Defence Dreams – Mock Test Set 4

NDA Mathematics Mock Test

50 Class 11 and 12 Mathematics questions covering Algebra, Calculus and Trigonometry.

AlgebraCalculusTrigonometryAuto result

Instructions: Select one answer for every question. There is no submit button. Complete all 50 questions and the result will appear below Question 50.

Part A: Algebra

Question 1. The roots of x^2 – 7x + 12 = 0 are:

2 and 63 and 41 and 12-3 and -4

Correct answer: 3 and 4

Question 2. Sum of roots of 2x^2 – 5x + 3 = 0 is:

-5/2-3/25/23/2

Correct answer: 5/2

Question 3. The fifth term of GP 3, 6, 12, … is:

24364896

Correct answer: 48

Question 4. Coefficient of x^2 in (1+x)^5 is:

5101520

Correct answer: 10

Question 5. Determinant of [[1,2],[3,4]] is:

-22510

Correct answer: -2

Question 6. The complex number (1+i)^2 equals:

12i1+i-2i

Correct answer: 2i

Question 7. log base 2 of 8 is:

23/234

Correct answer: 3

Question 8. The 10th term of AP 5, 8, 11, … is:

29303132

Correct answer: 32

Question 9. Number of ways to arrange 5 distinct objects is:

2560120240

Correct answer: 120

Question 10. Probability of getting a prime number on one die is:

1/31/22/31/6

Correct answer: 1/2

Question 11. Coefficient of x^3 in (1+x)^6 is:

10152030

Correct answer: 20

Question 12. Discriminant of x^2 + 4x + 5 is:

-404-16

Correct answer: -4

Question 13. If f(x)=2x-3, then f inverse of x is:

2x+3(x+3)/2(x-3)/23-2x

Correct answer: (x+3)/2

Question 14. If x+y=7 and x-y=1, x equals:

4378

Correct answer: 4

Question 15. Modulus of 3-4i is:

3457

Correct answer: 5

Question 16. Solutions of |x-2|=3 are:

2 and 35 and -1-5 and 13 and -3

Correct answer: 5 and -1

Question 17. Sum of first 10 terms of AP 3,5,7,… is:

100120140160

Correct answer: 120

Part B: Calculus

Question 18. Derivative of x^4-2x is:

x^3-24x^2-24x^3-24x^3+2

Correct answer: 4x^3-2

Question 19. Derivative of sin x is:

-sin xcos xtan xsec x

Correct answer: cos x

Question 20. Derivative of ln x is:

1/xxln xe^x

Correct answer: 1/x

Question 21. Integral of 2x dx is:

2x^2+Cx^2+Cx+C2+C

Correct answer: x^2+C

Question 22. Integral from 0 to 2 of x dx is:

1234

Correct answer: 2

Question 23. Limit as x approaches 0 of sin(5x)/x is:

01510

Correct answer: 5

Question 24. Slope of tangent to y=x^2 at x=3 is:

3569

Correct answer: 6

Question 25. Minimum point of x^2-4x is at x:

024-2

Correct answer: 2

Question 26. Derivative of e^x is:

1x e^(x-1)e^xln x

Correct answer: e^x

Question 27. Integral of sec^2 x dx is:

tan x+Csec x+Csin x+Ccos x+C

Correct answer: tan x+C

Question 28. If dy/dx=3x^2, then y is:

x^3+C3x^3+Cx^2+C3x+C

Correct answer: x^3+C

Question 29. Area under y=4-x^2 from -2 to 2 is:

8/316/3832/3

Correct answer: 32/3

Question 30. Second derivative of sin x is:

sin xcos x-sin x-cos x

Correct answer: -sin x

Question 31. Limit as x approaches 0 of sin(5x)/x is:

01510

Correct answer: 5

Question 32. For f(x)=x^3-3x, f'(2) is:

36912

Correct answer: 9

Question 33. Integral of 1/x dx is:

x^2/2+Cln|x|+C1/x^2+Ce^x+C

Correct answer: ln|x|+C

Question 34. Solution of dy/dx=y with y(0)=1 is:

xx^21+xe^x

Correct answer: e^x

Part C: Trigonometry

Question 35. sin^2 theta + cos^2 theta equals:

021tan theta

Correct answer: 1

Question 36. tan 45 degrees is:

01sqrt 3undefined

Correct answer: 1

Question 37. sin 30 degrees is:

01/2sqrt 3/21

Correct answer: 1/2

Question 38. cos 60 degrees is:

01/2sqrt 3/21

Correct answer: 1/2

Question 39. sec^2 x – tan^2 x equals:

10sec xtan x

Correct answer: 1

Question 40. sin(A+B) equals:

sin A cos B + cos A sin Bsin A cos B – cos A sin Bcos A cos Bsin A sin B

Correct answer: sin A cos B + cos A sin B

Question 41. cos pi equals:

0-11pi

Correct answer: -1

Question 42. General solution of sin theta=0 is:

theta=n pitheta=pi/2+n pitheta=2n pi+pi/2theta=45 degrees

Correct answer: theta=n pi

Question 43. 180 degrees in radians is:

pi/22 pipipi/4

Correct answer: pi

Question 44. tan x is undefined at:

0pi/2pi2 pi

Correct answer: pi/2

Question 45. sin 2x equals:

sin x cos xsin x + cos x2 sin x cos xsin x – cos x

Correct answer: 2 sin x cos x

Question 46. cos 2x can be written as:

1-2 sin^2 x2 sin^2 x-12 sin xsin x cos x

Correct answer: 1-2 sin^2 x

Question 47. The sine rule is:

a/sin A = b/sin B = c/sin Ca cos A = b cos Ba+b=csin A+sin B=sin C

Correct answer: a/sin A = b/sin B = c/sin C

Question 48. If tan theta=3/4 and theta is acute, sin theta is:

4/51/23/55/3

Correct answer: 3/5

Question 49. In 0 to 2 pi, 2 sin x=sqrt 3 gives:

pi/3 and 2pi/3pi/6 and 5pi/6pi/4 and 3pi/4pi/2 only

Correct answer: pi/3 and 2pi/3

Question 50. In 0 to 2 pi, cos x=0 gives:

0 and pipi/2 and 3pi/2pi/4 and 5pi/4pi/3 and 5pi/3

Correct answer: pi/2 and 3pi/2