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BITSAT Mathematics MCQ Practice

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1. In how many ways can a committee of 3 people be chosen from a group of 7 people?

  1. A. 210
  2. B. 35
  3. C. 42
  4. D. 21
Answer: 35
Explanation: 35 — verified fact for BITSAT Mathematics.
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2. What is the mode of the data set 2, 3, 3, 4, 5, 3?

  1. A. 2
  2. B. 5
  3. C. 3
  4. D. 4
Answer: 3
Explanation: 3 — verified fact for BITSAT Mathematics.
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3. What is the median of the data set 3, 5, 7, 9, 11?

  1. A. 5
  2. B. 6
  3. C. 7
  4. D. 9
Answer: 7
Explanation: 7 — verified fact for BITSAT Mathematics.
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4. What is the standard deviation of the data set 2, 4, 6, 8, 10?

  1. A. 8
  2. B. 4
  3. C. 2√2
  4. D. 2
Answer: 2√2
Explanation: 2√2 — verified fact for BITSAT Mathematics.
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5. What is the equation of the tangent to the curve y = x² + 1 at the point (1, 2)?

  1. A. y = 2x
  2. B. y = x + 1
  3. C. y = 2x + 1
  4. D. y = 2x - 1
Answer: y = 2x
Explanation: y = 2x — verified fact for BITSAT Mathematics.
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6. For what values of x is the function f(x) = x² - 4x + 3 strictly increasing?

  1. A. x < 2
  2. B. x > 4
  3. C. x > 2
  4. D. x < -2
Answer: x > 2
Explanation: x > 2 — verified fact for BITSAT Mathematics.
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7. The area A of a circle of radius r is A = πr². What is the rate of change of A with respect to r when r = 5?

  1. A. 5π
  2. B. 20π
  3. C. 25π
  4. D. 10π
Answer: 10π
Explanation: 10π — verified fact for BITSAT Mathematics.
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8. What are the direction cosines of the vector i + j + √2 k?

  1. A. (1, 1, √2)
  2. B. (1/2, 1/2, √2/2)
  3. C. (1/4, 1/4, 1/2)
  4. D. (1/√2, 1/√2, 1)
Answer: (1/2, 1/2, √2/2)
Explanation: (1/2, 1/2, √2/2) — verified fact for BITSAT Mathematics.
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9. In a linear programming problem, what is the term for the set of all points satisfying every constraint simultaneously?

  1. A. Objective region
  2. B. Optimal region
  3. C. Feasible region
  4. D. Boundary region
Answer: Feasible region
Explanation: Feasible region — verified fact for BITSAT Mathematics.
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10. An LPP objective function is Z = 3x + 4y. The feasible region's corner points are (0,0), (4,0), (0,3), and (2,2). At which point is Z maximised?

  1. A. (0, 0), giving Z = 0
  2. B. (4, 0), giving Z = 12
  3. C. (2, 2), giving Z = 14
  4. D. (0, 3), giving Z = 12
Answer: (2, 2), giving Z = 14
Explanation: (2, 2), giving Z = 14 — verified fact for BITSAT Mathematics.
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11. Two fair dice are rolled. What is the probability that both dice show the same number?

  1. A. 1/36
  2. B. 1/6
  3. C. 1/12
  4. D. 1/3
Answer: 1/6
Explanation: 1/6 — verified fact for BITSAT Mathematics.
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12. If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, what is P(A ∪ B)?

  1. A. 1.1
  2. B. 0.9
  3. C. 0.7
  4. D. 0.3
Answer: 0.7
Explanation: 0.7 — verified fact for BITSAT Mathematics.
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13. What is the mean of the data set 2, 4, 6, 8, 10?

  1. A. 6
  2. B. 5
  3. C. 30
  4. D. 8
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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14. A card is drawn at random from a standard deck of 52 playing cards. What is the probability it is a king?

  1. A. 1/52
  2. B. 1/13
  3. C. 1/4
  4. D. 4/13
Answer: 1/13
Explanation: 1/13 — verified fact for BITSAT Mathematics.
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15. Two fair dice are rolled together. What is the probability that the sum of the numbers is 7?

  1. A. 1/12
  2. B. 1/6
  3. C. 1/3
  4. D. 1/36
Answer: 1/6
Explanation: 1/6 — verified fact for BITSAT Mathematics.
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16. A fair coin is tossed once. What is the probability of getting a head?

  1. A. 1/2
  2. B. 1/4
  3. C. 1
  4. D. 1/3
Answer: 1/2
Explanation: 1/2 — verified fact for BITSAT Mathematics.
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17. Two vectors a and b satisfy a·b = 0 (both non-zero). What can be concluded about them?

  1. A. They are equal
  2. B. They are parallel to each other
  3. C. They are perpendicular to each other
  4. D. They have the same magnitude
Answer: They are perpendicular to each other
Explanation: They are perpendicular to each other — verified fact for BITSAT Mathematics.
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18. What is the unit vector in the direction of the vector 3i + 4j?

  1. A. 3i + 4j
  2. B. (3/5)i + (4/5)j
  3. C. (3/7)i + (4/7)j
  4. D. (4/5)i + (3/5)j
Answer: (3/5)i + (4/5)j
Explanation: (3/5)i + (4/5)j — verified fact for BITSAT Mathematics.
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19. What is the distance between the points (1, 2, 3) and (4, 6, 3) in 3D space?

  1. A. 4
  2. B. 5
  3. C. 25
  4. D. 6
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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20. What is the cross product of the unit vectors i and j?

  1. A. 1
  2. B. k
  3. C. -k
  4. D. i
Answer: k
Explanation: k — verified fact for BITSAT Mathematics.
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21. What is the dot product of vectors (1, 2, 3) and (4, 5, 6)?

  1. A. 32
  2. B. 15
  3. C. 21
  4. D. 46
Answer: 32
Explanation: 32 — verified fact for BITSAT Mathematics.
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22. What is the magnitude of the vector a = 2i + 3j + 4k?

  1. A. √14
  2. B. 29
  3. C. √29
  4. D. 9
Answer: √29
Explanation: √29 — verified fact for BITSAT Mathematics.
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23. Is the function f(x) = |x| differentiable at x = 0?

  1. A. No, it is continuous but not differentiable at x = 0
  2. B. No, it is not even continuous at x = 0
  3. C. Yes, it is differentiable everywhere
  4. D. Yes, but only from the right
Answer: No, it is continuous but not differentiable at x = 0
Explanation: No, it is continuous but not differentiable at x = 0 — verified fact for BITSAT Mathematics.
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24. What is the general solution of the differential equation dy/dx = 2x?

  1. A. y = x + C
  2. B. y = x²/2 + C
  3. C. y = 2x² + C
  4. D. y = x² + C
Answer: y = x² + C
Explanation: y = x² + C — verified fact for BITSAT Mathematics.
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25. What is the value of ∫(1/x) dx for x > 0?

  1. A. -1/x² + C
  2. B. ln|x| + C
  3. C. 1/x² + C
  4. D. x ln x + C
Answer: ln|x| + C
Explanation: ln|x| + C — verified fact for BITSAT Mathematics.
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26. What is the order of the differential equation d²y/dx² + y = 0?

  1. A. 1
  2. B. 2
  3. C. 3
  4. D. 0
Answer: 2
Explanation: 2 — verified fact for BITSAT Mathematics.
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27. What is the maximum value of the function f(x) = -x² + 4x + 1?

  1. A. 9
  2. B. 4
  3. C. 1
  4. D. 5
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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28. For the function f(x) = -x² + 4x + 1, at what value of x does the maximum occur?

  1. A. x = 4
  2. B. x = 2
  3. C. x = 1
  4. D. x = -2
Answer: x = 2
Explanation: x = 2 — verified fact for BITSAT Mathematics.
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29. What is the slope of the tangent to the curve y = x² at the point x = 3?

  1. A. 3
  2. B. 6
  3. C. 9
  4. D. 12
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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30. What is the value of ∫eˣ dx?

  1. A. eˣ + C
  2. B. e + C
  3. C. xeˣ + C
  4. D. eˣ⁺¹/(x+1) + C
Answer: eˣ + C
Explanation: eˣ + C — verified fact for BITSAT Mathematics.
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31. What is the value of the definite integral ∫₀¹ x² dx?

  1. A. 3
  2. B. 1
  3. C. 1/3
  4. D. 1/2
Answer: 1/3
Explanation: 1/3 — verified fact for BITSAT Mathematics.
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32. What is the value of ∫cos x dx?

  1. A. sin x + C
  2. B. -cos x + C
  3. C. cos x + C
  4. D. -sin x + C
Answer: sin x + C
Explanation: sin x + C — verified fact for BITSAT Mathematics.
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33. What is the value of the indefinite integral ∫x² dx?

  1. A. 3x² + C
  2. B. x³/3 + C
  3. C. 2x + C
  4. D. x³ + C
Answer: x³/3 + C
Explanation: x³/3 + C — verified fact for BITSAT Mathematics.
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34. What is the value of the derivative of f(x) = x³ - 3x at x = 2?

  1. A. 6
  2. B. 9
  3. C. 12
  4. D. 5
Answer: 9
Explanation: 9 — verified fact for BITSAT Mathematics.
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35. What is the derivative of ln x with respect to x (for x > 0)?

  1. A. ln x
  2. B. 1/x
  3. C. 1/x²
  4. D. x
Answer: 1/x
Explanation: 1/x — verified fact for BITSAT Mathematics.
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36. Using the product rule, what is the derivative of x²·sin x?

  1. A. 2x sin x - x²cos x
  2. B. 2x sin x + x²cos x
  3. C. x²cos x
  4. D. 2x cos x
Answer: 2x sin x + x²cos x
Explanation: 2x sin x + x²cos x — verified fact for BITSAT Mathematics.
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37. What is the derivative of sin x with respect to x?

  1. A. -cos x
  2. B. -sin x
  3. C. cos x
  4. D. sec²x
Answer: cos x
Explanation: cos x — verified fact for BITSAT Mathematics.
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38. What is the derivative of x³ with respect to x?

  1. A. 3x
  2. B. x²
  3. C. 3x²
  4. D. x³/3
Answer: 3x²
Explanation: 3x² — verified fact for BITSAT Mathematics.
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39. What is the value of lim(x→∞) (3x² + 2)/(x² + 1)?

  1. A. ∞
  2. B. 3
  3. C. 0
  4. D. 1
Answer: 3
Explanation: 3 — verified fact for BITSAT Mathematics.
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40. What is the value of lim(x→2) (x² - 4)/(x - 2)?

  1. A. 2
  2. B. 0
  3. C. undefined
  4. D. 4
Answer: 4
Explanation: 4 — verified fact for BITSAT Mathematics.
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41. What is the value of lim(x→0) (sin x)/x?

  1. A. 1
  2. B. 0
  3. C. ∞
  4. D. -1
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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42. What is the equation of the line with slope 2 passing through the origin?

  1. A. y = x + 2
  2. B. 2x + y = 0
  3. C. x = 2y
  4. D. y = 2x
Answer: y = 2x
Explanation: y = 2x — verified fact for BITSAT Mathematics.
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43. For the ellipse x²/25 + y²/9 = 1, what is the length of the major axis?

  1. A. 5
  2. B. 6
  3. C. 10
  4. D. 3
Answer: 10
Explanation: 10 — verified fact for BITSAT Mathematics.
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44. What is the length of the latus rectum of the parabola y² = 8x?

  1. A. 4
  2. B. 16
  3. C. 8
  4. D. 2
Answer: 8
Explanation: 8 — verified fact for BITSAT Mathematics.
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45. What is the area of the triangle with vertices (0, 0), (4, 0), and (0, 3)?

  1. A. 6
  2. B. 3.5
  3. C. 7
  4. D. 12
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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46. What is the eccentricity of the hyperbola x²/16 - y²/9 = 1?

  1. A. 3/4
  2. B. 4/3
  3. C. 5/4
  4. D. 4/5
Answer: 5/4
Explanation: 5/4 — verified fact for BITSAT Mathematics.
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47. What is the eccentricity of the ellipse x²/25 + y²/9 = 1?

  1. A. 4/5
  2. B. 3/5
  3. C. 16/25
  4. D. 5/4
Answer: 4/5
Explanation: 4/5 — verified fact for BITSAT Mathematics.
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48. For the parabola y² = 8x, what are the coordinates of the focus?

  1. A. (8, 0)
  2. B. (2, 0)
  3. C. (4, 0)
  4. D. (0, 2)
Answer: (2, 0)
Explanation: (2, 0) — verified fact for BITSAT Mathematics.
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49. What is the radius of the circle x² + y² - 4x - 6y + 4 = 0?

  1. A. 4
  2. B. 3
  3. C. 9
  4. D. 2
Answer: 3
Explanation: 3 — verified fact for BITSAT Mathematics.
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50. What is the centre of the circle x² + y² - 4x - 6y + 4 = 0?

  1. A. (2, -3)
  2. B. (4, 6)
  3. C. (-2, -3)
  4. D. (2, 3)
Answer: (2, 3)
Explanation: (2, 3) — verified fact for BITSAT Mathematics.
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51. What is the radius of the circle x² + y² = 9?

  1. A. 3
  2. B. 6
  3. C. 9
  4. D. 81
Answer: 3
Explanation: 3 — verified fact for BITSAT Mathematics.
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52. What is the equation of a circle with centre (2, 3) and radius 5?

  1. A. (x - 2)² + (y - 3)² = 25
  2. B. (x - 3)² + (y - 2)² = 25
  3. C. (x + 2)² + (y + 3)² = 25
  4. D. (x - 2)² + (y - 3)² = 5
Answer: (x - 2)² + (y - 3)² = 25
Explanation: (x - 2)² + (y - 3)² = 25 — verified fact for BITSAT Mathematics.
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53. What is the perpendicular distance from the point (3, 4) to the line 3x + 4y - 5 = 0?

  1. A. 3
  2. B. 5
  3. C. 20
  4. D. 4
Answer: 4
Explanation: 4 — verified fact for BITSAT Mathematics.
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54. What is the midpoint of the line segment joining (2, 3) and (6, 7)?

  1. A. (4, 4)
  2. B. (8, 10)
  3. C. (4, 5)
  4. D. (3, 4)
Answer: (4, 5)
Explanation: (4, 5) — verified fact for BITSAT Mathematics.
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55. What is the slope of the line 2x + 3y = 6?

  1. A. -3/2
  2. B. 2/3
  3. C. -2/3
  4. D. 3/2
Answer: -2/3
Explanation: -2/3 — verified fact for BITSAT Mathematics.
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56. What is the slope of the line passing through the points (1, 1) and (3, 5)?

  1. A. 4
  2. B. 1/2
  3. C. -2
  4. D. 2
Answer: 2
Explanation: 2 — verified fact for BITSAT Mathematics.
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57. What is the distance between the points (1, 2) and (4, 6)?

  1. A. 5
  2. B. 6
  3. C. 4
  4. D. 25
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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58. What is the value of cos 0° + sin 90°?

  1. A. -1
  2. B. 1
  3. C. 2
  4. D. 0
Answer: 2
Explanation: 2 — verified fact for BITSAT Mathematics.
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59. In a triangle, if two angles are 45° and 60°, what is the third angle?

  1. A. 60°
  2. B. 105°
  3. C. 75°
  4. D. 90°
Answer: 75°
Explanation: 75° — verified fact for BITSAT Mathematics.
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60. What is the value of tan 60° × tan 30°?

  1. A. 3
  2. B. 1/√3
  3. C. √3
  4. D. 1
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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61. What is the general solution of the equation sinθ = 0?

  1. A. θ = 2nπ, n ∈ Z
  2. B. θ = nπ, n ∈ Z
  3. C. θ = nπ/2, n ∈ Z
  4. D. θ = (2n+1)π/2, n ∈ Z
Answer: θ = nπ, n ∈ Z
Explanation: θ = nπ, n ∈ Z — verified fact for BITSAT Mathematics.
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62. What is the principal period of the function f(x) = sin x?

  1. A. π/2
  2. B. 4π
  3. C. π
  4. D. 2π
Answer: 2π
Explanation: 2π — verified fact for BITSAT Mathematics.
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63. What is the exact value of sin 75°?

  1. A. (√2 + 1)/2
  2. B. (√3 + 1)/2
  3. C. (√6 + √2)/4
  4. D. (√6 - √2)/4
Answer: (√6 + √2)/4
Explanation: (√6 + √2)/4 — verified fact for BITSAT Mathematics.
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64. If sinθ = 3/5 and θ is acute, what is the value of cosθ?

  1. A. 4/5
  2. B. 5/4
  3. C. 5/3
  4. D. 3/4
Answer: 4/5
Explanation: 4/5 — verified fact for BITSAT Mathematics.
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65. What is the value of cos²30° - sin²30°?

  1. A. 1/2
  2. B. 1
  3. C. 0
  4. D. √3/2
Answer: 1/2
Explanation: 1/2 — verified fact for BITSAT Mathematics.
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66. What is the value of sec²θ - tan²θ for any angle θ?

  1. A. 2
  2. B. 1
  3. C. -1
  4. D. 0
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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67. What is the value of 2 sin 30° cos 30° (using the identity 2sinθcosθ = sin2θ)?

  1. A. √3
  2. B. 1/2
  3. C. 1
  4. D. √3/2
Answer: √3/2
Explanation: √3/2 — verified fact for BITSAT Mathematics.
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68. Using the identity sin(A - B) = sinA cosB - cosA sinB, what is the exact value of sin 15°?

  1. A. (√2 - 1)/2
  2. B. (√6 - √2)/4
  3. C. (√6 + √2)/4
  4. D. (√3 - 1)/2
Answer: (√6 - √2)/4
Explanation: (√6 - √2)/4 — verified fact for BITSAT Mathematics.
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69. What is the value of cos 120°?

  1. A. 1/2
  2. B. -√3/2
  3. C. √3/2
  4. D. -1/2
Answer: -1/2
Explanation: -1/2 — verified fact for BITSAT Mathematics.
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70. What is the value of tan 45°?

  1. A. 1/√3
  2. B. 1
  3. C. 0
  4. D. √3
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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71. What is the value of sin 30° + cos 60°?

  1. A. √3/2
  2. B. 1/2
  3. C. 1
  4. D. 0
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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72. If A is a 3×3 matrix with |A| = 5, what is the value of |2A|?

  1. A. 20
  2. B. 5
  3. C. 40
  4. D. 10
Answer: 40
Explanation: 40 — verified fact for BITSAT Mathematics.
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73. What is the determinant of the 3×3 diagonal matrix with diagonal entries 1, 2, 3?

  1. A. 3
  2. B. 6
  3. C. 1
  4. D. 36
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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74. What is the inverse of the diagonal matrix [[2, 0], [0, 3]]?

  1. A. [[1/2, 0], [0, 1/3]]
  2. B. [[-2, 0], [0, -3]]
  3. C. [[1/3, 0], [0, 1/2]]
  4. D. [[2, 0], [0, 3]]
Answer: [[1/2, 0], [0, 1/3]]
Explanation: [[1/2, 0], [0, 1/3]] — verified fact for BITSAT Mathematics.
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75. What is the trace (sum of diagonal elements) of the matrix [[1, 2], [3, 4]]?

  1. A. 5
  2. B. 4
  3. C. -2
  4. D. 10
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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76. For what value of k is the matrix [[2, 4], [1, k]] singular (determinant zero)?

  1. A. k = -2
  2. B. k = 4
  3. C. k = 0
  4. D. k = 2
Answer: k = 2
Explanation: k = 2 — verified fact for BITSAT Mathematics.
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77. What is the transpose of the matrix [[1, 2, 3], [4, 5, 6]]?

  1. A. [[1, 4], [2, 5], [3, 6]]
  2. B. [[4, 5, 6], [1, 2, 3]]
  3. C. [[1, 2, 3], [4, 5, 6]]
  4. D. [[6, 5, 4], [3, 2, 1]]
Answer: [[1, 4], [2, 5], [3, 6]]
Explanation: [[1, 4], [2, 5], [3, 6]] — verified fact for BITSAT Mathematics.
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78. If matrix A has order 2×3 and matrix B has order 3×2, what is the order of the product AB?

  1. A. 3×2
  2. B. 3×3
  3. C. 2×2
  4. D. 2×3
Answer: 2×2
Explanation: 2×2 — verified fact for BITSAT Mathematics.
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79. If A = [[1, 2], [3, 4]], what is the element in the first row, first column of A²?

  1. A. 10
  2. B. 7
  3. C. 15
  4. D. 1
Answer: 7
Explanation: 7 — verified fact for BITSAT Mathematics.
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80. What is the determinant of the matrix [[1, 2], [3, 4]]?

  1. A. -10
  2. B. 10
  3. C. -2
  4. D. 2
Answer: -2
Explanation: -2 — verified fact for BITSAT Mathematics.
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