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BITSAT Mathematics MCQ Practice

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81. What is the determinant of the matrix [[2, 3], [1, 4]]?

  1. A. -5
  2. B. 8
  3. C. 5
  4. D. 11
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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82. In the binomial expansion of (2 + x)³, what is the coefficient of x²?

  1. A. 12
  2. B. 6
  3. C. 8
  4. D. 3
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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83. How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition?

  1. A. 625
  2. B. 24
  3. C. 60
  4. D. 120
Answer: 120
Explanation: 120 — verified fact for BITSAT Mathematics.
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84. What is the value of ¹⁰C₇?

  1. A. 210
  2. B. 720
  3. C. 10
  4. D. 120
Answer: 120
Explanation: 120 — verified fact for BITSAT Mathematics.
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85. How many subsets does a set with 4 elements have (including the empty set and the full set)?

  1. A. 24
  2. B. 8
  3. C. 32
  4. D. 16
Answer: 16
Explanation: 16 — verified fact for BITSAT Mathematics.
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86. In the expansion of (1 + x)⁴, what is the coefficient of x²?

  1. A. 12
  2. B. 8
  3. C. 6
  4. D. 4
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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87. In the binomial expansion of (x + y)⁵, what is the coefficient of the term x²y³?

  1. A. 15
  2. B. 20
  3. C. 5
  4. D. 10
Answer: 10
Explanation: 10 — verified fact for BITSAT Mathematics.
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88. In how many distinct ways can the letters of the word 'APPLE' be arranged?

  1. A. 24
  2. B. 60
  3. C. 30
  4. D. 120
Answer: 60
Explanation: 60 — verified fact for BITSAT Mathematics.
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89. In how many ways can 5 people be seated around a circular table?

  1. A. 120
  2. B. 20
  3. C. 24
  4. D. 60
Answer: 24
Explanation: 24 — verified fact for BITSAT Mathematics.
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90. How many diagonals does a regular hexagon have?

  1. A. 9
  2. B. 12
  3. C. 15
  4. D. 6
Answer: 9
Explanation: 9 — verified fact for BITSAT Mathematics.
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91. From a group of 5 men and 4 women, in how many ways can a committee of 2 men and 1 woman be formed?

  1. A. 20
  2. B. 36
  3. C. 40
  4. D. 60
Answer: 40
Explanation: 40 — verified fact for BITSAT Mathematics.
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92. In how many ways can the letters of the word 'MATHS' (all distinct letters) be arranged?

  1. A. 120
  2. B. 24
  3. C. 60
  4. D. 720
Answer: 120
Explanation: 120 — verified fact for BITSAT Mathematics.
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93. What is the value of ⁸C₂ (combinations of 8 items taken 2 at a time)?

  1. A. 56
  2. B. 28
  3. C. 16
  4. D. 64
Answer: 28
Explanation: 28 — verified fact for BITSAT Mathematics.
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94. What is the value of ⁶P₃ (permutations of 6 items taken 3 at a time)?

  1. A. 20
  2. B. 216
  3. C. 120
  4. D. 18
Answer: 120
Explanation: 120 — verified fact for BITSAT Mathematics.
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95. In how many ways can 5 distinct books be arranged on a shelf?

  1. A. 720
  2. B. 120
  3. C. 60
  4. D. 25
Answer: 120
Explanation: 120 — verified fact for BITSAT Mathematics.
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96. How many terms of the AP 2, 4, 6, 8, ... add up to 210?

  1. A. 15
  2. B. 14
  3. C. 13
  4. D. 12
Answer: 14
Explanation: 14 — verified fact for BITSAT Mathematics.
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97. If the 5th and 9th terms of an AP are 17 and 29 respectively, what is the common difference?

  1. A. 12
  2. B. 2
  3. C. 4
  4. D. 3
Answer: 3
Explanation: 3 — verified fact for BITSAT Mathematics.
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98. What is the sum of squares of the first 10 natural numbers (1² + 2² + ... + 10²)?

  1. A. 330
  2. B. 385
  3. C. 400
  4. D. 55
Answer: 385
Explanation: 385 — verified fact for BITSAT Mathematics.
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99. What is the sum of the first 50 natural numbers?

  1. A. 1250
  2. B. 2550
  3. C. 1275
  4. D. 1225
Answer: 1275
Explanation: 1275 — verified fact for BITSAT Mathematics.
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100. In an AP, the 3rd term is 7 and the 7th term is 19. What is the first term?

  1. A. 3
  2. B. 1
  3. C. 4
  4. D. -2
Answer: 1
Explanation: 1 — verified fact for BITSAT Mathematics.
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101. What is the geometric mean of 4 and 16?

  1. A. 64
  2. B. 10
  3. C. 8
  4. D. 6
Answer: 8
Explanation: 8 — verified fact for BITSAT Mathematics.
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102. What is the arithmetic mean of 4 and 16?

  1. A. 10
  2. B. 8
  3. C. 20
  4. D. 12
Answer: 10
Explanation: 10 — verified fact for BITSAT Mathematics.
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103. What is the sum to infinity of a GP with first term 4 and common ratio 1/2?

  1. A. 4
  2. B. 8
  3. C. 6
  4. D. 16
Answer: 8
Explanation: 8 — verified fact for BITSAT Mathematics.
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104. What is the sum of the first 6 terms of a GP with first term 1 and common ratio 2?

  1. A. 32
  2. B. 63
  3. C. 64
  4. D. 31
Answer: 63
Explanation: 63 — verified fact for BITSAT Mathematics.
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105. A geometric progression has first term 2 and common ratio 3. What is its 5th term?

  1. A. 162
  2. B. 54
  3. C. 81
  4. D. 486
Answer: 162
Explanation: 162 — verified fact for BITSAT Mathematics.
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106. What is the sum of the first 20 terms of an AP with first term 2 and common difference 3?

  1. A. 620
  2. B. 600
  3. C. 610
  4. D. 590
Answer: 610
Explanation: 610 — verified fact for BITSAT Mathematics.
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107. An arithmetic progression has first term 3 and common difference 4. What is its 10th term?

  1. A. 36
  2. B. 35
  3. C. 39
  4. D. 43
Answer: 39
Explanation: 39 — verified fact for BITSAT Mathematics.
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108. If the sum of the roots of a quadratic equation is 5 and the product is 6, what is the equation?

  1. A. x² + 5x + 6 = 0
  2. B. x² - 5x - 6 = 0
  3. C. x² - 6x + 5 = 0
  4. D. x² - 5x + 6 = 0
Answer: x² - 5x + 6 = 0
Explanation: x² - 5x + 6 = 0 — verified fact for BITSAT Mathematics.
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109. For what value of k does the equation x² + kx + 4 = 0 have real and equal roots?

  1. A. k = ±8
  2. B. k = ±4
  3. C. k = ±16
  4. D. k = ±2
Answer: k = ±4
Explanation: k = ±4 — verified fact for BITSAT Mathematics.
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110. What is the discriminant of the quadratic equation 3x² + 2x - 1 = 0?

  1. A. 4
  2. B. -8
  3. C. 8
  4. D. 16
Answer: 16
Explanation: 16 — verified fact for BITSAT Mathematics.
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111. If one root of x² - kx + 12 = 0 is 4, what is the value of k?

  1. A. 4
  2. B. 12
  3. C. 7
  4. D. 3
Answer: 7
Explanation: 7 — verified fact for BITSAT Mathematics.
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112. If α and β are the roots of x² - 6x + 8 = 0, what is the value of αβ?

  1. A. 6
  2. B. -8
  3. C. 4
  4. D. 8
Answer: 8
Explanation: 8 — verified fact for BITSAT Mathematics.
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113. If α and β are the roots of x² - 6x + 8 = 0, what is the value of α + β?

  1. A. -6
  2. B. 6
  3. C. 8
  4. D. 2
Answer: 6
Explanation: 6 — verified fact for BITSAT Mathematics.
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114. If the roots of x² - 7x + k = 0 are equal, what is the value of k?

  1. A. 49/4
  2. B. 7/4
  3. C. 7
  4. D. 49
Answer: 49/4
Explanation: 49/4 — verified fact for BITSAT Mathematics.
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115. For the quadratic equation 2x² - 4x + 3 = 0, what is the nature of its roots?

  1. A. Real and equal roots
  2. B. Rational roots
  3. C. Real and distinct roots
  4. D. Complex (non-real) roots, since discriminant < 0
Answer: Complex (non-real) roots, since discriminant < 0
Explanation: Complex (non-real) roots, since discriminant < 0 — verified fact for BITSAT Mathematics.
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116. What are the roots of the quadratic equation x² - 5x + 6 = 0?

  1. A. 2 and -3
  2. B. -2 and -3
  3. C. 1 and 6
  4. D. 2 and 3
Answer: 2 and 3
Explanation: 2 and 3 — verified fact for BITSAT Mathematics.
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117. For what real value of x is the complex number z = (x - 2i)(3 + i) purely real?

  1. A. x = -2
  2. B. x = 6
  3. C. x = -6
  4. D. x = 2
Answer: x = -6
Explanation: x = -6 — verified fact for BITSAT Mathematics.
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118. What is the value of i + i² + i³ + i⁴?

  1. A. 0
  2. B. -1
  3. C. 1
  4. D. 4
Answer: 0
Explanation: 0 — verified fact for BITSAT Mathematics.
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119. How many non-real roots does x² + 1 = 0 have?

  1. A. 0
  2. B. 1
  3. C. 2
  4. D. 4
Answer: 2
Explanation: 2 — verified fact for BITSAT Mathematics.
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120. If z = 1 - i, what is z² equal to?

  1. A. -2i
  2. B. -2
  3. C. 2i
  4. D. 2
Answer: -2i
Explanation: -2i — verified fact for BITSAT Mathematics.
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121. What is the conjugate of the complex number z = 5 - 2i?

  1. A. -5 - 2i
  2. B. 5 + 2i
  3. C. 2 - 5i
  4. D. -5 + 2i
Answer: 5 + 2i
Explanation: 5 + 2i — verified fact for BITSAT Mathematics.
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122. If z1 = 2 + 3i and z2 = 1 - i, what is z1 + z2?

  1. A. 1 + 4i
  2. B. 3 - 2i
  3. C. 3 + 2i
  4. D. 1 + 2i
Answer: 3 + 2i
Explanation: 3 + 2i — verified fact for BITSAT Mathematics.
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123. What is the argument of the complex number z = -1 + i√3?

  1. A. 2π/3
  2. B. π/3
  3. C. π/6
  4. D. 5π/6
Answer: 2π/3
Explanation: 2π/3 — verified fact for BITSAT Mathematics.
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124. What is the value of (2 + 3i)(2 - 3i)?

  1. A. 4 + 9i
  2. B. 13i
  3. C. 13
  4. D. 4 - 9i
Answer: 13
Explanation: 13 — verified fact for BITSAT Mathematics.
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125. What is the modulus of the complex number z = 3 + 4i?

  1. A. 25
  2. B. 7
  3. C. 5
  4. D. 1
Answer: 5
Explanation: 5 — verified fact for BITSAT Mathematics.
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126. If ω is a complex cube root of unity (ω ≠ 1), what is the value of ω + ω²?

  1. A. 1
  2. B. 0
  3. C. -2
  4. D. -1
Answer: -1
Explanation: -1 — verified fact for BITSAT Mathematics.
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127. If |z| = 2 for a complex number z, what is |z²|?

  1. A. 4
  2. B. 2
  3. C. 16
  4. D. 8
Answer: 4
Explanation: 4 — verified fact for BITSAT Mathematics.
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128. What is the value of i^101, where i = √-1?

  1. A. 1
  2. B. -i
  3. C. i
  4. D. -1
Answer: i
Explanation: i — verified fact for BITSAT Mathematics.
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129. If z = (1+i)/(1-i), what is the value of z?

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