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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.
| 751. |
If a + b + c = 4 and ab + bc + ca = 2, then a3 + b3 + c3 – 3abc is equal to∶ |
| A. | 32 |
| B. | 36 |
| C. | 48 |
| D. | 40 |
| Answer» E. | |
| 752. |
If x + y = 4 and x3 + y3 = 12, then the value of x4 + y4 = ? |
| A. | 146/9 |
| B. | 146/3 |
| C. | 146/5 |
| D. | 146/7 |
| Answer» B. 146/3 | |
| 753. |
If 2x2 + ax + b, when divided by x – 3, leaves a remainder of 31, x2 + bx + a, when divided by x – 3, leaves a remainder of 24, then a + b equals. |
| A. | 7 |
| B. | -7 |
| C. | 23 |
| D. | -23 |
| Answer» B. -7 | |
| 754. |
If x2 - 3x + 1 = 0, what is the value of \({x^3} + \frac{1}{{{x^3}}}?\) |
| A. | 3 |
| B. | 7 |
| C. | 11 |
| D. | 18 |
| Answer» E. | |
| 755. |
In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. a2 - 58a - 120 = 0II. 20b2 + 26b - 6 = 0 |
| A. | a < b |
| B. | a > b |
| C. | a ≤ b |
| D. | a ≥ b |
| E. | a = b or the relationship cannot be determined |
| Answer» F. | |
| 756. |
Find the product of (a + b + 2c) (a2 + b2 + 4c2– ab – 2bc – 2ca). |
| A. | a3 + b3 + 8c3–abc |
| B. | a3 + b3 + 8c3– 6abc |
| C. | a3 + b3 + 8c3– 2abc |
| D. | a3 + b3 + 6c3– 6abc |
| Answer» C. a3 + b3 + 8c3– 2abc | |
| 757. |
If the sum of two numbers is 25 and their product is 156. Find the larger number. |
| A. | 11 |
| B. | 12 |
| C. | 13 |
| D. | 15 |
| Answer» D. 15 | |
| 758. |
If (1/a) + (1/b) + (1/c) = 0 and a + b + c = 11, then what is the value of a³ + b³ + c³ - 3abc? |
| A. | 1331 |
| B. | 2662 |
| C. | 3993 |
| D. | 14641 |
| Answer» B. 2662 | |
| 759. |
If one root of the equation (l – m)x2 – (6l – 6m)x + 1 = 0 is double the other and the ratio l ∶ smaller root is 5 ∶ 8, then which of the following is true? |
| A. | m > 9/8 |
| B. | m > 8/9 |
| C. | m = 9/8 |
| D. | m ≤ 9/8 |
| Answer» D. m ≤ 9/8 | |
| 760. |
If (8 - 10x) - (13x - 2) = - 9, then the value of x is |
| A. | - 19/23 |
| B. | 19/23 |
| C. | - 1/23 |
| D. | 1/23 |
| Answer» C. - 1/23 | |
| 761. |
Consider the matrix \(P = \left[ {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}}\\ 0&1&0\\ {\frac{{ - 1}}{{\sqrt 2 }}}&0&{\frac{1}{{\sqrt 2 }}} \end{array}} \right]\)Which one of the following statements about P is INCORRECT? |
| A. | Determinant of P is equal to 1. |
| B. | P is orthogonal |
| C. | Inverse of P is equal to its transpose |
| D. | All eigenvalues of P are real numbers |
| Answer» E. | |
| 762. |
Leela got married 6 years ago. Today her age is 5/4 times her age at the time of marriage. Her son’s age is 1/10 times her age. What is the present age of her son? |
| A. | 1 year |
| B. | 2 years |
| C. | 3 years |
| D. | 4 years |
| Answer» D. 4 years | |
| 763. |
If \(\vec a = \left(\vec i + 2\vec j - 3\vec k\right)\) and \(\vec b = \left(3\vec i - \vec j + 2\vec k\right)\) then the angle between \(\left(\vec a + \vec b\right)\) and \(\left(\vec a - \vec b\right)\) is? |
| A. | π / 3 |
| B. | π / 4 |
| C. | π / 2 |
| D. | 2π / 3 |
| Answer» D. 2π / 3 | |
| 764. |
If \(x - \frac{1}{x} = 13\), then the value of \({x^2} + \frac{1}{{{x^2}}}\) is: |
| A. | 165 |
| B. | 171 |
| C. | 167 |
| D. | 169 |
| Answer» C. 167 | |
| 765. |
If \(A = \left[ {\begin{array}{*{20}{c}} 4&2\\ { - 1}&1 \end{array}} \right]\) then (A – 2I) (A – 3I) is |
| A. | A |
| B. | I |
| C. | 0 |
| D. | 5 I |
| Answer» D. 5 I | |
| 766. |
If 3x + 4y - 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z - 4 = 18, then what is the value of x + y + z - 34? |
| A. | -28 |
| B. | -14 |
| C. | -31 |
| D. | -45 |
| Answer» D. -45 | |
| 767. |
If (3x + 9) is greater than or equal to (5x + 7), then find the maximum possible value of x: |
| A. | 3 |
| B. | 1 |
| C. | 4 |
| D. | 2 |
| Answer» C. 4 | |
| 768. |
A matrix X has a dimension of 2 × 2. If the eigenvalues of this matrix is 5 and 6, what would be the eigen values of X2? |
| A. | 2.5 and 3 |
| B. | 5 and 6 |
| C. | 10 and 12 |
| D. | 25 and 36 |
| Answer» E. | |
| 769. |
A 4 × 4 matrix [P] is given below\(\left[ P \right]=\left[ \begin{matrix} 0 & 1 & 3 & 0 \\ -2 & 3 & 0 & 4 \\ 0 & 0 & 6 & 1 \\ 0 & 0 & 1 & 6 \\ \end{matrix} \right]\)The eigenvalues of [P] are |
| A. | 0, 3, 6, 6 |
| B. | 1, 2, 3, 4 |
| C. | 3, 4, 5, 7 |
| D. | 1, 2, 5, 7 |
| Answer» E. | |
| 770. |
if \(9^{x-\frac{1}{2}}-2^{2x-2}=4^x-3^{2x-3}\), then x is |
| A. | 3/2 |
| B. | 2/5 |
| C. | 3/4 |
| D. | 4/9 |
| Answer» B. 2/5 | |
| 771. |
If a vector \(\rm \vec a\) makes an equal angle with the coordinate axes and has magnitude 3, then the angle between \(\rm \vec a\) and each of the three coordinate axes is |
| A. | \(\cos^{-1}\left(\dfrac{1}{\sqrt{3}}\right)\) |
| B. | \(\sin^{-1}\left(\dfrac{1}{\sqrt{3}}\right)\) |
| C. | \(\dfrac{\pi}{6}\) |
| D. | \(\dfrac{\pi}{3}\) |
| Answer» B. \(\sin^{-1}\left(\dfrac{1}{\sqrt{3}}\right)\) | |
| 772. |
If product of two numbers is 432 and one number is 16. What is the second number? |
| A. | 17 |
| B. | 23 |
| C. | 33 |
| D. | 27 |
| Answer» E. | |
| 773. |
Given that the determinant of the matrix \(\left[ {\begin{array}{*{20}{c}} 1&3&0\\ 2&6&4\\ { - 1}&0&2 \end{array}} \right]\) is -12, the determinant of the matrix \(\left[ {\begin{array}{*{20}{c}} 2&6&0\\ 4&{12}&8\\ { - 2}&0&4 \end{array}} \right]\) is |
| A. | -96 |
| B. | -24 |
| C. | 24 |
| D. | 96 |
| Answer» B. -24 | |
| 774. |
A function f(x, y) is said to be homogeneous of degree n in the variables x and y if it can be expressed in the form |
| A. | \({x^n}\phi \left( {\frac{y}{x}} \right)\) |
| B. | \({y^n}\phi \left( {\frac{x}{y}} \right)\) |
| C. | Both 1) and 2) |
| D. | None of the above |
| Answer» D. None of the above | |
| 775. |
If \(\left( {x + \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^4} + \frac{1}{{{x^4}}}} \right)\left( {{x^8} + \frac{1}{{{x^8}}}} \right)\left( {{x^{16}} + \frac{1}{{{x^{16}}}}} \right)?\) |
| A. | \(\frac{{\left( {{x^{32}} - \frac{1}{{{x^{32}}}}} \right)}}{{x - \frac{1}{x}}}\) |
| B. | \(\frac{{\left( {{x^8} - \frac{1}{{{x^8}}}} \right)}}{{x - \frac{1}{x}}}\) |
| C. | \(\frac{{\left( {{x^{64}} - \frac{1}{{{x^{64}}}}} \right)}}{{x - \frac{1}{x}}}\) |
| D. | \(\frac{{\left( {{x^{16}} - \frac{1}{{{x^{16}}}}} \right)}}{{x - \frac{1}{x}}}\) |
| Answer» B. \(\frac{{\left( {{x^8} - \frac{1}{{{x^8}}}} \right)}}{{x - \frac{1}{x}}}\) | |
| 776. |
If (x - a) and (x - b) are the factors of the quadratic equation x2 - 11x + 28 = 0 then find the value of (a + b)2 |
| A. | 9 |
| B. | 49 |
| C. | 16 |
| D. | 121 |
| Answer» E. | |
| 777. |
Find the value of X3 (X3 – X2 – X), when X = 4. |
| A. | 2816 |
| B. | 3328 |
| C. | 2516 |
| D. | 3332 |
| Answer» B. 3328 | |
| 778. |
If \(\left| {{\rm{\vec a}}} \right| = 2\) and \(\left| {{\rm{\vec b}}} \right| = 3\), then \({\left| {{\rm{\vec a}} \times {\rm{\vec b}}} \right|^2} + {\left| {{\rm{\vec a}} \cdot {\rm{\vec b}}} \right|^2}\) is equal to |
| A. | 72 |
| B. | 64 |
| C. | 48 |
| D. | 36 |
| Answer» E. | |
| 779. |
If x + y = 52 and x - y = 20, then what is the value of x : y? |
| A. | 3 : 4 |
| B. | 7 : 5 |
| C. | 9 : 4 |
| D. | 3 : 2 |
| Answer» D. 3 : 2 | |
| 780. |
If \(\overrightarrow {{\rm{a}}} \) and \(\overrightarrow {{\rm{b}}} \) are vectors such that \(\overrightarrow {|{\rm{a}}} \left| { = 2,{\rm{\;}}\overrightarrow {|{\rm{b}}} } \right| = 7\) and \(\overrightarrow {{\rm{a\;}}} \times {\rm{\;\vec b}} = 3{\rm{\hat i}} + 2{\rm{\hat j}} + 6{\rm{\hat k}},\) then what is the acute angle between \(\overrightarrow {{\rm{a}}} \) and \(\overrightarrow {{\rm{b}}} \)? |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» B. 45° | |
| 781. |
For a matrix [M] \(= \left[ {\begin{array}{*{20}{c}} {\frac{3}{5}}&{\frac{4}{5}}\\ x&{\frac{3}{5}} \end{array}} \right]\), the transpose of the matrix is equal to the inverse of the matrix [M]T = [M]-1. The value of x is given by |
| A. | \(- \frac{4}{5}\) |
| B. | \(- \frac{3}{5}\) |
| C. | \(\frac{3}{5}\) |
| D. | \(\frac{4}{5}\) |
| Answer» B. \(- \frac{3}{5}\) | |
| 782. |
If (x3 – 2√2 y3) ÷ (x – √2y) = (Ax2 + Bxy + Cy2) then, (2A + 4√2 B – 4C) = ? |
| A. | 0 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 783. |
A vector \(\vec r=a \hat i+b \hat j\) is equally inclined to both x and y axes. If the magnitude of the vector is 2 units, then what are the values of a and b respectively? |
| A. | \(\dfrac{1}{2}, \dfrac{1}{2}\) |
| B. | \(\dfrac{1}{\sqrt2}, \dfrac{1}{\sqrt2}\) |
| C. | √2, √2 |
| D. | 2, 2 |
| Answer» D. 2, 2 | |
| 784. |
Directions: Solve the following question and mark the best possible option.Let m and n be positive integers, If x2 + mx + 2n = 0 and x2 + 2nx + m = 0 have real roots, then the smallest possible value of m + n is |
| A. | 5 |
| B. | 8 |
| C. | 7 |
| D. | 6 |
| Answer» E. | |
| 785. |
If x + 1/x = 7, then x3 + 1/x3 is equal to∶ |
| A. | 322 |
| B. | 365 |
| C. | 343 |
| D. | 364 |
| Answer» B. 365 | |
| 786. |
If \(\frac{{11 - 13x}}{x} + \frac{{11 - 13y}}{y} + \frac{{11 - 13z}}{z} = 5\), then what is the value of \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\)? |
| A. | 1 |
| B. | 13/11 |
| C. | 13/5 |
| D. | 4 |
| Answer» E. | |
| 787. |
If (2x – 5)3 + (x – 4)3 + (x – 11)3 = 3 (2x – 5) (x – 4) (x – 11), then what is the value of x? |
| A. | 18 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» D. 7 | |
| 788. |
If \(\vec a \:and\: \vec b\) are two vectors such that \(|\vec a + \vec b|= |\vec a - \vec b|=4,\) then which one of the following is correct? |
| A. | \(\vec a \:and\: \vec b\) must be unit vectors. |
| B. | \(\vec a\) must be parallel to \(\vec b.\) |
| C. | \(\vec a\) must be perpendicular to \(\vec b.\) |
| D. | \(\vec a\) must be equal to \(\vec b.\) |
| Answer» D. \(\vec a\) must be equal to \(\vec b.\) | |
| 789. |
If (27x3 – 343y3) ÷ (3x – 7y) = Ax2 + By2 + 7Cyx, then the value of (4A – B + 5C) is∶ |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 790. |
If a + b + c = 5, a2 + b2 + c2 = 27 and a3 + b3 + c3 = 125, then the value of 4abc is: |
| A. | 20 |
| B. | 15 |
| C. | -20 |
| D. | -15 |
| Answer» D. -15 | |
| 791. |
One of the roots of the equation x2 – 12x + k = 0 is x = 3. The other root is: |
| A. | x = - 4 |
| B. | x = 9 |
| C. | x = 4 |
| D. | x = - 9 |
| Answer» C. x = 4 | |
| 792. |
If x + y + z = 0, then what is (y + z - x)3 + (z + x - y)3 + (x + y -z)3 equal to? |
| A. | (x + y + z)3 |
| B. | 3(x + y) (y + z) (x + z) |
| C. | 24xyz |
| D. | -24xyz |
| Answer» E. | |
| 793. |
If α, β are the roots of 3x2 – 5x + 7 = 0, then α3 + β3 = _____. |
| A. | \(\frac{{ - 90}}{{27}}\) |
| B. | \(\frac{{90}}{{27}}\) |
| C. | \(\frac{{ - 190}}{{27}}\) |
| D. | \(\frac{{190}}{{27}}\) |
| Answer» D. \(\frac{{190}}{{27}}\) | |
| 794. |
If C is the midpoint of AB and P in any point outside AB, then |
| A. | \(\overline{PA}+\overline{PB}=2\overline{PC}\) |
| B. | \(\overline{PA}+\overline{PB}=\overline{PC}\) |
| C. | \(\overline{PA}+\overline{PB}=2\overline{PC}=0\) |
| D. | \(\overline{PA}+\overline{PB}=\overline{PC}=0\) |
| Answer» B. \(\overline{PA}+\overline{PB}=\overline{PC}\) | |
| 795. |
If α and β are the roots of the quadratic equation x2 + kx – 15 = 0 such that α – β = 8, then what is the positive value of k? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |
| 796. |
A two-digit number is such that the product of its digits is 6. If 9 is added to the number, the digits are reversed. The number is |
| A. | 16 |
| B. | 35 |
| C. | 43 |
| D. | 23 |
| Answer» E. | |
| 797. |
If \(x + \dfrac{1}{x}=5\), then is equal to \(\dfrac{2x}{3x^2 - 5x + 3}\) |
| A. | 5 |
| B. | \(\dfrac{1}{5}\) |
| C. | 3 |
| D. | \(\dfrac{1}{3}\) |
| Answer» C. 3 | |
| 798. |
If \(3x+6y+9z = \dfrac{20}{3}, 6x+9y + 3z = \dfrac{17}{3}\) and \(18x+ 27y - z = \dfrac{113}{9}\), then what is the value of \(75x+113y \ ?\) |
| A. | 163/3 |
| B. | 143/6 |
| C. | 218/9 |
| D. | 311/3 |
| Answer» B. 143/6 | |
| 799. |
If x2 - 16x + 59 = 0, then what is the value of (x - 6)2 + [1/(x - 6)2]? |
| A. | 14 |
| B. | 18 |
| C. | 16 |
| D. | 20 |
| Answer» C. 16 | |
| 800. |
A and B together have Rs. 50,000. If 4/5th of A’s amount is equal to 1/5th of B’s. how much amount B has? |
| A. | Rs. 20,000 |
| B. | Rs. 40,000 |
| C. | Rs. 12,500 |
| D. | Rs. 10,000 |
| Answer» C. Rs. 12,500 | |