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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.
| 1401. |
If \(\frac{x}{y} = \frac{{a + 2}}{{a - 2}}\), then \(\frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}} = \)? |
| A. | \(\frac{{2a}}{{{a^2} + 2}}\) |
| B. | \(\frac{{4a}}{{{a^2} + 4}}\) |
| C. | 1 |
| D. | None of the above |
| Answer» C. 1 | |
| 1402. |
In matrix equation [A]{X} = {R},\(\left[ {\rm{A}} \right] = \left[ {\begin{array}{*{20}{c}} 4&8&4\\ 8&{16}&{ - 4}\\ 4&{ - 4}&{15} \end{array}} \right],\;\left\{ X \right\} = \left\{ {\begin{array}{*{20}{c}} 2\\ 1\\ 4 \end{array}} \right\}\;and\;\left\{ R \right\} = \left\{ {\begin{array}{*{20}{c}} {32}\\ {16}\\ {64} \end{array}} \right\}.\)One of the eigenvalues of matrix [A] is |
| A. | 4 |
| B. | 8 |
| C. | 15 |
| D. | 16 |
| Answer» E. | |
| 1403. |
If \(\vec a = \;\hat i + 2\hat j - 3\hat k\;and\;\vec b = 2\hat i + 3\hat j + \hat k\) then find a unit vector in the direction of \({\vec a + \;\vec b}\) ? |
| A. | \(\frac{3}{{\sqrt {38} }}\;\hat i - \frac{5}{{\sqrt {38}}}\;\hat j - \frac{2}{{\sqrt {38} }}\hat k\) |
| B. | \(\frac{3}{{\sqrt {38} }}\;\hat i + \frac{5}{{\sqrt {38}}}\;\hat j + \frac{2}{{\sqrt {38} }}\hat k\) |
| C. | \(\frac{3}{{\sqrt {38} }}\;\hat i + \frac{5}{{\sqrt {38}}}\;\hat j - \frac{2}{{\sqrt {38} }}\hat k\) |
| D. | None of these |
| Answer» D. None of these | |
| 1404. |
In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer:I. (x – 13)2 = 0II. y2 = 169 |
| A. | x > y |
| B. | x ≥ y |
| C. | x < y |
| D. | x ≤ y |
| E. | x = y or the relation cannot be determined |
| Answer» C. x < y | |
| 1405. |
If α, β are the roots of ax2 + bx + c = 0, then \(\frac{{{\alpha ^2}}}{\beta } + \frac{{{\beta ^2}}}{\alpha } =\) ______ |
| A. | \(\frac{{{b^2} - 2ac}}{{{c^2}}}\) |
| B. | \(\frac{{3abc - {b^3}}}{{{a^2}c}}\) |
| C. | \(\frac{{{b^2} - 2ac}}{{ac}}\) |
| D. | \(\frac{{3abc - {b^3}}}{{{a^3}}}\) |
| Answer» C. \(\frac{{{b^2} - 2ac}}{{ac}}\) | |
| 1406. |
Given that (5x – 3)3 + (2x + 5)3 + 27(4 – 3x) 3 = 9(3 – 5x) (2x + 5) (3x – 4), then the value of (2x + 1) is: |
| A. | 13 |
| B. | -15 |
| C. | 15 |
| D. | -13 |
| Answer» D. -13 | |
| 1407. |
If sec θ = 4x and tan θ= 4/x, (x ≠ 0) then the value of 8(x2 - 1/x2) is: |
| A. | 1/2 |
| B. | 1/6 |
| C. | 1/8 |
| D. | 1/4 |
| Answer» B. 1/6 | |
| 1408. |
Find the quadratic equation with real coefficients which has (-5 -i) as a root. |
| A. | x2 - 26x - 10 = 0 |
| B. | x2 + 10x + 26 = 0 |
| C. | x2 - 26x + 10 = 0 |
| D. | x2 - 10x = 26 = 0 |
| Answer» C. x2 - 26x + 10 = 0 | |
| 1409. |
If \(x = \frac{{\sqrt 7\; - \;\sqrt 5 }}{{\sqrt 5\; + \;\sqrt 7 }}\) and y is reciprocal of x, then what is the value of \(\sqrt {\left( {{x^3} + {y^3}} \right)}\)? |
| A. | 5√47 |
| B. | 6√47 |
| C. | 3√47 |
| D. | √47 |
| Answer» C. 3√47 | |
| 1410. |
Let A be (n x n) real valued square symmetric matrix of rank 2 with \(\mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n A_{ij}^2 = 50\). Consider the following statements.(I) One eigenvalue must be in [–5, 5](II) The eigenvalue with the largest magnitude must be strictly greater than 5Which of the above statements about eigenvalues of A is/are necessarily CORRECT? |
| A. | Both I and II |
| B. | I only |
| C. | II only |
| D. | Neither I nor II |
| Answer» C. II only | |
| 1411. |
If a + b + c = 3 and none of a, b and c is equal to 1, then what is the value of 1/[(1 – a)(1 – b)] + 1/[(1 – b)(1 – c)] + 1/[(1 – c)(1 – a)]? |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | 6 |
| Answer» B. 1 | |
| 1412. |
Ram reads 1/5th of a book, If 60 pages are still left to read, then how many pages are there in the book? |
| A. | 75 |
| B. | 90 |
| C. | 105 |
| D. | 120 |
| Answer» B. 90 | |
| 1413. |
ax3 + bx2 + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ 0. Which of the following statements is true? |
| A. | d can be chosen to ensure that x = 0 is a root for any given set a, b, c. |
| B. | No choice of coefficients can make all roots identical. |
| C. | a, b, c, d can be chosen to ensure that all roots are complex. |
| D. | c alone can ensure that all roots are real. |
| Answer» B. No choice of coefficients can make all roots identical. | |
| 1414. |
Price of a diamond is directly proportional to square of its weight. A man broke the diamond accidently in three pieces in the ratio of 3 : 5 : 7 and thus loses Rs 42600. What was the original price (in Rs) of the diamond? |
| A. | 11786 |
| B. | 60000 |
| C. | 67500 |
| D. | 75000 |
| Answer» D. 75000 | |
| 1415. |
Find the unit digit in the given factor (3451)51 × (531)43.A. 6B. 4C. 1D. 9 |
| A. | B |
| B. | C |
| C. | D |
| D. | A |
| Answer» C. D | |
| 1416. |
If (x2 - 1) is a factor of ax4 + bx3 + cx2 + dx + e, then which one of the following is correct? |
| A. | a + b + c = d + e |
| B. | a + b + e = c + d |
| C. | b + c + d = a + e |
| D. | a + c + e = b + d |
| Answer» E. | |
| 1417. |
If x2 – 3x – 1 = 0, then the value of (x2 + 8x – 1) (x3 + x-1)-1 is: |
| A. | 3 |
| B. | 8 |
| C. | 3/8 |
| D. | 1 |
| Answer» E. | |
| 1418. |
If (x - 2)2 + (y + 3)2 + (z - 15)2 = 0, then what is the value of x + y + z - 5? |
| A. | 5 |
| B. | 9 |
| C. | 15 |
| D. | 20 |
| Answer» C. 15 | |
| 1419. |
(3a - 4b)3 is equal to: |
| A. | 9a2 - 16b2 |
| B. | 27a3 - 64b3 |
| C. | 27a3 - 64b3 - 108a2b + 144ab2 |
| D. | 9a2 - 24ab + 16b2 |
| Answer» D. 9a2 - 24ab + 16b2 | |
| 1420. |
If \(\bar a\) and \(\bar b\) are unit vectors and θ is the angle between them then \(\left| {\frac{{\bar a - \bar b}}{2}} \right|\) is |
| A. | \(\sin \frac{\theta }{2}\) |
| B. | sin θ |
| C. | 2 sin θ |
| D. | sin 2θ |
| Answer» B. sin θ | |
| 1421. |
In the following question, two equations are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.A. 3x2 – 7x + 4 = 0B. 2y2 – 3y + 1 = 0 |
| A. | if x > y |
| B. | if x ≥ y |
| C. | if x < y |
| D. | if x ≤ y |
| E. | if x = y or the relationship cannot be established. |
| Answer» C. if x < y | |
| 1422. |
In a fraction when 3 is added to its numerator and denominator it becomes 4/5. And it becomes 1/2 when 2 is subtracted from both the numerator and denominator. Find the fraction. |
| A. | 15/16 |
| B. | 14/16 |
| C. | 11/16 |
| D. | 9/16 |
| Answer» D. 9/16 | |
| 1423. |
If x4 + (1/x4) = 34, then what is the value of x3 – (1/x3)? |
| A. | 0 |
| B. | 6 |
| C. | 8 |
| D. | 14 |
| Answer» E. | |
| 1424. |
If \(2\frac{1}{2}\) kg of vegetable costs Rs 120, then what is the cost of 1/2 kg vegetable?A. 60B. 36C. 24D. 48 |
| A. | D |
| B. | A |
| C. | C |
| D. | B |
| Answer» D. B | |
| 1425. |
If \({\rm{a\;}} + {\rm{\;}}\frac{1}{{\rm{a}}}{\rm{\;}} = {\rm{\;}}3,\) then \(\left( {{{\rm{a}}^4}{\rm{\;}} + {\rm{\;}}\frac{1}{{{{\rm{a}}^4}}}} \right)\) is equal to: |
| A. | 77 |
| B. | 81 |
| C. | 47 |
| D. | 27 |
| Answer» D. 27 | |
| 1426. |
For the matrix \(\begin{bmatrix} 1 & 5 \\\ 3 & 3\end{bmatrix}\), the eigen-vectors are |
| A. | \(\begin{bmatrix} 1 \\\ -1\end{bmatrix}\) and \(\begin{bmatrix} 3 \\\ -3\end{bmatrix}\) |
| B. | \(\begin{bmatrix} 1 \\\ 1\end{bmatrix}\) and \(\begin{bmatrix} -5/3 \\\ 1\end{bmatrix}\) |
| C. | \(\begin{bmatrix} 1 \\\ 3\end{bmatrix}\) and \(\begin{bmatrix} 5 \\\ 3\end{bmatrix}\) |
| D. | \(\begin{bmatrix} -1 \\\ 1\end{bmatrix}\) and \(\begin{bmatrix} 5/3 \\\ 1\end{bmatrix}\) |
| Answer» C. \(\begin{bmatrix} 1 \\\ 3\end{bmatrix}\) and \(\begin{bmatrix} 5 \\\ 3\end{bmatrix}\) | |
| 1427. |
If λ is an integer and α, β are the roots of 4x2 – 16x + λ/4 = 0 such that 1 < α < 2 and 2 < β < 3, then how many values can λ take? |
| A. | 3 |
| B. | 9 |
| C. | 14 |
| D. | 15 |
| Answer» E. | |
| 1428. |
If (2a - 3)2 + (3b - 5)2 + (4c - 7)2 = 0, then find the value of √(4a + 3b + 4c).A. 6√2B. 9√2C. 12√2D. 3√2 |
| A. | C |
| B. | A |
| C. | B |
| D. | D |
| Answer» E. | |
| 1429. |
Amal needs a motorcycle. The motorcycle costs Rs. 92750. He has only Rs. 87150 in his hand. How much more money does he need to buy the motorcycle? |
| A. | Rs. 5700 |
| B. | Rs. 5500 |
| C. | Rs. 5600 |
| D. | Rs. 5650 |
| Answer» D. Rs. 5650 | |
| 1430. |
If 2 is a zero of polynomialf(x) = ax2 - 3(a - 1)x - 1, then value of a is |
| A. | 5 / 2 |
| B. | -2 / 5 |
| C. | -5 / 2 |
| D. | None of these |
| Answer» B. -2 / 5 | |
| 1431. |
If 8(a + b)3 + (a - b)3 = (3a + b) (Aa2 + Bab + Cb2), then what is the value of (A + B - C)? |
| A. | 10 |
| B. | 2 |
| C. | 4 |
| D. | 11 |
| Answer» C. 4 | |
| 1432. |
Consider the following linear system.x + 2y - 3z = a2x + 3y + 3z = b5x + 9y - 6z = cThis system is consistent if a, b and c satisfy the equation |
| A. | 7a - b - c = 0 |
| B. | 3a + b - c = 0 |
| C. | 3a - b + c = 0 |
| D. | 7a - b + c = 0 |
| Answer» C. 3a - b + c = 0 | |
| 1433. |
A crate of egg holds one rotten egg out of every 25 egg in it. If 5 out of 8 rotten eggs are unusable and there are total 10 unusable eggs in the crate, then calculate the number of eggs in the crate. |
| A. | 380 |
| B. | 400 |
| C. | 420 |
| D. | 440 |
| Answer» C. 420 | |
| 1434. |
In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark the correct answer.I. x2 = 625II. y = √625 |
| A. | x > y |
| B. | x ≥ y |
| C. | x < y |
| D. | x ≤ y |
| E. | x = y or the relation cannot be determined |
| Answer» E. x = y or the relation cannot be determined | |
| 1435. |
If \(s + \frac{1}{s} = 4\) then find the value of \({s^2} + \frac{1}{{{s^2}}}\). |
| A. | 14 |
| B. | 16 |
| C. | 20 |
| D. | 24 |
| Answer» B. 16 | |
| 1436. |
If α + β + γ = 5, αβ + βγ + γα = 7 and αβγ = 3, then the equation where roots are α, β and γ is: |
| A. | x3 - 7 = 0 |
| B. | x3 - 5x2 + 7x - 3 = 0 |
| C. | x3 + 7x2 - 3 = 0 |
| D. | x2 + 7x2 + 3 = 0 |
| Answer» C. x3 + 7x2 - 3 = 0 | |
| 1437. |
If x, y, z are the three factors of a3– 7a – 6, then value of x + y + z will be |
| A. | 3a |
| B. | 3 |
| C. | 6 |
| D. | a |
| Answer» B. 3 | |
| 1438. |
If 4x2 - 40x + 10 = 0, then the value of x2 - 10x + 5 equals to: |
| A. | 2.5 |
| B. | 1.5 |
| C. | 0 |
| D. | - 2.5 |
| Answer» B. 1.5 | |
| 1439. |
If a ⊗ \(b = \left( {a + b} \right)\;\left( {a \times b} \right),\) then find the value of 6 ⊗ 5. |
| A. | 110 |
| B. | 220 |
| C. | 330 |
| D. | 440 |
| Answer» D. 440 | |
| 1440. |
If the volume of parallelepiped formed by the vectors \(\hat i + \lambda \hat j + \hat k,\;\hat j + \lambda \hat k,{\rm{\;and\;}}\lambda \hat i + {\rm{\hat k}}\) is minimum, then λ is equal to: |
| A. | \(- \frac{1}{{\sqrt 3 }}\) |
| B. | \(\frac{1}{{\sqrt 3 }}\) |
| C. | √3 |
| D. | \(- \sqrt 3\) |
| Answer» C. √3 | |
| 1441. |
If x2 - 3x + 1 = 0, then what is the value of \({x^2} + \frac{1}{{{x^2}}}?\) |
| A. | 3 |
| B. | 7 |
| C. | 9 |
| D. | 11 |
| Answer» C. 9 | |
| 1442. |
Let \(\left\) and \(\left\) be real sequences and let for some k ϵ N, 0 ≤ xn ≤ yn for n ≥ k.Then, which of the following statements is true? |
| A. | Divergence of ∑ yn ⇒ Divergence of ∑ xn |
| B. | ∑ xn and ∑ yn are always divergent |
| C. | Convergence of ∑ xn ⇒ Convergence of ∑ yn |
| D. | Convergence of ∑ yn ⇒ Convergence of ∑ xn |
| Answer» E. | |
| 1443. |
Find the factors of the expression 3x2 – 5x – 8. |
| A. | (x + 1) and (3x + 8) |
| B. | (x + 1) and (3x – 8) |
| C. | (x – 1) and (3x + 8) |
| D. | (x – 1) and (3x – 8) |
| Answer» C. (x – 1) and (3x + 8) | |
| 1444. |
If \(x^4 + \dfrac{1}{x^4}=322, x \neq 0\), then one of the values of \(\left(x - \dfrac{1}{x}\right)\) is |
| A. | 6 |
| B. | 8 |
| C. | 2 |
| D. | 4 |
| Answer» E. | |
| 1445. |
If the mean age of combined group of boys and girls is 18 years and the mean of age of boys is 20 and that of girls is 16, then what is the percentage of boys in the group? |
| A. | 60 |
| B. | 50 |
| C. | 45 |
| D. | 40 |
| Answer» C. 45 | |
| 1446. |
\(\frac{{63.5 \times 63.5 \times 63.5 + 36.5 \times 36.5 \times 36.5}}{{6.35 \times 6.35 + 3.65 \times 3.65 - 6.35 \times 3.65}}\) is equal to∶ |
| A. | 100 |
| B. | 1,000 |
| C. | 1,00,000 |
| D. | 10,000 |
| Answer» E. | |
| 1447. |
Let α ∈ R and three vectors \(\vec a = \alpha \hat i + \hat j + 3\hat k,\;\vec b = 2\hat i + \hat j - \alpha \hat k,{\rm{\;and\;}}\vec c = \alpha \hat i - 2\hat j + 3\hat k\). Then the set \(S = \left\{ {\alpha :\vec a,\;\vec b{\rm{\;and\;}}\vec c{\rm{\;are\;coplanar}}} \right\}\) |
| A. | Is singleton |
| B. | Is empty |
| C. | Contains exactly two positive numbers |
| D. | Contains exactly two numbers only one of which is positive |
| Answer» C. Contains exactly two positive numbers | |
| 1448. |
Given that:\(\frac{1}{{1 + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{x}}}}}}} = \frac{5}{8}\)then what is the value of x? |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | 4 |
| Answer» B. 3 | |
| 1449. |
If the product of eigenvalues of the matrix \(A =\left[ {\begin{array}{*{20}{c}} {1}&{2}&{-1}\\ {3}&{5}&{2}\\ {1}&{k}&{2} \end{array}} \right]\) is -8, then the value of k will be: |
| A. | 3 |
| B. | 2 |
| C. | -2 |
| D. | -3 |
| Answer» B. 2 | |
| 1450. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}}1&2&{ - 2}\\2&5&{ - 4}\\3&7&{ - 5}\end{array}} \right]\) then A-1 is |
| A. | A2 – A + 5I |
| B. | A2 + A – 5I |
| C. | A3 – A2 + 5A |
| D. | A2 – 2A + 5I |
| Answer» B. A2 + A – 5I | |