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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.
| 701. |
Given, a + 1/a = 2, what is the value of a118 + 1/a117? |
| A. | 1 |
| B. | 118 |
| C. | 2 |
| D. | 117 |
| Answer» D. 117 | |
| 702. |
For Multiplication of matrix which of the following is true |
| A. | All Square Matrices can be multiplied |
| B. | M × N matrix can be multiplied with M × N matrix |
| C. | M × N matrix can be multiplied with N × A matrix |
| D. | None of these |
| Answer» D. None of these | |
| 703. |
If a + b + c = 7 and ab + bc + ca = 1, then a3 + b3 + c3 – 3abc is equal to: |
| A. | 322 |
| B. | 325 |
| C. | 422 |
| D. | 412 |
| Answer» B. 325 | |
| 704. |
Choose the correct options from the quadratic equation \(x + {1 \over x} = 3\) , x ≠ 0 and ax2 + bx + c = 0 |
| A. | a = -1, b = -3, c = 1 |
| B. | a = 1, b = 3, c = -1 |
| C. | a = -1, b = 3, c = -1 |
| D. | a = 1, b = -3, c = 1 |
| Answer» E. | |
| 705. |
If \(x + y + z = 6\) and \(xy + zx + zy = 10\), then find the value of x3 + y3 + z3 – 3xyz. |
| A. | 16 |
| B. | 26 |
| C. | 36 |
| D. | 46 |
| Answer» D. 46 | |
| 706. |
If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 - 3abc? |
| A. | 365 |
| B. | 444 |
| C. | 666 |
| D. | 999 |
| Answer» D. 999 | |
| 707. |
Forces \(4\hat{i}-3\hat{j}+7\hat{k}\) and \(-2\hat{i}+2\hat{j}-8\hat{k}\) are acting on a particle and displaced it from the point (5, 7, 1) to (2, 5, -6), then the work done by the force is |
| A. | 25 |
| B. | 9 |
| C. | 15 |
| D. | 7 |
| Answer» D. 7 | |
| 708. |
Find the value of \(\sqrt {{{20}^2} - {{16}^2}}\) |
| A. | 12 |
| B. | 18 |
| C. | 16 |
| D. | 14 |
| Answer» B. 18 | |
| 709. |
If x + 2 is a factor of x2 + ax + 8 then a = _______ |
| A. | -2 |
| B. | 2 |
| C. | 6 |
| D. | None of the above |
| Answer» D. None of the above | |
| 710. |
Find the value of \(\frac{{\left( {0.064 - 0.008} \right)\left( {0.16 - 0.04} \right)}}{{\left( {0.16 + 0.08 + 0.04} \right){{\left( {0.4 + 0.2} \right)}^3}}}\) |
| A. | 1/3 |
| B. | 2/3 |
| C. | 1/9 |
| D. | 3/2 |
| Answer» D. 3/2 | |
| 711. |
If x + 1/x = 4√3, then x2 + 1/x2is equal to∶ |
| A. | 52 |
| B. | 46 |
| C. | 44 |
| D. | 56 |
| Answer» C. 44 | |
| 712. |
If z and ω are two complex numbers such that |zω| = 1 and \({\rm{arg\;}}\left( z \right) - {\rm{arg\;}}\left( {\rm{\omega }} \right) = \frac{\pi }{2}\) then: |
| A. | \(\bar z{\rm{\omega }} = i\) |
| B. | \(z{\rm{\bar \omega }} = \frac{{ - 1 + i}}{{\sqrt 2 }}\) |
| C. | \(\bar z{\rm{\omega }} = - i\) |
| D. | \(z{\rm{\bar \omega }} = \frac{{1 - i}}{{\sqrt 2 }}\) |
| Answer» D. \(z{\rm{\bar \omega }} = \frac{{1 - i}}{{\sqrt 2 }}\) | |
| 713. |
Factorise - (x4 + x2 + 25) |
| A. | (x2 + 3x + 5) (x2 + 3x - 5) |
| B. | (x2 + 3x + 5) (x2 - 3x + 5) |
| C. | (x2 + x + 5) (x2 - x + 5) |
| D. | None of these |
| Answer» C. (x2 + x + 5) (x2 - x + 5) | |
| 714. |
If (x - 1) and (x + 1) are two factors of the polynominal x6 - 1, then its other factors are |
| A. | (x2 + 1), (x2 + x + 1) |
| B. | (x2 + 1), (x2 - x - 1) |
| C. | (x2 - x + 1), (x2 + x + 1) |
| D. | (x2 - x - 1), (x2 + x - 1) |
| Answer» D. (x2 - x - 1), (x2 + x - 1) | |
| 715. |
If 7x - (3/2) × (4x - 9) = 6.5, then the value of x is? |
| A. | 7 |
| B. | 20 |
| C. | -7 |
| D. | -20 |
| Answer» D. -20 | |
| 716. |
If x2 - 6x + 1 = 0, then the value of \({x^2} + \frac{1}{{{x^2}}}\) is |
| A. | 30 |
| B. | 34 |
| C. | 32 |
| D. | None of the above |
| Answer» C. 32 | |
| 717. |
Consider the following simultaneous equation (with c1 and c2 beings constants):3x1 + 2x2 = c14x1 + x2 = c2The characteristic equation for these simultaneous equations is |
| A. | λ2 – 4λ – 5 = 0 |
| B. | λ2 – 4λ + 5 = 0 |
| C. | λ2 + 4λ – 5 = 0 |
| D. | λ2 + 4λ + 5 = 0 |
| Answer» B. λ2 – 4λ + 5 = 0 | |
| 718. |
If x2 + x = 19, then what is the value of (x + 5)2 + [1/(x + 5)2]? |
| A. | 77 |
| B. | 79 |
| C. | 81 |
| D. | 83 |
| Answer» C. 81 | |
| 719. |
Consider the matrix \(\left[ {\begin{array}{*{20}{c}} 5&{ - 1}\\ 4&1 \end{array}} \right]\) which one of the following statements is TRUE for the eigenvalues and eigenvectors of the matrix? |
| A. | Eigen value 3 has a multiplicity of 2 and only one independent eigen vector exists |
| B. | Eigen value 3 has a multiplicity of 2 and two independent eigen vectors exist |
| C. | Eigen value 3 has a multiplicity of 2 and no independent eigen vector exists |
| D. | Eigen values are 3 and –3 and two independent eigen vectors exist. |
| Answer» B. Eigen value 3 has a multiplicity of 2 and two independent eigen vectors exist | |
| 720. |
If (a + c + 1) = 0, then find the value of (a3 + c3 + 1 – 3ac) |
| A. | -1 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» E. | |
| 721. |
If 5x/2 - (4/3) × (9x/2 - 6) = -x/2, then what is the value of x? |
| A. | -8/3 |
| B. | 3/8 |
| C. | 8/3 |
| D. | -3/8 |
| Answer» D. -3/8 | |
| 722. |
If loga ab = x then, logb ab is equal to |
| A. | \(\frac{1}{x}\) |
| B. | \(\frac{x}{{1 + x}}\) |
| C. | \(\frac{x}{{1 - x}}\) |
| D. | \(\frac{x}{{x - 1}}\) |
| Answer» E. | |
| 723. |
Consider the row vectors v = (1, 0) and w = (2, 0). The rank of the matrix M = 2vTv + 3wTw, where the superscript T denotes the transpose, is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 724. |
In the solution of simultaneous equations by the Gauss elimination method for solving equations, triangularization leads to |
| A. | singular matrix |
| B. | upper triangular matrix |
| C. | diagonal matrix |
| D. | lower triangular matrix |
| Answer» C. diagonal matrix | |
| 725. |
If a = 2017, b = 2016 and c = 2015, then what is the value of a2 + b2 + c2 - ab - bc - ca? |
| A. | -2 |
| B. | 0 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 726. |
If tan A + cot A = √5, What is the value of tan3 A + cot3 A ? |
| A. | √5 |
| B. | 3 |
| C. | 2√5 |
| D. | \(^2\sqrt 5 \) |
| Answer» D. \(^2\sqrt 5 \) | |
| 727. |
If ab + xy - xb = 0 and bc + yz - cy = 0, then what \(\frac{x}{a} + \frac{c}{z} \) equal to? |
| A. | \(\frac{y}{b}\) |
| B. | \(\frac{b}{y}\) |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 728. |
If x4 + x-4 = 1154, (x > 0) then the value of 2(x – 3)2 is: |
| A. | 16 |
| B. | 12 |
| C. | 20 |
| D. | 15 |
| Answer» B. 12 | |
| 729. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 – 20x + 91 = 0II. y2 + 16y + 63 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or the relationship between x and y cannot be established. |
| Answer» B. x < y | |
| 730. |
If x2 - 6x - 27 > 0, then which one of the following is correct? |
| A. | -3 < x < 9 |
| B. | x < 9 or x > - 3 |
| C. | x > 9 or x < - 3 |
| D. | x < - 3 only |
| Answer» D. x < - 3 only | |
| 731. |
If \(3\sqrt 7 + \sqrt {343} = 26.45\), then find the value of \(\sqrt {252} + 20\sqrt 7 \) |
| A. | 39.4 |
| B. | 68.77 |
| C. | 56.8 |
| D. | 92.3 |
| Answer» C. 56.8 | |
| 732. |
A man who recently died left a sum of Rs. 3,90,000 to be divided among his wife, five sons and four daughters. He directed that each son should receive 3 times as much as each daughter receives and that each daughter should receive twice as much as their mother receives. What was the wife’s share? |
| A. | Rs. 14,000 |
| B. | Rs. 12,000 |
| C. | Rs. 10,000 |
| D. | Rs. 9,000 |
| Answer» D. Rs. 9,000 | |
| 733. |
If a2 + b2 = 169, ab = 60, (a > b), then (a2 – b2) is equal to: |
| A. | 149 |
| B. | 139 |
| C. | 119 |
| D. | 129 |
| Answer» D. 129 | |
| 734. |
Consider the following system of equations in three real variables x1, x2 and x32x1 – x2 + 3x3 = 13x2 – 2x2 + 5x3 = 2-x1 – 4x2 + x3 = 3The system of equations has: |
| A. | No solutions |
| B. | A unique solution |
| C. | More than one but a finite number of solutions |
| D. | An infinite number of solutions |
| Answer» C. More than one but a finite number of solutions | |
| 735. |
If x + 3y + 2 = 0 then value of x3 + 27y3 + 8 - 18xy is: |
| A. | 1 |
| B. | -2 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 736. |
If \(\vec a, \vec b\:and \: \vec c\) are coplanar, then what is \((2\vec a\times 3\vec b)\cdot4\vec c+(5\vec b\times 3\vec c)\cdot6\vec a\) equal to? |
| A. | 114 |
| B. | 66 |
| C. | 0 |
| D. | -66 |
| Answer» D. -66 | |
| 737. |
If ab + bc + ca = 8 and a + b + c = 12 then (a2 + b2 + c2) is equal to∶ |
| A. | 160 |
| B. | 144 |
| C. | 134 |
| D. | 128 |
| Answer» E. | |
| 738. |
If 5x/2 - ¼ (6x - 5/3) = 7/6, then the value of x is ______. |
| A. | 5/4 |
| B. | 3/4 |
| C. | 3/7 |
| D. | 5/7 |
| Answer» C. 3/7 | |
| 739. |
Consider the following inequalities in respect of vectors \({\rm{\vec a}}\:and\;{\rm{\vec b}}\):1. \(\left| {{\rm{\vec a}} + {\rm{\vec b}}} \right| \le \left| {{\rm{\vec a}}} \right| + \left| {{\rm{\vec b}}} \right|\)2. \(\left| {{\rm{\vec a}} - {\rm{\vec b}}} \right| \ge \left| {{\rm{\vec a}}} \right| - \left| {{\rm{\vec b}}} \right|\)Which of the above is/are correct |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 740. |
\(\left[ {\begin{array}{*{20}{c}} 1&2&3\\ 4&5&6\\ 7&8&9 \end{array}} \right]\)Trace of the given matrix is |
| A. | 6 |
| B. | 24 |
| C. | 15 |
| D. | 45 |
| Answer» D. 45 | |
| 741. |
If \(\frac{4}{3}\left(x^2 + \frac{1}{x^2}\right) = 110 \frac{2}{3}\) find \(\frac{1}{9}\left(x^3 - \frac{1}{x^3}\right)\) where x > 0. |
| A. | 74 |
| B. | 76 |
| C. | 84 |
| D. | 85 |
| Answer» D. 85 | |
| 742. |
In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. x2 - 5x - 84 = 0II. y2 - 3y - 88 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | Either x = y or Relationship between x and y cannot be established |
| Answer» F. | |
| 743. |
Constant forces \(\rm \vec P\) = 2î - 5ĵ + 6k̂ and \(\rm \vec Q\) = -î + 2ĵ - k̂ act on a particle. The work done when the particle is displaced from A whose position vector is 4î - 3ĵ - 2k̂, to B whose position vector is 6î + ĵ - 3k̂, is: |
| A. | 10 units. |
| B. | -15 units. |
| C. | -50 units. |
| D. | 25 units. |
| Answer» C. -50 units. | |
| 744. |
For what value of ‘y’, \({x^2} + \frac{1}{{12}}x + {y^2}\) is a perfect square? |
| A. | 1/24 |
| B. | 1/12 |
| C. | 1/6 |
| D. | 1/3 |
| Answer» B. 1/12 | |
| 745. |
Factorization [x2 + (a + b + c)x + ab + bc] is |
| A. | (x + b)(x + a + c) |
| B. | (x + a)(x + b + c) |
| C. | (x + c)(x + a + b) |
| D. | (x + b)(x + a + b + c) |
| Answer» B. (x + a)(x + b + c) | |
| 746. |
If \(\frac{x}{a} + \frac{y}{b} = a + b\) and \(\frac{x}{a^2} + \frac{y}{b^2} = 2\), then what is \(\frac{x}{a^2} - \frac{y}{b^2}\) equal to? |
| A. | -2 |
| B. | -1 |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 747. |
In a school, the total number of students was 160 in the year 2015. In the following year, the number of girls decreased by 20 and the number of boys increased by 20. As a result, the number of boys became 7 times the number of girls. During 2015, the number of boys was how much more than the number of girls? |
| A. | 100 |
| B. | 90 |
| C. | 80 |
| D. | 70 |
| Answer» D. 70 | |
| 748. |
(a + 2b)2 - (a - 2b)2 is equal to: |
| A. | 6ab |
| B. | 10ab |
| C. | 8ab |
| D. | 4ab |
| Answer» D. 4ab | |
| 749. |
For what value of β, do the simultaneous equations7 x + 2y = -314x + 6y = β have a unique value? |
| A. | for all real values of β |
| B. | ]beta = 0 |
| C. | β ≠ -6 |
| D. | β = -6 |
| Answer» B. ]beta = 0 | |
| 750. |
If x/2 + y/5 = 12 and 4x/3 – y/3 = 19, then find the value of x and y. |
| A. | x = -18, y = -15 |
| B. | x = 8, y = 5 |
| C. | x = 18, y = 15 |
| D. | x = -8, y = -5 |
| Answer» D. x = -8, y = -5 | |