Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

If P(A) = 0.5, P(B) = 0.2, P(B/A) = 0.2 then P(A/B) is(A) 0.5 (B) 0.2 (C) 0.3(D) 0.7

Answer»

Correct option:

(A) 0.5 

2.

The value of ∫dx/(a2 + x2) is(A) sin-1 x/a(B) 1/a tan-1x/a(C) sec-1 x/a(D) None of these

Answer»

Correct option :

(B) 1/a tan-1x/a

3.

The area enclosed between the curve y2 = 4x and the line y = x is(A) 1/2(B) 2/3(C) 4/3(D) 8/3

Answer»

Correct option:

(D) 8/3

4.

If P(A) = 3/8, P(B) = 5/8 and P(A ∪ B) = 3/4, then P(B/A) is (a) 1/4(b) 1/3(c) 2/3(d) 1/2

Answer»

Answer is (c) 2/3

5.

If |vector(a x b)| = 4 and |vector(a . b)| = 2 then |vector a|2 .|vector b|2 is(A) 2 (B) 6 (C) 8 (D) 20

Answer»

Correct option:

(D) 20

6.

The direction cosines of the normal to the plane 3x - 3y - 6z - 3 = 0 are(a) 2/7,-3/7,- 6/7(b) 2/7,3/7,6/7(c) -2/7,3/7,- 6/7(d) None of these

Answer»

Answer is (a) 2/7,-3/7,- 6/7

7.

\[\frac{2 \cos ^{2} 60^{\circ}+3 \sec ^{2} 30^{\circ}-2 \tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 45^{\circ}}=?\](a) \( \frac{15}{7} \)(b) \( \frac{10}{3} \)(c) \( \frac{15}{8} \)(d) \( \frac{10}{7} \)

Answer» Hello,

Your answer is 10/3
8.

The direction cosine of a normal to the plane 2x – 3y –6z + 14 = 0 are(A) (2/7,-3/7,-6/7)(B) (-2/7,-3/7,6/7)(C) (-2/7,-3/7,-6/7)(D) None of these

Answer»

Correct option:

(A) (2/7,-3/7,-6/7)

9.

The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is(A) π/4(B) π/6(C) π/3(D) π/2

Answer»

Correct option:

(C) π/3

10.

The equation vector r = λ i represents(A) x-axis (B) y-axis (C) z-axis (D) None of these

Answer»

Correct option:

(A) x-axis 

11.

The direction cosine of any normal to the xy- plane are(A) (1,0,0) (B) (0,1,0) (C) (1,1,0)(D) (0,0,1)

Answer»

Correct option:

(D) (0,0,1)

12.

If a2 = 23/25, then a is (a) rational(b) irrational(c) whole number(d) integer

Answer»

Correct answer is: (b) irrational

a2=23/25, then a

= √23/5, which is irrational

13.

If LCM(x, 18) =36 and HCF(x, 18) =2, then x is(a) 2(b) 3(c) 4(d) 5

Answer»

Correct answer is: (c) 4

LCM X HCF = Product of two numbers 36 X 2 = 18 X \(x\) 

\(x\) = 4

14.

If a = (√3 + √2)-3 and b = (√3 - √2)-3, find (a + 1)-1 + (b + 1)-1 .

Answer»

a = (\(\sqrt3 + \sqrt2\))-3 and b = (\(\sqrt3 - \sqrt2\))-3

Now (a + 1)-1 + (b + 1)-1 = \(\frac1{a+1}+\frac1{b+1}=\frac{a+b+2}{(a+1)(b+1)}\)

\(\therefore\) (a + 1)-1 + (b + 1)-1 = \(\frac{a+b+2}{ab+a+b+1}\)-----(1)

Now, ab  =  (\(\sqrt3 + \sqrt2\))-3 (\(\sqrt3 - \sqrt2\))-3

= ((\(\sqrt3 + \sqrt2\))(\(\sqrt3 - \sqrt2\)))-3 (\(\because\) ambm = (ab)m)

= ((√3)2 - (√2)2)-3(\(\because\) (a + b) (a - b) = a2 - b2)

 = (3 - 2)-3 = 1-3 = \(\frac1{1^3}=1\)

\(\therefore\) (a + 1)-1 + (b + 1)-1 = \(\frac{a+b+2}{1 + a + b+1}\) (From 1)

 = \(\frac{a+b+2}{a + b + 2}=1\) 

Hence, (a + 1)-1 + (b + 1)-1 = 1

15.

In ∆ABC right angled at B, if tan A= √3, then cos A cos C- sin A sin C = (a) -1(b) 0(c) 1(d) √3/2

Answer»

Correct answer is: (b) 0

tan A= √3 = tan 60° so ∠A=60°, Hence ∠C = 30°.

So cos A cos C- sin A sin C = (1/2)x (√3/2) - (√3/2)x (1/2) =0

16.

If a ∶ b = 4 ∶ 7 and b ∶ c = 9 ∶ 4 then find the a ∶ b ∶ c.1. 36 ∶ 63 ∶ 282. 24 ∶ 35 ∶ 143. 40 ∶ 15 ∶ 174. 45 ∶ 35 ∶ 63

Answer» Correct Answer - Option 1 : 36 ∶ 63 ∶ 28

Given:

a ∶ b = 4 ∶ 7

b ∶ c = 9 ∶ 4

Calculations:

Making the ratio of b in both the condition as equal

a

b

c

4 × 9 = 36

7 × 9 = 63

 

 

9 × 7 = 63

4 × 7 = 28


The ratio of a, b and c = 36 ∶ 63 ∶ 28

a b c is 36 63 28

17.

If √3tanθ = 1, then the value of θ is(A) 30°(B) 60°(C) 45°(D) 90°

Answer»

Correct option is: (A) 30°

18.

How much times does the second hand of a clock take to complete an angle equal to 270°?(A) 30 seconds (B) 45 seconds (C) 60 seconds (D) 40 seconds

Answer»

Correct option is: (B) 45 seconds

19.

The area of the triangle formed by points A(0, 8), B(6, 12) and C(-16, -4) is – (A) 48 sq. units (B) 8 sq. units (C) 6 sq. units (D) 4 sq. units

Answer»

Correct answer is (D) 4 sq. units

20.

Consider the following statement:"If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."This statement is a/an1. definition2. theorem3. axiom4. proposition

Answer» Correct Answer - Option 2 : theorem

  • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. This statement is a theorem.
  • Theorem is said to be proposition that is not self-evident but that can be proved from accepted premises and so is established as a law or principle. 
  • There are many properties of a parallelogram. We draw a parallelogram and draw both its diagonals intersecting at the point. Measure the lengths of these lines. We observe that the mid-point of the diagonals. Repeat this activity with some more parallelograms.
  • Each time we will find that the mid-point of both the diagonal. We can use the previous concept like length, mid-points etc. Hence we can prove this theorem by accepted premises.
21.

If tanθ = tan45°, then the value of θ is(A) 30°(B) 45°(C) 60°(D) 90°

Answer»

Correct option is: (B) 45°

22.

If √3 tan A – 3 = 0 then A = (A) 900 (B) 600 (C) 450 (D) 300

Answer»

Correct answer is (B) 600 

23.

cos2θ - 1 =(A) –sin2θ (B) sin2θ (C) 0 (D) cot2θ

Answer»

Correct answer is (A) –sin2θ

24.

Which of the following is equal to 7 ?(A) 7sec2θ – 7tan2θ(B) 7sec2θ + 7tan2θ(C) 1 – 7cos2θ(D) 7sec2θ – 7cos2θ

Answer»

Correct option is: (A) 7sec2θ – 7tan2θ

25.

√3tan60° + tan45° =(A) 4 (B) 3 (C) 2 (D) 1

Answer»

Correct option is: (A) 4

26.

If sinθ = 0.1, then the value of sin3θ will be(A) 0.286 (B) 0.386 (C) 0.296 (D) 0.396

Answer»

Correct option is: (C) 0.296

27.

cot x . tan x = (A) 1 (B) -1 (C) 0 (D) 2

Answer»

Correct answer is (A) 1

28.

\(\left(\frac{sec\,35^\circ}{cosec\,55^\circ}\right)^2 =\)((sec 35°)/(cosec 55°))2 =(A) -1 (B) 0 (C) 1 (D) 2

Answer»

Correct answer is (C) 1

29.

If 3sinθ = 2, then the value of cosecθ will be(A) 2/3(B) 3/2(C) 1/3(D) 1/2

Answer»

Correct option is: (B) \(\frac{3}{2}\)

30.

Sin30° =(A) 1(B) 1/2(C) √3/2(D) 1/√2

Answer»

Correct answer is (B) 1/2

31.

Distance between the points (7cosθ, 0) and (0, 7sinθ) is(A) 6 (B) 7 (C) 14 (D) 49

Answer»

Correct option is: (D) 49

32.

If A = B = 45°, then sin(A – B) =(A) 1 (B) 0 (C) -1 (D) 2

Answer»

Correct option is: (B) 0

33.

Which of the following has the maximum value ? (A) cos 45° (B) sin 0° (C) cot 45° (D) cos 60°

Answer»

Correct answer is (C) cot 45°

34.

tan (45° – A) =(A) 1 - tan/1 + tan(B) 1 + tan/1 - tanA(C) 1 + tanA(D) 1 - tanA

Answer»

Correct option is: (A) \(\frac{1-tan}{1+tan}\)

35.

Sin245° + cos245° = (A) 0 (B) 1 (C) -1 (D) 2

Answer»

Correct option is: (B) 1

36.

\(\frac{1}{sec∅}=\)1/sec ∅ = (A) tan∅ (B) cos∅ (C) sec∅ (D) cosec∅

Answer»

Correct answer is (B) cos∅

37.

If ∅ = 45° then sec∅ + cosec∅ = (A) 1 (B) √2 (C) 2 (D) 2√2

Answer»

Correct answer is (D) 2√2

38.

If cosecA = √2, then the value of cot2A will be(A) 1 (B) 2(C) √2(D) 3

Answer»

Correct option is: (A) 1

39.

If sinθ = 1/2, where angle θ lies between 0 and π, then the value of θ will be(A) 60°, 120°(B) 30°, 150°(C) 30°, 135°(D) 30°, 120°

Answer»

Correct option is: (B) 30°, 150°

40.

If cosec∅ = K then the value of cos∅ is –(A) \(\frac{\sqrt{K^2 + 1}}{K}\)(B) \(\frac{\sqrt{K^2 - 1}}{K}\)(C) \(\frac{K}{\sqrt{K^2 - 1}}\)(D) \(\frac{K}{\sqrt{K^2 + 1}}\)

Answer»

Correct answer is (B) \(\frac{\sqrt{K^2 - 1}}{K}\)

41.

If sinθ = 1/√2, then the value of θ will be(A) 30°(B) 45°(C) 60°(D) 90°

Answer»

Correct option is: (B) 45°

42.

If r = 10 cm, l = 20 cm, then the value of θ (in radian) is(A) 4 (B) 2 (C) 1 (D) 3

Answer»

Correct option is: (B) 2

43.

The distance of the point (5, 12) from the origin is (A) 13 (B) 17 (C) 7 (D) 30

Answer»

Correct option is: (A) 13

44.

Which one of the following is used with cout as operator ?  A. <<B. >>C. >D. <

Answer»

Correct option is: A. <<

45.

If sinθ = 3/5, then the value of cosθ is(A) 4/5(B) 5/3(C) 5/4(D) 3/4

Answer»

Correct option is: (A) \(\frac{4}{5}\)

46.

Which one of the following is used with cin as operator ?A. &lt;&lt;B. &gt;&gt;C. &gt;D. &lt;

Answer»

Correct option is: B. >>

47.

If the roots of 2x2 - 6x + k = 0 are real and equal, find k.

Answer»

The roots of the quadratic equation are real and equal.

∴ b² - 4ac = 0 

(-6)² - 4 × 2 × k = 0 

- 8k = -36

k = 9 / 2

48.

A language which has the capability to generate new data types is called…….. A. Extensible B. Overloaded C. Encapsulated D. Reprehensible

Answer»

Correct option is: A. Extensible

49.

Solve the following simultaneous equations. 101x + 99y = 501, 99x + 101y = 499

Answer»

101x + 99y = 501 .............(I) 

99x + 101y = 499 .............(II)

Adding equations (I) and (II) and dividing by 200

x + y = 5 .............(III)

Subtracting (II) from (I) and dividing by 2 

x - y = 1 ............(IV)

Solving equations (III) and (IV),

x = 3 

y = 2

50.

What is the way to suddenly come out or quit any loop in C++? A. Continue; Statement B. Break; Statement C. Leave; Statement D. Quit; Statement

Answer»

Correct option is: B. Break; Statement