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 |
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Answer» Correct option: (A) 0.5 |
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| 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 |
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Answer» Correct option : (B) 1/a tan-1x/a |
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| 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 |
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Answer» Correct option: (D) 8/3 |
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| 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 |
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Answer» Answer is (c) 2/3 |
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| 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 |
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Answer» Correct option: (D) 20 |
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| 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 |
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Answer» Answer is (a) 2/7,-3/7,- 6/7 |
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| 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) \( \frac{10}{7} \) |
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Answer» Hello, Your answer is 10/3 |
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| 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 |
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Answer» Correct option: (A) (2/7,-3/7,-6/7) |
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| 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 |
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Answer» Correct option: (C) π/3 |
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| 10. |
The equation vector r = λ i represents(A) x-axis (B) y-axis (C) z-axis (D) None of these |
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Answer» Correct option: (A) x-axis |
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| 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) |
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Answer» Correct option: (D) (0,0,1) |
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| 12. |
If a2 = 23/25, then a is (a) rational(b) irrational(c) whole number(d) integer |
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Answer» Correct answer is: (b) irrational a2=23/25, then a = √23/5, which is irrational |
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| 13. |
If LCM(x, 18) =36 and HCF(x, 18) =2, then x is(a) 2(b) 3(c) 4(d) 5 |
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Answer» Correct answer is: (c) 4 LCM X HCF = Product of two numbers 36 X 2 = 18 X \(x\) \(x\) = 4 |
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| 14. |
If a = (√3 + √2)-3 and b = (√3 - √2)-3, find (a + 1)-1 + (b + 1)-1 . |
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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 |
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| 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 |
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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 |
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| 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 |
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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 is 36 ∶ 63 ∶ 28 |
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| 17. |
If √3tanθ = 1, then the value of θ is(A) 30°(B) 60°(C) 45°(D) 90° |
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Answer» Correct option is: (A) 30° |
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| 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 |
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Answer» Correct option is: (B) 45 seconds |
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| 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 |
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Answer» Correct answer is (D) 4 sq. units |
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| 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
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| 21. |
If tanθ = tan45°, then the value of θ is(A) 30°(B) 45°(C) 60°(D) 90° |
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Answer» Correct option is: (B) 45° |
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| 22. |
If √3 tan A – 3 = 0 then A = (A) 900 (B) 600 (C) 450 (D) 300 |
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Answer» Correct answer is (B) 600 |
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| 23. |
cos2θ - 1 =(A) –sin2θ (B) sin2θ (C) 0 (D) cot2θ |
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Answer» Correct answer is (A) –sin2θ |
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| 24. |
Which of the following is equal to 7 ?(A) 7sec2θ – 7tan2θ(B) 7sec2θ + 7tan2θ(C) 1 – 7cos2θ(D) 7sec2θ – 7cos2θ |
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Answer» Correct option is: (A) 7sec2θ – 7tan2θ |
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| 25. |
√3tan60° + tan45° =(A) 4 (B) 3 (C) 2 (D) 1 |
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Answer» Correct option is: (A) 4 |
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| 26. |
If sinθ = 0.1, then the value of sin3θ will be(A) 0.286 (B) 0.386 (C) 0.296 (D) 0.396 |
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Answer» Correct option is: (C) 0.296 |
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| 27. |
cot x . tan x = (A) 1 (B) -1 (C) 0 (D) 2 |
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Answer» Correct answer is (A) 1 |
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| 28. |
\(\left(\frac{sec\,35^\circ}{cosec\,55^\circ}\right)^2 =\)((sec 35°)/(cosec 55°))2 =(A) -1 (B) 0 (C) 1 (D) 2 |
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Answer» Correct answer is (C) 1 |
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| 29. |
If 3sinθ = 2, then the value of cosecθ will be(A) 2/3(B) 3/2(C) 1/3(D) 1/2 |
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Answer» Correct option is: (B) \(\frac{3}{2}\) |
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| 30. |
Sin30° =(A) 1(B) 1/2(C) √3/2(D) 1/√2 |
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Answer» Correct answer is (B) 1/2 |
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| 31. |
Distance between the points (7cosθ, 0) and (0, 7sinθ) is(A) 6 (B) 7 (C) 14 (D) 49 |
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Answer» Correct option is: (D) 49 |
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| 32. |
If A = B = 45°, then sin(A – B) =(A) 1 (B) 0 (C) -1 (D) 2 |
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Answer» Correct option is: (B) 0 |
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| 33. |
Which of the following has the maximum value ? (A) cos 45° (B) sin 0° (C) cot 45° (D) cos 60° |
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Answer» Correct answer is (C) cot 45° |
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| 34. |
tan (45° – A) =(A) 1 - tan/1 + tan(B) 1 + tan/1 - tanA(C) 1 + tanA(D) 1 - tanA |
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Answer» Correct option is: (A) \(\frac{1-tan}{1+tan}\) |
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| 35. |
Sin245° + cos245° = (A) 0 (B) 1 (C) -1 (D) 2 |
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Answer» Correct option is: (B) 1 |
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| 36. |
\(\frac{1}{sec∅}=\)1/sec ∅ = (A) tan∅ (B) cos∅ (C) sec∅ (D) cosec∅ |
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Answer» Correct answer is (B) cos∅ |
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| 37. |
If ∅ = 45° then sec∅ + cosec∅ = (A) 1 (B) √2 (C) 2 (D) 2√2 |
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Answer» Correct answer is (D) 2√2 |
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| 38. |
If cosecA = √2, then the value of cot2A will be(A) 1 (B) 2(C) √2(D) 3 |
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Answer» Correct option is: (A) 1 |
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| 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° |
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Answer» Correct option is: (B) 30°, 150° |
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| 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) \(\frac{K}{\sqrt{K^2 + 1}}\) |
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Answer» Correct answer is (B) \(\frac{\sqrt{K^2 - 1}}{K}\) |
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| 41. |
If sinθ = 1/√2, then the value of θ will be(A) 30°(B) 45°(C) 60°(D) 90° |
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Answer» Correct option is: (B) 45° |
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| 42. |
If r = 10 cm, l = 20 cm, then the value of θ (in radian) is(A) 4 (B) 2 (C) 1 (D) 3 |
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Answer» Correct option is: (B) 2 |
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| 43. |
The distance of the point (5, 12) from the origin is (A) 13 (B) 17 (C) 7 (D) 30 |
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Answer» Correct option is: (A) 13 |
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| 44. |
Which one of the following is used with cout as operator ? A. <<B. >>C. >D. < |
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Answer» Correct option is: A. << |
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| 45. |
If sinθ = 3/5, then the value of cosθ is(A) 4/5(B) 5/3(C) 5/4(D) 3/4 |
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Answer» Correct option is: (A) \(\frac{4}{5}\) |
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| 46. |
Which one of the following is used with cin as operator ?A. <<B. >>C. >D. < |
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Answer» Correct option is: B. >> |
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| 47. |
If the roots of 2x2 - 6x + k = 0 are real and equal, find k. |
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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 |
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| 48. |
A language which has the capability to generate new data types is called…….. A. Extensible B. Overloaded C. Encapsulated D. Reprehensible |
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Answer» Correct option is: A. Extensible |
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| 49. |
Solve the following simultaneous equations. 101x + 99y = 501, 99x + 101y = 499 |
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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 |
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| 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 |
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Answer» Correct option is: B. Break; Statement |
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