector b are vectors such that |vector a| = 2, = |vector b| = 7 and vector(a x b) = 3i + 2j + 6k, then what is the acute angle between vector a and vector b ? a. 30° b. 45° c. 60° d. 90°

Answer»

Correct option a. 30°

Explanation:

sinθ = vector(|a x b|)/(|vector a||vector b|)

= 7/2 x 7

= 1/2

⇒ θ = 30°

Discussion

81.	If A + B + C = 180°, then what is sin 2A – sin 2B – 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
Answer» Correct option d. –4 sin A cos B cos C Explanation: sin 2A - sin 2B - sin 2C = 2cos (A + B) sin (A - B) sin( 2A + 2B) = 2cos(A + B) sin(A - B) + 2sin (A + B) cos(A + B) = 2cos(A + B ) [sin(A - B) sin (A + B)] = - 2cosC[ 2sin A cosB] = - 4 sin A cosBcosC

81.

If A + B + C = 180°, then what is sin 2A – sin 2B – 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

Answer»

Correct option d. –4 sin A cos B cos C

Explanation:

sin 2A - sin 2B - sin 2C

= 2cos (A + B) sin (A - B) sin( 2A + 2B)

= 2cos(A + B) sin(A - B) + 2sin (A + B) cos(A + B)

= 2cos(A + B ) [sin(A - B) sin (A + B)]

= - 2cosC[ 2sin A cosB]

= - 4 sin A cosBcosC

Discussion

82.	The sum of all real roots of the equation \|x − 3\|2 + \|x −3\| − 2 = 0 A. 2 B. 3 C. 4 D. 6
Answer» Correct option D. 6 Explanation: This is quadratic equation in the form of \|x - 3\|. Let \|x - 3\| = t Therefore equation becomes ‘t² + t - 2= 0’ Solving the equation, we get t = 1 (-ve value is neglected as t is +ve) ∴ x = 4, 2 Sum of roots = 6

82.

The sum of all real roots of the equation |x − 3|2 + |x −3| − 2 = 0 A. 2 B. 3 C. 4 D. 6

Answer»

Correct option D. 6

Explanation:

This is quadratic equation in the form of |x - 3|.

Let |x - 3| = t

Therefore equation becomes ‘t² + t - 2= 0’

Solving the equation, we get t = 1 (-ve value is neglected as t is +ve)

∴ x = 4, 2

Sum of roots = 6

Discussion

83.	What is the moment about the point i + 2j - k of a force represented by 3i + k acting through the point 2i - j + 3k?a. - 3i + 11j + 9k b. 3i + 2j + 9k c. 3i + 4j + 9k d. i + j + k
Answer» Correct option a. - 3i + 11j + 9k Explanation: vector r = (2i - j + 3k) - (i + 2j - k) = i - 3j + 4k vector τ = r x F = (i- 3j + 4k) x (3i + k) = - 3i + 11j + 9k

83.

What is the moment about the point i + 2j - k of a force represented by 3i + k acting through the point 2i - j + 3k?a. - 3i + 11j + 9k b. 3i + 2j + 9k c. 3i + 4j + 9k d. i + j + k

Answer»

Correct option a. - 3i + 11j + 9k

Explanation:

vector r = (2i - j + 3k) - (i + 2j - k)

= i - 3j + 4k

vector τ = r x F = (i- 3j + 4k) x (3i + k)

= - 3i + 11j + 9k

Discussion

84.	How many different permutations can be made out of the letters of the word ‘PERMUTATION’? A. 19958400 B. 19954800 C. 19952400 D. 39916800
Answer» Correct option A. 19958400 Explanation: There are 11 letters in the word ‘PERMUTATION’ and ‘T’ is repeated two times. ∴ Number of permutations = 11!/2! = 19958400

84.

How many different permutations can be made out of the letters of the word ‘PERMUTATION’? A. 19958400 B. 19954800 C. 19952400 D. 39916800

Answer»

Correct option A. 19958400

Explanation:

There are 11 letters in the word ‘PERMUTATION’ and ‘T’ is repeated two times.

∴ Number of permutations = 11!/2! = 19958400

Discussion

85.	What is C(n, r) + 2C(n, r – 1) + C(n, r) equal to? a. C(n + 1, r) b. C(n –1, r + 1) c. C(n, r + 1) d. C(n + 2, r)
Answer» Correct option d. C(n + 2, r) Explanation: ⁿ_rC + ⁿ_{(r - 1)}C + ⁿ_{(r - 2)}C = ^{(n + 1)}_rC + ^{(n + 1)}_{(r - 1)}C = ^{(n + 2)}_rC

85.

What is C(n, r) + 2C(n, r – 1) + C(n, r) equal to? a. C(n + 1, r) b. C(n –1, r + 1) c. C(n, r + 1) d. C(n + 2, r)

Answer»

Correct option d. C(n + 2, r)

Explanation:

ⁿ_rC + ⁿ_{(r - 1)}C + ⁿ_{(r - 2)}C

= ^{(n + 1)}_rC + ^{(n + 1)}_{(r - 1)}C = ^{(n + 2)}_rC

Discussion

86.	If A and B are two invertible square matrices of same order, then what is (AB)–1 equal to? a. B–1A–1 b. A–1B–1 c. B–1A d. A–1B
Answer» Correct option a. B^–1A^–1 Explanation: (AB)^-1 = B^-1A^-1

86.

If A and B are two invertible square matrices of same order, then what is (AB)–1 equal to? a. B–1A–1 b. A–1B–1 c. B–1A d. A–1B

Answer»

Correct option a. B^–1A^–1

Explanation:

(AB)^-1 = B^-1A^-1

Discussion

87.	If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a a. 3 × 5 matrix b. 5 × 3 matrix c. 3 × 2 matrix d. 5 × 2 matrix
Answer» Correct option a. 3 × 5 matrix Explanation: (A)_{(2 x 3)} x (B)_{(3 x 5)} = (AB)_{2 x 5} ∴ B must be 3 x 5 matrix

87.

If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a a. 3 × 5 matrix b. 5 × 3 matrix c. 3 × 2 matrix d. 5 × 2 matrix

Answer»

Correct option a. 3 × 5 matrix

Explanation:

(A)_{(2 x 3)} x (B)_{(3 x 5)} = (AB)_{2 x 5}

∴ B must be 3 x 5 matrix

Discussion

88.	What is the value of ((-1 + i√3)/2)3n + ((-1 + i√3)/2)3n where i = √(-1)?a. 3 b. 2 c. 1 d. 0
Answer» Correct option b. 2 Explanation: (w)³ⁿ + (w²)³ⁿ (w³)ⁿ + (w³)²ⁿ = 1 + 1 = 2

88.

What is the value of ((-1 + i√3)/2)3n + ((-1 + i√3)/2)3n where i = √(-1)?a. 3 b. 2 c. 1 d. 0

Answer»

Correct option b. 2

Explanation:

(w)³ⁿ + (w²)³ⁿ

(w³)ⁿ + (w³)²ⁿ

= 1 + 1 = 2

Discussion

89.	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
Answer» Correct option a. 185 Explanation: No. of triangle = ¹²C₃ - ⁷C₃ = 220 – 35 = 185

89.

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

Answer»

Correct option a. 185

Explanation:

No. of triangle = ¹²C₃ - ⁷C₃ = 220 – 35 = 185

Discussion

90.	If (0.2)x = 2 and log10 2 = 0.3010, then what is the value of x to the nearest tenth? a. –10.0 b. –0.5 c. –0.4 d. –0.2
Answer» Correct option c. – 0.4 Explanation: (0.2)^X = 2 x log₁₀2/10 = log₁₀2 x[log₁₀2 – log₁₀ 10] = log₁₀2 x[0.3010 –1] = 0.3010 x = - (0. 3010)/(0.6990) ≈ - 0.43

90.

If (0.2)x = 2 and log10 2 = 0.3010, then what is the value of x to the nearest tenth? a. –10.0 b. –0.5 c. –0.4 d. –0.2

Answer»

Correct option c. – 0.4

Explanation:

(0.2)^X = 2

x log₁₀2/10 = log₁₀2

x[log₁₀2 – log₁₀ 10] = log₁₀2

x[0.3010 –1] = 0.3010

x = - (0. 3010)/(0.6990) ≈ - 0.43

Discussion

91.	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
Answer» Correct option b. kl Explanation: B = adj A, l = Identity matrix, \|A\| = k AB = A(adj A) = \|A\|l = kl

91.

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

Answer»

Correct option b. kl

Explanation:

B = adj A, l = Identity matrix, |A| = k

AB = A(adj A) = |A|l = kl

Discussion

92.	For a square matrix A, which of the following properties hold? 1. (A-1) -1A2. det(A-1) = 1/detA3. (λA)-1 λA-1 where λ is a scalarSelect 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
Answer» Correct option a. 1 and 2 only Explanation: Statement 1 and 2 are correct. Statement 3 is incorrect because (λA)^-1 = 1/λA^-1, λ ≠ 0

92.

For a square matrix A, which of the following properties hold? 1. (A-1) -1A2. det(A-1) = 1/detA3. (λA)-1 λA-1 where λ is a scalarSelect 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

Answer»

Correct option a. 1 and 2 only

Explanation:

Statement 1 and 2 are correct.

Statement 3 is incorrect because

(λA)^-1 = 1/λA^-1, λ ≠ 0

Discussion

93.	A square matrix A is called orthogonal if a. A = A2 b. A’ = A–1 c. A = A–1 d. A = A’ Where A’ is the transpose of A
Answer» Correct option a. A = A² Explanation: If A^–1 = A^T, then A is orthogonal matrix.

93.

A square matrix A is called orthogonal if a. A = A2 b. A’ = A–1 c. A = A–1 d. A = A’ Where A’ is the transpose of A

Answer»

Correct option a. A = A²

Explanation:

If A^–1 = A^T, then A is orthogonal matrix.

Discussion

94.	If A, B and C are subsets of a Universal set, then which one of the following is not correct? 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) Where A’ is the complement of A
Answer» Correct option c. A' ∪ (B ∪ C) = (C' ∩ B)' ∩ A Explanation: Checking through option ‘C” is incorrect.

94.

If A, B and C are subsets of a Universal set, then which one of the following is not correct? 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) Where A’ is the complement of A

Answer»

Correct option c. A' ∪ (B ∪ C) = (C' ∩ B)' ∩ A

Explanation:

Checking through option ‘C” is incorrect.

Discussion

95.	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
Answer» Correct option a. 2664 Explanation: 543 + 534 + 453 + 435 + 354 + 345 = 2664

95.

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

Answer»

Correct option a. 2664

Explanation:

543 + 534 + 453 + 435 + 354 + 345 = 2664

Discussion

96.	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
Answer» Correct option b. 2481 Explanation: The no. with all distinct digits = 5 × 9 × 8 × 7 = 2520 ∴ x = 5001 – 2520 = 2481

96.

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

Answer»

Correct option b. 2481

Explanation:

The no. with all distinct digits = 5 × 9 × 8 × 7 = 2520

∴ x = 5001 – 2520 = 2481

Discussion

97.	Consider the following statements: 1. If 10 is added to each entry on a list then the average increase by 10. 2. If 10 is added to each entry on a list, then the standard deviation increase by 10. 3. If each entry on a list is doubled, then the average doubles. Which of the above statement are correct? a. 1, 2 and 3 b. 1 and 2 only c. 1 and 3 only d. 2 and 3 only
Answer» Correct option c. 1 and 3 only

97.

Consider the following statements: 1. If 10 is added to each entry on a list then the average increase by 10. 2. If 10 is added to each entry on a list, then the standard deviation increase by 10. 3. If each entry on a list is doubled, then the average doubles. Which of the above statement are correct? a. 1, 2 and 3 b. 1 and 2 only c. 1 and 3 only d. 2 and 3 only

Answer»

Correct option c. 1 and 3 only

Discussion

98.	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
Answer» Correct option b. 4 Explanation: Variance will not change by adding or subtracting a fixed value to all the elements.

98.

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

Answer»

Correct option b. 4

Explanation:

Variance will not change by adding or subtracting a fixed value to all the elements.

Discussion

99.	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
Answer» Correct option C. 0.3 Explanation: Condition for triangle: a + b > c Case 1: 3, 5, 7 Case 2: 5, 7, 9 Case 3: 3, 7, 9 ∴ Required probability = 3/10 = 0.3

99.

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

Answer»

Correct option C. 0.3

Explanation:

Condition for triangle: a + b > c

Case 1: 3, 5, 7

Case 2: 5, 7, 9

Case 3: 3, 7, 9

∴ Required probability = 3/10 = 0.3

Discussion

100.	Consider the following statements: 1. Variance is unaffected by change of origin and change of scale. 2. 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
Answer» Correct option B. 2 only Explanation: Variance does not depend upon change of origin and unit of observations but it depends upon scale.

100.

Consider the following statements: 1. Variance is unaffected by change of origin and change of scale. 2. 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

Answer»

Correct option B. 2 only

Explanation:

Variance does not depend upon change of origin and unit of observations but it depends upon scale.

Discussion

Explore topic-wise InterviewSolutions in .

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 × 8! × 8! B. (8!)3 C. 24 × 8! × 8! D. 16!

Three sides of a trapezium be the angle between a pair of adjacent sides.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

Three sides of a trapezium be the angle between a pair of adjacent sides.What is the maximum area of the trapezium? a. 36√3 cm2 b. 30√3 cm2 c. 27√3 cm2d. 24√3 cm2

Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) &lt; 0 b. g(x) &gt; 0 c. g(x) = 0 d. g(x) ≥ 0

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)

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]

In which one of the following intervals is the function f(x) = x2 – 5x + 6 decreasing? a. (- ∞, 2] b. [3, ∞] c. (- ∞, ∞) d. (2, 3)

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. z, 2, z d. x, 1, z

The differential equation of the family of curves y = p cos (ax) + q sin (ax), where p, q are arbitrary constants, isa. d2y/dx2 - a2y = 0b. d2y/dx2 - ay = 0c. d2y/dx2 + ay = 0d. d2y/dx2 + a2y = 0

If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more isa. 1/6b. 4/11c. 3/11d. 2/11

The smallest positive integer n for which (1 + i/1− i)n = 1, is A. 1 B. 4 C. 8 D. 16

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

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

The set of all points, where the function f(x) = √1− e − x2 is differentiable, is A. (0, ∞)B. (-∞, ∞)C. (-∞, ∞) ∪(0, ∞) D. (-1, ∞)

What is sin105° + cos105° equal to ? a. sin 50° b. cos 50° c. 1/√2 d. 0

What is the value of the sum∑(in + in + 1), for n ∈ [n = 2, 11] where i = √(-1)?a. i b. 2i c. –2i d. 1 + i

What is (sin5x - sin3x)/(cos5x + cos3x) equal to? a. sin x b. cos x c. tan x d. cot x

If sin x = 1/√5 , sin y = 1/√10 , where 0 &lt; x &lt; π/2, 0 &lt; y &lt; π/2, then what is (x + y) equal to? a. π b. π/2 c. π/4 d. 0

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

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 = 4 d. x2 + y2 + z2 + 4x + 6y + 8z = 4

What is (vector a - vector b) x (vector a + vector b) equal to?a. vector 0b. vector a x vector bc. 2(vector a x vector b)d. |vector a|2 - |vector b|2

If the vectors k and vector A are parallel to each other, then what is k vector k x vector A equal to? a. k2 vector A b. vector 0 c. - k2 vector A d.vector A

If a and b are two unit vectors, then the vector (a + b) × (a × b) is parallel to A. (a − b) B. (a + b) C. (2a − b) D. (2a + b)

If vector F = i + 3j+ 2k acts on a particle to displace it from the point A(i + 2j− 3k) to the point B(3i − j + 5k). The work done by the force will be A. 5 units B. 7 units C. 9 units D. 10 units

If vector a and vector b are vectors such that |vector a| = 2, = |vector b| = 7 and vector(a x b) = 3i + 2j + 6k, then what is the acute angle between vector a and vector b ? a. 30° b. 45° c. 60° d. 90°

If A + B + C = 180°, then what is sin 2A – sin 2B – 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

The sum of all real roots of the equation |x − 3|2 + |x −3| − 2 = 0 A. 2 B. 3 C. 4 D. 6

What is the moment about the point i + 2j - k of a force represented by 3i + k acting through the point 2i - j + 3k?a. - 3i + 11j + 9k b. 3i + 2j + 9k c. 3i + 4j + 9k d. i + j + k

How many different permutations can be made out of the letters of the word ‘PERMUTATION’? A. 19958400 B. 19954800 C. 19952400 D. 39916800

What is C(n, r) + 2C(n, r – 1) + C(n, r) equal to? a. C(n + 1, r) b. C(n –1, r + 1) c. C(n, r + 1) d. C(n + 2, r)

If A and B are two invertible square matrices of same order, then what is (AB)–1 equal to? a. B–1A–1 b. A–1B–1 c. B–1A d. A–1B

If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a a. 3 × 5 matrix b. 5 × 3 matrix c. 3 × 2 matrix d. 5 × 2 matrix

What is the value of ((-1 + i√3)/2)3n + ((-1 + i√3)/2)3n where i = √(-1)?a. 3 b. 2 c. 1 d. 0

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

If (0.2)x = 2 and log10 2 = 0.3010, then what is the value of x to the nearest tenth? a. –10.0 b. –0.5 c. –0.4 d. –0.2

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

For a square matrix A, which of the following properties hold? 1. (A-1) -1A2. det(A-1) = 1/detA3. (λA)-1 λA-1 where λ is a scalarSelect 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

A square matrix A is called orthogonal if a. A = A2 b. A’ = A–1 c. A = A–1 d. A = A’ Where A’ is the transpose of A

If A, B and C are subsets of a Universal set, then which one of the following is not correct? 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) Where A’ is the complement of A

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

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

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

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

Consider the following statements: 1. Variance is unaffected by change of origin and change of scale. 2. 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

Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0

If sin x = 1/√5 , sin y = 1/√10 , where 0 < x < π/2, 0 < y < π/2, then what is (x + y) equal to? a. π b. π/2 c. π/4 d. 0