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MCQOPTIONS
This section includes 1894 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
If the vectors \({\rm{\alpha \hat i}} + {\rm{\alpha \hat j}} + {\rm{\gamma \hat k}},{\rm{\;\hat i}} + {\rm{\hat k}}\) and \({\rm{\gamma \hat i}} + {\rm{\gamma \hat j}} + {\rm{\beta \hat k}}\) lie on a plane, where α, β and γ are distinct non-negative numbers, then γ is |
| A. | Arithmetic mean of α and β |
| B. | Geometric mean of α and β |
| C. | Harmonic mean of α and β |
| D. | None of the above |
| Answer» C. Harmonic mean of α and β | |
| 52. |
If a4 + 1/a4 = 50, a > 0 ,then find the value of a3 + 1/a3. |
| A. | \(\sqrt {2(1 + \sqrt {13} } ) + \left( { - 1 + 2\sqrt {13} } \right)\) |
| B. | \(\sqrt {2(1 + \sqrt {13} } ) - \left( { - 1 - 2\sqrt {13} } \right)\) |
| C. | \(\sqrt {2(1 + \sqrt {13} } )\left( { - 1 + 2\sqrt {13} } \right)\) |
| D. | \(\sqrt {2(1 - \sqrt {13} } )\left( { - 1 + 2\sqrt {13} } \right)\) |
| Answer» D. \(\sqrt {2(1 - \sqrt {13} } )\left( { - 1 + 2\sqrt {13} } \right)\) | |
| 53. |
If 24√3x3 + 5√5y3 = (2√3x + √5y) × (Ax2 - Bxy + Cy2), then what is the value of (A2 - B2 + C2) ? |
| A. | 189 |
| B. | 111 |
| C. | 109 |
| D. | 169 |
| Answer» D. 169 | |
| 54. |
If a2 + b2 = 80 and ab = 32, then calculate the value of \(\frac{{a - b}}{{a + b}}\). |
| A. | 0.337 |
| B. | 0.339 |
| C. | 0.333 |
| D. | 0.335 |
| Answer» D. 0.335 | |
| 55. |
Find the value of 'x', if 50x = 6482 - 2482 |
| A. | 6980 |
| B. | 7168 |
| C. | 6880 |
| D. | 7190 |
| Answer» C. 6880 | |
| 56. |
In the given matrix \(\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&2\\ 0&1&0\\ 1&2&1 \end{array}} \right]\), one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are |
| A. | {(4, 2, 1)|𝛼 ≠ 0, 𝛼 ∈ ℝ} |
| B. | {(−4, 2, 1)|𝛼 ≠ 0, 𝛼∈ℝ} |
| C. | \(\left\{ {\alpha \left( {\sqrt 2 0,\;1} \right){\rm{|}}\alpha \; \ne \;0,\;\alpha \in } \mathbb{R} \right\}\) |
| D. | \($\left\{ {\alpha \left( { - \sqrt 2 ,\;0,\;1} \right)|\alpha \; \ne \;0,\;\alpha \epsilon \mathbb{R} } \right\}\;$\) |
| Answer» C. \(\left\{ {\alpha \left( {\sqrt 2 0,\;1} \right){\rm{|}}\alpha \; \ne \;0,\;\alpha \in } \mathbb{R} \right\}\) | |
| 57. |
If \(x(5 - \frac{2}{x}) = \frac{5}{x}\), then the value of \(x^2 + \frac{1}{x^2}\) is equal to: |
| A. | \(2\frac{4}{25}\) |
| B. | \(2\frac{1}{25}\) |
| C. | \(\frac{4}{25}\) |
| D. | \(2\frac{3}{25}\) |
| Answer» B. \(2\frac{1}{25}\) | |
| 58. |
If x2 + kx + k = 0 has repeated roots, then the value of k will satisfy: |
| A. | k < 0 or k > 4 |
| B. | k = 4 only |
| C. | k = 4 or k = 0 |
| D. | 0 < k < 4 |
| Answer» D. 0 < k < 4 | |
| 59. |
In a given fraction, if the numerator is multiplied by 3 and denominator is increased by 1, we get \(\frac{7}{6}\). But if the numerator is increased by 4 and the denominator is decreased by 3, then we get \(\frac{1}{2}.\) Find the fraction? |
| A. | \(\frac{{28}}{{25}}\) |
| B. | \(\frac{{37}}{{52}}\) |
| C. | \(\frac{{21}}{{53}}\) |
| D. | \(\frac{{42}}{{81}}\) |
| Answer» D. \(\frac{{42}}{{81}}\) | |
| 60. |
Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram? |
| A. | 30 years |
| B. | 32 years |
| C. | 36 years |
| D. | 40 years |
| Answer» C. 36 years | |
| 61. |
If a + b = 10 and ab = 5, then what is the value of a2 + b2? |
| A. | 80 |
| B. | 90 |
| C. | 100 |
| D. | 110 |
| Answer» C. 100 | |
| 62. |
In the following questions two equations numbered I and II are given. You have to solve both the equations and –I) x2 – 7x + 12 = 0II) y2 + 12y + 32 = 0 |
| A. | If x > y |
| B. | If x ≥ y |
| C. | If x < y |
| D. | If x ≤ y |
| E. | If x = y or the relationship can not be established |
| Answer» B. If x ≥ y | |
| 63. |
If x + 1/x = √3, then the value of x18 + x12 + x6 + 1 is: |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 64. |
Consider the following system of equations2x1 + x2 + x3 = 0,x2 – x3 = 0,x1 + x2 = 0,This system has |
| A. | A unique solution |
| B. | No solution |
| C. | Infinite number of solutions |
| D. | Five solutions |
| Answer» D. Five solutions | |
| 65. |
If x = 2, y = 1, z = -3 then x3 + y3 + z3 - 3xyz equals |
| A. | 6 |
| B. | 2 |
| C. | 8 |
| D. | 0 |
| Answer» E. | |
| 66. |
A + B = 10, A - B = 2, A2 - B2 = ? |
| A. | 30 |
| B. | 40 |
| C. | 20 |
| D. | 80 |
| Answer» D. 80 | |
| 67. |
\(\dfrac{(5.5)^4 - (3.5)^4}{(5.5)^2 + (3.5)^2}\) is equal to: |
| A. | 180 |
| B. | 18 |
| C. | 42.5 |
| D. | 1.8 |
| Answer» C. 42.5 | |
| 68. |
Given that217x + 131y = 913131x + 217y = 827then x and y are respectively |
| A. | 5 and 7 |
| B. | 3 and 2 |
| C. | -5 and -7 |
| D. | 2 and 5 |
| E. | None of the above/More than one of the above |
| Answer» C. -5 and -7 | |
| 69. |
Given that (x + 2) and (x + 3) are factor of x3 + ax + b, the values of a and b and the remaining factor is: |
| A. | a = -7, b = -6, (x + 1) |
| B. | a = -5, b = 4, (x + 1) |
| C. | a = 5, b = 2, (x + 2) |
| D. | a = -19, b = -30, (x - 5) |
| Answer» E. | |
| 70. |
If the cost of 2 tables and 3 chairs is Rs. 500, then find the cost of 8 tables and 12 chairs? |
| A. | Rs. 2200 |
| B. | Rs. 2000 |
| C. | Rs. 3000 |
| D. | Rs. 1800 |
| Answer» C. Rs. 3000 | |
| 71. |
If \(Y = \;\frac{{2 - X}}{{1 + X}}\), then what is the value of \(\frac{1}{{Y + 1}} + \frac{{2Y + 1}}{{{Y^2} - 1}}?\) |
| A. | \(\frac{{\left( {1 + X} \right)\;\left( {2 - X} \right)}}{{2X - 1}}\) |
| B. | \(\frac{{\left( {1 - X} \right)\;\left( {2 + X} \right)}}{{X - 1}}\) |
| C. | \(\frac{{\left( {1 + X} \right)\;\left( {2 - X} \right)}}{{1 - 2X}}\) |
| D. | \(\frac{{\left( {1 + X} \right)\;\left( {1 - 2X} \right)}}{{2 - X}}\) |
| Answer» D. \(\frac{{\left( {1 + X} \right)\;\left( {1 - 2X} \right)}}{{2 - X}}\) | |
| 72. |
If a + b = 8, ab = – 12, then a3 + b3 = ? |
| A. | 833 |
| B. | –244 |
| C. | 800 |
| D. | –833 |
| Answer» D. –833 | |
| 73. |
If x + y + z = 0, then what is the value of \(\frac{{{x^2}}}{{3z}} + \frac{{{y^3}}}{{3xz}} + \frac{{{z^2}}}{{3x}}\)? |
| A. | 0 |
| B. | xz |
| C. | y |
| D. | 3y |
| Answer» D. 3y | |
| 74. |
Let \(\vec{a}=\hat{i}-\hat{j},\text{ }\!\!~\!\!\text{ }\vec{b}=\hat{i}+\hat{j}+\hat{k}\text{ }\!\!~\!\!\text{ and }\!\!~\!\!\text{ }\vec{c}\) be a vector such that \(\vec{a}\times \vec{c}+\vec{b}=\vec{0}\text{ }\!\!~\!\!\text{ and }\!\!~\!\!\text{ }\vec{a}\cdot \vec{c}=4,~\text{then }\!\!~\!\!\text{ }{{\left| {\vec{c}} \right|}^{2}}\) is equal to: |
| A. | \(\frac{19}{2}\) |
| B. | 9 |
| C. | 8 |
| D. | \(\frac{17}{2}\) |
| Answer» B. 9 | |
| 75. |
If x - 2y = 3 and xy = 5, find the value of x2 - 4y2 |
| A. | 21 |
| B. | 20 |
| C. | 23 |
| D. | 22 |
| Answer» B. 20 | |
| 76. |
If the root of p(x) = 0 is \(\sqrt{2}\), then the zero of p(x) is _______. |
| A. | -2 |
| B. | 2 |
| C. | 0 |
| D. | \(\sqrt{2}\) |
| Answer» E. | |
| 77. |
Fill up the blanks \(\left( {3\;4\;7} \right)\left[ {\begin{array}{*{20}{c}}1\\2\\?\end{array}} \right] = 18\) |
| A. | 2 |
| B. | 4 |
| C. | 1 |
| D. | 5 |
| Answer» D. 5 | |
| 78. |
If (x – 2)3 + (x – 3)3 + (x – 10)3 = (x – 2) (x – 3) (3x – 30), then what is the value of x? |
| A. | 7 |
| B. | 5 |
| C. | 18 |
| D. | 3 |
| Answer» C. 18 | |
| 79. |
If (10a3 + 4b3) : (11a3 - 15b3) = 7 : 5, then (3a + 5b) : (9a - 2b) =? |
| A. | 3 : 2 |
| B. | 10 : 13 |
| C. | 8 : 7 |
| D. | 5 : 4 |
| Answer» C. 8 : 7 | |
| 80. |
If 3a = 27b = 81c and abc = 144, then the value of \(12\left( {\frac{1}{a} + \frac{1}{{2b}} + \frac{1}{{5c}}} \right)\) is: |
| A. | 17/120 |
| B. | 18/10 |
| C. | 33/10 |
| D. | 18/120 |
| Answer» D. 18/120 | |
| 81. |
If the quadratic equation (a2 - b2) x2 + (b2 - c2) x + c2 - a2 = 0 has equal roots, then which of the following is true: |
| A. | b2 = c2 + 2a2 |
| B. | b2 + c2 = 2a2 |
| C. | b2 - c2 = 2a2 |
| D. | b2 + c2 = a2 |
| Answer» C. b2 - c2 = 2a2 | |
| 82. |
Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors, no two of which are collinear. If the vector \(\vec{a}+2\vec{b}\) is collinear with \(\vec{c}\) and \(\vec{b}+3\vec{c}\) is collinear with \(\vec{a}\), then \(\vec{a} + 2\vec{b}+6\vec{c}\) is equal to |
| A. | \(\lambda \vec{a}\) |
| B. | \(\lambda \vec{b}\) |
| C. | \(\lambda \vec{c}\) |
| D. | \(\vec{0}\) |
| Answer» E. | |
| 83. |
If \(\sqrt {5x - 6} + \sqrt {5x + 6} = 6\), then what is the value of x? |
| A. | -4 |
| B. | 0 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 84. |
A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the one's digit. What is the number? |
| A. | 63 |
| B. | 54 |
| C. | 81 |
| D. | 72 |
| Answer» B. 54 | |
| 85. |
If x = 0.139, then what is the value of \(\sqrt {4{x^2} + 4x\ + 1}\) |
| A. | 1.39 |
| B. | 1.278 |
| C. | 2.139 |
| D. | 1.69 |
| Answer» C. 2.139 | |
| 86. |
If the vectors \(\rm \vec{a}=2\hat{i}-3\hat{j}+\hat{k}, \vec{b}=\hat{i}+2\hat{j}-3\hat{k}\) and \(\rm \vec{c}=\hat{j}+p \hat{k}\) are coplanar, then what is the value of p? |
| A. | 1 |
| B. | -1 |
| C. | 5 |
| D. | -5 |
| Answer» C. 5 | |
| 87. |
If 7m + 1 = 2401, then find the value of 22m + 2 . |
| A. | 224 |
| B. | 256 |
| C. | 264 |
| D. | 286 |
| Answer» C. 264 | |
| 88. |
ABCD is a quadrilateral whose diagonals are AC and BD. Which one of the following is correct? |
| A. | \(\overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CD}}} = \overrightarrow {{\rm{AC}}} + \overrightarrow {{\rm{DB}}} \) |
| B. | \(\overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CD}}} = \overrightarrow {{\rm{BD}}} + \overrightarrow {{\rm{CA}}} \) |
| C. | \(\overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CD}}} = \overrightarrow {{\rm{AC}}} + \overrightarrow {{\rm{BD}}} \) |
| D. | \(\overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CD}}} = \overrightarrow {{\rm{BC}}} + \overrightarrow {{\rm{AD}}}\) |
| Answer» C. \(\overrightarrow {{\rm{BA}}} + \overrightarrow {{\rm{CD}}} = \overrightarrow {{\rm{AC}}} + \overrightarrow {{\rm{BD}}} \) | |
| 89. |
If \(x + \frac{1}{x} = 5\), then \(x^2 + \frac{1}{x^2} =\) |
| A. | 25 |
| B. | 23 |
| C. | 27 |
| D. | 32 |
| Answer» C. 27 | |
| 90. |
If x3 - y3 = 112 and x - y = 4, then what is the value of x2 + y2? |
| A. | 16 |
| B. | 20 |
| C. | 24 |
| D. | 28 |
| Answer» D. 28 | |
| 91. |
Let \(\rm \vec{a}\), \(\rm \vec{b}\) and \(\rm \vec{c}\) be the position vectors of the three vertices A, B, C of a triangle respectively. Then the area of this triangle is given by: |
| A. | \(\rm \dfrac{1}{2} (\vec{a}\times \vec{b})\vec{c}\) |
| B. | \(\rm \dfrac{1}{2} |\vec{a}\times \vec{b} + \vec{b} \times \vec{c}+\vec{c}\times \vec{a}|\) |
| C. | \(\rm \vec{a}\times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}\) |
| D. | None of these |
| Answer» C. \(\rm \vec{a}\times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}\) | |
| 92. |
If A, B & C are vectors and A = 1.ux + 2.uy + 3.uz, B = 1.ux + 1.uy + 1.uz and C = 3.ux + 2.uy + 1.uz, then (A × B).C is: |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» D. -1 | |
| 93. |
If x4 + x-4 = 47, (x > 0), then the value of (2x -3)2 is |
| A. | 4 |
| B. | 5 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 94. |
If a - b = 2 and ab = 24, then what is the value of a3 - b3? |
| A. | 280 |
| B. | 124 |
| C. | 140 |
| D. | 152 |
| Answer» E. | |
| 95. |
A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations make a sum of Rs. 12450. The number of Rs. 20 notes is |
| A. | 200 |
| B. | 144 |
| C. | 125 |
| D. | 110 |
| Answer» D. 110 | |
| 96. |
If a + b = 8 and ab = 15, then what is the value of a3 + b3? |
| A. | 98 |
| B. | 152 |
| C. | 124 |
| D. | 260 |
| Answer» C. 124 | |
| 97. |
If 27x + 27[x-(1/3)] = 99, then what is the value of x? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |
| 98. |
\(\frac{{{{\left( {798\; + \;579} \right)}^2} - {{\left( {798 - 579} \right)}^2}}}{{\left( {798\; \times \;579} \right)}} = ?\) |
| A. | 2 |
| B. | 6 |
| C. | 4 |
| D. | 8 |
| Answer» D. 8 | |
| 99. |
For what value of k, the expression x3 - 18x2 + k will be a perfect square? |
| A. | -9 |
| B. | -81 |
| C. | 9 |
| D. | 81 |
| Answer» E. | |
| 100. |
For what value of k can the expression x3 + kx2 – 7x + 6 be resolved into three linear factors? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |