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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.
| 1651. |
If x = 1 + \(\sqrt{2}\), then find the value of \(\sqrt x + {1 \over \sqrt x}\) |
| A. | 2.1014 |
| B. | 2.1973 |
| C. | 1.9996 |
| D. | 1.9876 |
| Answer» C. 1.9996 | |
| 1652. |
Given k = - 3, find the value of k3 + 3k:A. - 36B. 36C. 37D. - 37 |
| A. | B |
| B. | C |
| C. | D |
| D. | A |
| Answer» E. | |
| 1653. |
If 5x + 1/3x = 4, then what is the value of \(9{x^2} + \frac{1}{{25{x^2}}}\)? |
| A. | 144/125 |
| B. | 119/25 |
| C. | 174/125 |
| D. | 114/25 |
| Answer» E. | |
| 1654. |
Euclidean norm (length) of the vector [4 – 2 - 6]T is |
| A. | √48 |
| B. | √24 |
| C. | √12 |
| D. | √56 |
| Answer» E. | |
| 1655. |
If a3 - b3 = 91 and a - b = 1, then what is the value of ab? |
| A. | 27 |
| B. | 6 |
| C. | 9 |
| D. | 30 |
| Answer» E. | |
| 1656. |
If x + 1/x = c + 1/c then the value of x is: |
| A. | c, 1/c |
| B. | c, c2 |
| C. | c, 2c |
| D. | 0, 1 |
| Answer» B. c, c2 | |
| 1657. |
Calculate:\((40.7×40.7×40.7+1)/(40.7×40.7-40.7+1)\)A. 417B. 4.17C. 41.7D. 441.7 |
| A. | C |
| B. | D |
| C. | B |
| D. | A |
| Answer» B. D | |
| 1658. |
Ram is 4 times as old as his son. Four years hence, the sum of their ages will be 43 years. The present age of the son is: |
| A. | 3 years |
| B. | 5 years |
| C. | 6 yeas |
| D. | 7 years |
| Answer» E. | |
| 1659. |
Determine the value of ‘r’ for which the equation 13x + 5 = rx + 18 has no solution. |
| A. | 0 |
| B. | 5 |
| C. | 13 |
| D. | 18 |
| Answer» D. 18 | |
| 1660. |
A bird is flying in a straight line with velocity vector 10î + 6ĵ + k̂, measured in km/hr. If starting point is (1, 2, 3), how much time does it to take to reach a point in space that is 13 meter high from the ground? |
| A. | 600 seconds |
| B. | 360 seconds |
| C. | 36 seconds |
| D. | 60 seconds |
| Answer» D. 60 seconds | |
| 1661. |
Pick up the incorrect statement from the following options.If A is Coefficient Matrix, K is Augmented Matrix and R is the Rank of Matrix |
| A. | If R (A) ≠ R (K), the equations are inconsistent and have no solutions |
| B. | If R (A) = R (K) = n, the equations are consistent and have unique solutions |
| C. | If R (A) = R (K) < n, the equations are consistent and have an infinite number of solutions |
| D. | If R (A) = R (K) > n, the equations are consistent and have an infinite number of solutions |
| Answer» E. | |
| 1662. |
If (x + 1/x) = 3, then find the value of (x3 + 1/x3) ÷ (x2 + 1/x2).A. 18/5B. 26/3C. 18/7D. 54/5 |
| A. | D |
| B. | B |
| C. | A |
| D. | C |
| Answer» E. | |
| 1663. |
If x = 1 – y and x2 = 2 – y2, then what is the value of xy? |
| A. | 1 |
| B. | 2 |
| C. | -1/2 |
| D. | -1 |
| Answer» D. -1 | |
| 1664. |
If x + 1/x = 4, then value of x3 + 1/x3 = ? |
| A. | 64 |
| B. | 52 |
| C. | 96 |
| D. | 85 |
| Answer» C. 96 | |
| 1665. |
Characteristics roots of matrix A and AT |
| A. | Different |
| B. | Same |
| C. | Cannot say about roots |
| D. | None of these |
| Answer» C. Cannot say about roots | |
| 1666. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x3 + 512 = 0II. y2 - 64 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or relationship between x and y cannot be established. |
| Answer» E. x = y or relationship between x and y cannot be established. | |
| 1667. |
If a + b + c = -11, then what is the value of (a + 4)3 + (b + 5)3 + (c + 2)3 - 3(a + 4)(b + 5)(c + 2)? |
| A. | -1331 |
| B. | -121 |
| C. | 0 |
| D. | 1331 |
| Answer» D. 1331 | |
| 1668. |
If x + y + z = 19, x2 + y2 + z2 = 133 and xz = y2, then the difference between z and x is: |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 6 |
| Answer» B. 4 | |
| 1669. |
If x2 – 9x + 1 = 0, then what is the value of x3 + 1/x3? |
| A. | 54 |
| B. | 108 |
| C. | 702 |
| D. | 810 |
| Answer» D. 810 | |
| 1670. |
If x = 5 - 2√6, then what is the value of √x +(1/√x)? |
| A. | 5 |
| B. | 2 |
| C. | 2√3 |
| D. | 2√2 |
| Answer» D. 2√2 | |
| 1671. |
If the position vector \({\rm{\vec a}}\) of the point (5, n) is such that \(\left| {{\rm{\vec a}}} \right| = 13\), then the value/values of n can be |
| A. | ± 8 |
| B. | ± 12 |
| C. | 8 only |
| D. | 12 only |
| Answer» C. 8 only | |
| 1672. |
If (x/y)a - 4 = (y/x)2a - 5, then what is the relation between x and y? |
| A. | x > y |
| B. | Cannot be determined |
| C. | x < y |
| D. | x = y |
| Answer» C. x < y | |
| 1673. |
Given that the vector \(\vec \alpha {\rm{\;and\;}}\vec \beta \) are non-collinear. The values of x and y for which \(\vec u - \;\overrightarrow {v\;} = \;\vec w\) holds true if \(\vec u = 2x\vec \alpha + y\vec \beta,\) \(\vec v = 2y\vec \alpha + 3{\rm{x}}\vec \beta \) and \(\vec w = 2\vec \alpha - 5\vec \beta \), are |
| A. | x = 2, y = 1 |
| B. | x = 1, y = 2 |
| C. | x = -2, y = 1 |
| D. | x = -2, y = -1 |
| Answer» B. x = 1, y = 2 | |
| 1674. |
If 2 is a zero polynomial p(x) = 4x2 + 2x - 5a, then value of a is |
| A. | 5 |
| B. | 4 |
| C. | 5/4 |
| D. | -4 |
| Answer» C. 5/4 | |
| 1675. |
Find the characteristic equation of the system with the following plant matrix:\(A = \left[ {\begin{array}{*{20}{c}}0&1\\{ - 2}&{ - 3}\end{array}} \right]\) |
| A. | λ3 + λ2 + 3λ + 6 = 0 |
| B. | λ2 + 3λ + 4 = 0 |
| C. | λ3 + λ2 + 3λ + 4 = 0 |
| D. | λ2 + 3λ + 2 = 0 |
| Answer» E. | |
| 1676. |
If X : Y = 13 : 12 and X – Y = 2, then what is value of 2X + 3Y? |
| A. | 144 |
| B. | 124 |
| C. | 120 |
| D. | 136 |
| Answer» C. 120 | |
| 1677. |
If 2x(x + y + z) = 250, 2y(x + y + z) = 100, 2z(x + y + z) = 100, then find the value of (3x + 6y + 15z). |
| A. | 110 |
| B. | 95 |
| C. | 85 |
| D. | 69 |
| Answer» C. 85 | |
| 1678. |
If x(2x + 3) = 90 and 7y-1/2 + 2y-1/2 = y1/2 (x and y are positive numbers), then what is the value of x2 + y2? |
| A. | 45 |
| B. | 109 |
| C. | 117 |
| D. | 126 |
| Answer» D. 126 | |
| 1679. |
Calculate the value of \(\frac{{\left( {59881{\rm{\;}} \times {\rm{\;}}59881 - 49681{\rm{\;}} \times {\rm{\;}}49681} \right)}}{{10200}}\) |
| A. | 110956 |
| B. | 109562 |
| C. | 109652 |
| D. | 109662 |
| Answer» C. 109652 | |
| 1680. |
( a – b )2 + ( a + b )2 – ( a + b )( a – b ) =______ |
| A. | 3a2 + b2 |
| B. | a2 + b2 |
| C. | a2 + 3b2 |
| D. | 2a2 + 2b2 |
| Answer» D. 2a2 + 2b2 | |
| 1681. |
If a2 - 2a = 1, then what is the value of \({a^3} - \frac{1}{{{a^3}}}\)? |
| A. | 14 |
| B. | 18 |
| C. | 21 |
| D. | 24 |
| Answer» B. 18 | |
| 1682. |
If α and β are roots of the equation 3x2 – 13x + 14 = 0, what is the value of (α/β) + (β/α)? |
| A. | 65/28 |
| B. | 53/14 |
| C. | 9 |
| D. | 85/42 |
| Answer» E. | |
| 1683. |
If x2 + y2 + z2 = 133, xy + yz + zx = 114 and xyz = 216, then the value of x3 + y3 + z3 is: |
| A. | 948 |
| B. | 942 |
| C. | 1009 |
| D. | 999 |
| Answer» D. 999 | |
| 1684. |
If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2 + 15x + 1)? |
| A. | 1/5 |
| B. | 1/10 |
| C. | 2/5 |
| D. | 10 |
| Answer» C. 2/5 | |
| 1685. |
If x = 2 + √5 then the value of x3 + x-3 is: |
| A. | 36√5 |
| B. | 40√5 |
| C. | 46√5 |
| D. | 34√5 |
| Answer» E. | |
| 1686. |
On a map, 1 inch represents 250 miles. What is the actual distance between two cities if they are \(4\frac{1}{2}\) inches apart on the map? |
| A. | 1100 miles |
| B. | 1125 miles |
| C. | 1150 miles |
| D. | 1200 miles |
| Answer» C. 1150 miles | |
| 1687. |
A force \(\vec F = 3\hat i + 2\hat j - 4\hat k\) is applied at the point (1, -1, 2). What is the moment of the force about the point (2, -1, 3)? |
| A. | î +4ĵ + 4k̂ |
| B. | 2î + ĵ + 2k̂ |
| C. | 2î - 7ĵ - 2k̂ |
| D. | 2î + 4ĵ - k̂ |
| Answer» D. 2î + 4ĵ - k̂ | |
| 1688. |
A force \(\vec F = 3\hat i + 4\;\hat j - 3\;\hat k\) is applied at the point P, whose position vector is \(\vec r = 2\hat i - 2\hat j - 3\hat k\). What is the magnitude of the moment of the force about the origin? |
| A. | 23 units |
| B. | 19 units |
| C. | 18 units |
| D. | 21 units |
| Answer» B. 19 units | |
| 1689. |
If 3a – (3/a) – 3 = 0, then what is the value of a3 – (1/a3) + 2? |
| A. | 0 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 1690. |
If \(\rm \vec{a},\vec{b},\vec{c}\) are three non-zero vectors with no two of which are collinear, \(\rm \vec{a}+2\vec{b}\) is collinear with \(\rm \vec {c}\) and \(\rm \vec{b}+3\vec{c}\) is collinear with \(\rm \vec {a}\), then \(\rm |\vec{a} +2 \vec{b}+6\vec{c}|\) will be equal to |
| A. | Zero |
| B. | 9 |
| C. | 1 |
| D. | None of the above |
| Answer» B. 9 | |
| 1691. |
Consider a vector p in 2-dimensional space. Let its direction (counter-clockwise angle with the positive x-axis) be θ. Let p be an eigenvector of a 2 × 2 matrix A with corresponding eigenvalue λ, λ > 0. If we denote the magnitude of a vector v by ||v||, identify the VALID statement regarding p', where p' = Ap. |
| A. | Direction of p' = λθ, ||p'|| = λ ||p|| |
| B. | Direction of p' = θ, ||p'|| = ||p||/λ |
| C. | Direction of p' = λθ, ||p'|| = ||p|| |
| D. | Direction of p' = θ, ||p'|| = λ||p|| |
| Answer» E. | |
| 1692. |
If [x – (1/x)] = 2, then what is the value of [x6 - (1/x6)]? |
| A. | 114√3 + 1 |
| B. | 134√2 |
| C. | 142√2 + 3 |
| D. | 140√2 |
| Answer» E. | |
| 1693. |
If 9x 3y = 2187 and 23x 22y – 4xy = 0, then what can be the value of (x + y)? |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» D. 7 | |
| 1694. |
For A = \(\left[ {\begin{array}{*{20}{c}} 1&{\tan x}\\ { - \tan x}&1 \end{array}} \right]\), the determinant of ATA-1 is: |
| A. | sec2 x |
| B. | cos 4x |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 1695. |
If a + b - c = 12 and a2 + b2 + c2 = 110, then which among the following relation sis true?(p) ab + bc + ca = 34(q) ab + bc - ca = 17(r) ab - bc + ca = 17(s) ab - bc - ca = 17 |
| A. | (q) |
| B. | (s) |
| C. | (r) |
| D. | (p) |
| Answer» C. (r) | |
| 1696. |
Consider the systems, each consisting of m linear equations in n variables.I. If m < n, then all such systems have a solutionII. If m > n, then none of these systems has a solutionIII. If m = n, then there exists a system which has a solutionWhich one of the following is CORRECT? |
| A. | I, II and III are true |
| B. | Only II and III are true |
| C. | Only III is true |
| D. | None of them is true |
| Answer» D. None of them is true | |
| 1697. |
If α and β are the two zeros of the polynomial 25x2 – 15x + 2, then what is a quadratic polynomial whose zeros are (2α)-1 and (2β)-1 ? |
| A. | x2 + 30x + 2 |
| B. | 8x2 – 30x + 25 |
| C. | 8x2 – 30x |
| D. | x2 + 30x |
| Answer» C. 8x2 – 30x | |
| 1698. |
If 3x7 - 27x5 + 5x3 - 45x + 7 is divided by x + 3, then the remainder is _____? |
| A. | 0 |
| B. | 7 |
| C. | 9 |
| D. | 11 |
| Answer» C. 9 | |
| 1699. |
If x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 7, then the value of \(\left( {\frac{1}{{{x^2}}}\; + \;\frac{1}{{{y^2}}}} \right)\) is: |
| A. | 5/2 |
| B. | 7/4 |
| C. | 7/3 |
| D. | 5/4 |
| Answer» E. | |
| 1700. |
If α and β are the roots of the equation x2 + x - 1 = 0, then what is the equation whose roots are α5 and β5? |
| A. | x2 + 7x - 1 = 0 |
| B. | x2 - 7x - 1 = 0 |
| C. | x2 - 11x - 1 = 0 |
| D. | x2 + 11x - 1 = 0 |
| Answer» E. | |