MCQOPTIONS
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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.
| 1851. |
if \(\left| {\vec a} \right| = 7,\;\left| {\vec b} \right| = 11\) and \(\left| {\vec a + \vec b\;} \right| = 10\sqrt 3 \), then \(\left| {\vec a - \vec b} \right|\) is equal to |
| A. | 40 |
| B. | 10 |
| C. | \(4\sqrt {10} \) |
| D. | \(2\sqrt {10}\) |
| Answer» E. | |
| 1852. |
If (x – 1/x = 1), then what is the value of \(\frac{1}{x}\left( {\frac{1}{{x - 1}} - \frac{1}{{x + 1}} + \frac{1}{{{x^2} + 1}} - \frac{1}{{{x^2} - 1}}} \right)\)? |
| A. | ±√5 |
| B. | 2/5 |
| C. | ±2/√5 |
| D. | 4/(5 ± √5) |
| Answer» E. | |
| 1853. |
A two digit number is 4 times the sum of its two digits. The number that is formed by reversing its digits is 27 more than the original number. What is the number? |
| A. | 27 |
| B. | 36 |
| C. | 42 |
| D. | 54 |
| Answer» C. 42 | |
| 1854. |
If a + b + c + d = 4 then the value of \(\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}\; + \;\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}\; + \;\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}\; + \;\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}\) is |
| A. | 0 |
| B. | 1 |
| C. | 4 |
| D. | 1 + abcd |
| Answer» B. 1 | |
| 1855. |
If the vectors 2i – 3j + 3k and 3i + xj + 2k are orthogonal then x = |
| A. | 2 |
| B. | 4 |
| C. | -2 |
| D. | 1 |
| Answer» C. -2 | |
| 1856. |
If \(a = \sqrt {5 + 2\sqrt 2 } \) and \(b = \sqrt {5 - 2\sqrt 2 } \) then find the value of a2 – b2. |
| A. | 2 |
| B. | 4 |
| C. | √2 |
| D. | 4√2 |
| Answer» E. | |
| 1857. |
A biquadratic equation has how many possible roots? |
| A. | 4 |
| B. | 2 |
| C. | 3 |
| D. | 5 |
| Answer» B. 2 | |
| 1858. |
If (a – b) : (a + b) = 1 : 5 ?Then what is (a2 –b2) : (a2 + b2) equal to |
| A. | 6 : 13 |
| B. | 4 : 13 |
| C. | 5 : 13 |
| D. | 8 : 13 |
| Answer» D. 8 : 13 | |
| 1859. |
If 2x - 8 > 4y - 2, then which of the following identities are true? |
| A. | x - 2y < 3 |
| B. | 2y - x < 3 |
| C. | x - 2y > 6 |
| D. | x - 2y > 3 |
| Answer» E. | |
| 1860. |
Given that x8 - 34x4 + 1 = 0, x > 0. What is the value of (x3 + x-3)? |
| A. | 6√2 |
| B. | 5√4 |
| C. | 10√2 |
| D. | 5√6 |
| Answer» D. 5√6 | |
| 1861. |
A number when divided by 119, 11 obtained as the remainder. On dividing the same number by 17, what will be the remainder? |
| A. | 14 |
| B. | 12 |
| C. | 13 |
| D. | 11 |
| Answer» E. | |
| 1862. |
If 3x2 + ax - 12 is completely divisible by x - 8 then the value of a is: |
| A. | - 24.5 |
| B. | 24.5 |
| C. | 22.5 |
| D. | - 22.5 |
| Answer» E. | |
| 1863. |
If C is a skew-symmetric matrix of order n and X is n × 1 column matrix, then XT CX is a |
| A. | scalar matrix |
| B. | null matrix |
| C. | unit matrix |
| D. | matrix will all elements 1 |
| Answer» C. unit matrix | |
| 1864. |
If [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2, then the value of (A + B + C) is: |
| A. | 26 |
| B. | 19 |
| C. | 16 |
| D. | 13 |
| Answer» D. 13 | |
| 1865. |
If Shaam sells 2.5 kg of his homemade jam for Rs. 78.60, what is the cost of 5.5 kg of the jam? (in Rs.) |
| A. | Rs. 171.92 |
| B. | Rs. 172.92 |
| C. | Rs. 173.92 |
| D. | Rs. 174.92 |
| Answer» C. Rs. 173.92 | |
| 1866. |
If (3x – 1)3 + (4x – 3)3 + (2x + 1)3 = 3(3x – 1)(4x – 3)(2x + 1) and x ≠ 1/3, then x = ? |
| A. | 1/2 |
| B. | 1/4 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 1867. |
How many real zeros in the polynomial x3 - x2 + 2? |
| A. | 3 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 1868. |
If x + (1/x) = 3√2, then what is the value of x5 + (1/x5)? |
| A. | 178√3 |
| B. | 789√2 |
| C. | 1581√2 |
| D. | 717√2 |
| Answer» E. | |
| 1869. |
If \(\vec{a}, \vec{b}\) and \(\vec{a}+\vec{b}\) are vectors of magnitude α then the magnitude of the vector \(\vec{a}-\vec{b}\) is |
| A. | \(\sqrt{2}\alpha\) |
| B. | \(\sqrt{3}\alpha\) |
| C. | 2α |
| D. | 3α |
| Answer» C. 2α | |
| 1870. |
If the position vectors of A and B are \(\mathop a\limits^ \to\) and \(\mathop b\limits^ \to\) respectively, then the position vector of mid-point of AB is: |
| A. | \(\mathop a\limits^ \to + \mathop b\limits^ \to\) |
| B. | \(\mathop a\limits^ \to - \mathop b\limits^ \to\) |
| C. | \(\frac{1}{2}\left( {\mathop a\limits^ \to + \mathop b\limits^ \to } \right)\) |
| D. | \(\frac{1}{2}\left( {\mathop a\limits^ \to - \mathop b\limits^ \to } \right)\) |
| Answer» D. \(\frac{1}{2}\left( {\mathop a\limits^ \to - \mathop b\limits^ \to } \right)\) | |
| 1871. |
If A is m × n matrix such that AB & BA both are defined, then B is a matrix of order |
| A. | n × n |
| B. | m × m |
| C. | m × n |
| D. | n × m |
| Answer» E. | |
| 1872. |
If x : y = 2 : 1, then (x2 – y2 ) : (x2 + y2 ) is: |
| A. | 1 : 3 |
| B. | 5 : 3 |
| C. | 3 : 1 |
| D. | 3 : 5 |
| Answer» E. | |
| 1873. |
How many pairs of natural numbers are there such that the difference of their squares is 35? |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 1874. |
Consider the matrix \(M = \left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0\\ 1&{ - 2}&1\\ 0&{ - 1}&1 \end{array}} \right]\). One of the eigenvectors of M is |
| A. | \(\left[ {\begin{array}{*{20}{c}} 1\\ { - 1}\\ 1 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} 1\\ 1\\ { - 1} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} { - 1}\\ 1\\ { - 1} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} 1\\ 1\\ 1 \end{array}} \right]\) |
| Answer» E. | |
| 1875. |
A shopkeeper bears an expenditure of Rs. 122 for the production of every item. He also incurs an additional expenditure of Rs. 27,000 which is not related to the number of items produced. He will have to sell the item for Rs. 225 during the season. If he fails to do so, he will have to sell each item for Rs. 75. If he produces 1500 items and is able to sell all the items produced, how much items do he sell during the season so that he does not make any profit or loss? |
| A. | 650 |
| B. | 1000 |
| C. | 750 |
| D. | 850 |
| Answer» B. 1000 | |
| 1876. |
If the sum of a real number and its reciprocal is 26/5, then how many such numbers are possible? |
| A. | None |
| B. | One |
| C. | Two |
| D. | Four |
| Answer» D. Four | |
| 1877. |
If a + 1/a = -2 then the value of a1000 + a-1000 is |
| A. | 2 |
| B. | 0 |
| C. | 1 |
| D. | 1/2 |
| Answer» B. 0 | |
| 1878. |
If x = √6 + √5, then \({x^2} + \frac{1}{{{x^2}}} - 2 = \) |
| A. | \(\sqrt[2]{6}\) |
| B. | \(\sqrt[2]{5}\) |
| C. | 24 |
| D. | 20 |
| Answer» E. | |
| 1879. |
If one root of the equation Ax2 + Bx + C = 0 is two and a half times the other, then which of the following is TRUE? |
| A. | 7B2 = 3CA |
| B. | 7B2 = 4CA |
| C. | 7B2 = 36CA |
| D. | 10B2 = 49CA |
| Answer» E. | |
| 1880. |
If a = 5, b = 4, c = 8 then find the value of (a3 + b3 + c3 – 3abc)/(ab + bc + ca – a2 – b2 – c2).A. 15B. 17C. -17D. -15 |
| A. | B |
| B. | C |
| C. | D |
| D. | A |
| Answer» C. D | |
| 1881. |
After solving the system2x1 + 4x2 - 6x3 = - 8x1 + 3x2 + x3 = 10 and2x1 - 4x2 - 2x3 = - 12Using the Gauss-Jordan method, the values of x1, x2 and x3 are |
| A. | 1, 2, 3 |
| B. | 1, 3, 2 |
| C. | 3, 2, 1 |
| D. | 3, 1, 2 |
| Answer» B. 1, 3, 2 | |
| 1882. |
If 3, 5 are the eigenvalues of a square matrix A of order 2, then the eigenvalues of the matix A3 will be |
| A. | 27, 125 |
| B. | 9, 15 |
| C. | 3, 5 |
| D. | 9, 25 |
| Answer» B. 9, 15 | |
| 1883. |
α and β are the roots of the quadratic equation. If α + β = 8 and α - β = 2√5, then which of the following equation will have roots α4 and β4? |
| A. | x2 - 1522x + 14641 = 0 |
| B. | x2 + 1921x + 14641 = 0 |
| C. | x2 - 1764x + 14641 = 0 |
| D. | x2 + 2520x + 14641 = 0 |
| Answer» B. x2 + 1921x + 14641 = 0 | |
| 1884. |
If x = 23, find the value of x8 - 24x7 + 24x6 - 24x5 + 24x4 - 24x3 + 24x2 - 24x + 1. |
| A. | -22 |
| B. | -20 |
| C. | -18 |
| D. | -24 |
| Answer» B. -20 | |
| 1885. |
A complete factorisation of x4 + 64 is: |
| A. | (x2 + 8)2 |
| B. | (x2 + 8)(x2– 8) |
| C. | (x2– 4x + 8)(x2 – 4x – 8) |
| D. | (x2 + 4x + 8)(x2– 4x + 8) |
| Answer» E. | |
| 1886. |
If 3x2 + 6x – 17 = 0, then (x + 1)2 is equal to ______. |
| A. | 20 |
| B. | 20/3 |
| C. | 6 |
| D. | 14/3 |
| Answer» C. 6 | |
| 1887. |
Forces 3î + 2ĵ + 5k̂ and 2î + ĵ - 3k̂ are acting on a particle and displace it from the point 2î - ĵ - 3k̂ to the point 4î - 3ĵ + 7k̂. The work done by the force is: |
| A. | 18 units. |
| B. | 30 units. |
| C. | 24 units. |
| D. | 36 units. |
| Answer» D. 36 units. | |
| 1888. |
Every diagonal element of a skew-symmetric matrix is |
| A. | 1 |
| B. | 0 |
| C. | Purely real |
| D. | None of these |
| Answer» C. Purely real | |
| 1889. |
If the sum of square of the age of a person today, after one year and after two years is equal to 2030. What is the present age of the person. |
| A. | 23 |
| B. | 27 |
| C. | 25 |
| D. | 30 |
| Answer» D. 30 | |
| 1890. |
If x4 + x-4 = 194, x > 0, then the value of \(x+\dfrac{1}{x}\) is: |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 14 |
| Answer» B. 6 | |
| 1891. |
If (8, 2) is a solution of x + 4y - 2k = 0, then find the value of k2. |
| A. | 36 |
| B. | 49 |
| C. | 64 |
| D. | 81 |
| Answer» D. 81 | |
| 1892. |
If x = a + 1/a and y = a – 1/a then √(x4 + y4 – 2x2y2) is equal to: |
| A. | 8 |
| B. | 8/a2 |
| C. | 16a2 |
| D. | 4 |
| Answer» E. | |
| 1893. |
If \(\frac{A}{B}\; + \;\frac{B}{A}\; = \;1,\) then find A3 + B3. |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» D. -1 | |
| 1894. |
If x + 1/x = 2, then find the value of x2 + 1/x2. |
| A. | 1 |
| B. | –2 |
| C. | 0 |
| D. | 2 |
| Answer» E. | |