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.
| 451. |
If a – b = 4 and ab = 45 find the value of a3 - b3 |
| A. | 604 |
| B. | 370 |
| C. | 253 |
| D. | 199 |
| Answer» B. 370 | |
| 452. |
If x - 1/x = 7, then x3 – 1/x3 is equal to: |
| A. | 480 |
| B. | 500 |
| C. | 364 |
| D. | 376 |
| Answer» D. 376 | |
| 453. |
If x - 3y = 2 and x + y = 6, then the values of x and y will be |
| A. | 5, -1 |
| B. | 5, 1 |
| C. | 1, 5 |
| D. | -1, 5 |
| Answer» C. 1, 5 | |
| 454. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 - 12x + 35 = 0II. y2 - 10y + 24 = 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» F. | |
| 455. |
If x = 2 + √3, then what is the value of [√(2x) + 1/√(2x)] |
| A. | 2√3 |
| B. | 3√3 |
| C. | (3√3 + 1)/2 |
| D. | 2√3 + 1 |
| Answer» D. 2√3 + 1 | |
| 456. |
If a – b = 5 and a2 + b2 = 97, ab = ? A. 48B. 32C. 36D. 72 |
| A. | A |
| B. | C |
| C. | B |
| D. | D |
| Answer» C. B | |
| 457. |
If x = 2 + √5 then the value of (x3 – x-3) is: |
| A. | 52 |
| B. | 76 |
| C. | -76 |
| D. | -52 |
| Answer» C. -76 | |
| 458. |
If x/(y + z – x) = y/(z + x – y) = z/(x + y – z) = r, then r cannot take any value except___ |
| A. | - 1/2 |
| B. | 1 |
| C. | 1 or - 1/2 |
| D. | -1 or 1/2 |
| Answer» D. -1 or 1/2 | |
| 459. |
A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting? |
| A. | 189 |
| B. | 159 |
| C. | 161 |
| D. | 153 |
| Answer» E. | |
| 460. |
If (5x – y)/(5x + y) = 3/7, then what is the value of (4x2 + y2 – 4xy)/(9x2 + 16y2 + 24xy)? |
| A. | 0 |
| B. | 3/7 |
| C. | 18/49 |
| D. | 1/6 |
| Answer» B. 3/7 | |
| 461. |
In the matrix equation Px = q, which of the following is a necessary condition for existence of at least one solution for unknown vector x? |
| A. | Matrix P must be singular. |
| B. | Matrix P must be square |
| C. | Augmented matrix [Pq] must have the same rank as matrix P. |
| D. | Vector q must have only non-zero elements. |
| Answer» D. Vector q must have only non-zero elements. | |
| 462. |
If \(p = \sqrt {72 - \sqrt {72 - \sqrt {72 - \sqrt {72 - \ldots \infty } } } } \), then find the value of 2p2 + 1. |
| A. | -129 |
| B. | -163 |
| C. | 129 |
| D. | 163 |
| Answer» D. 163 | |
| 463. |
\(\frac{{8 \times {{\left( {3.75} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5\;}}\)= _________. |
| A. | 9.5 |
| B. | 8.5 |
| C. | 7.5 |
| D. | 6.5 |
| Answer» C. 7.5 | |
| 464. |
If (4x + 16) ÷ 4x = 9, then find the value of 5x ÷ [12x2 + (14/11)x + 2].A. 29/57B. 51/111C. 55/124D. 68/121 |
| A. | B |
| B. | C |
| C. | A |
| D. | D |
| Answer» C. A | |
| 465. |
If x = 4 + √15, then what is the value of [x2 + (1/x2)]? |
| A. | 62 |
| B. | 64 |
| C. | 34 |
| D. | 36 |
| Answer» B. 64 | |
| 466. |
If A + B = 12 and AB = 17, what is the value of A3 + B3? |
| A. | 1116 |
| B. | 1166 |
| C. | 1106 |
| D. | 1213 |
| Answer» B. 1166 | |
| 467. |
Amir divides 850 gifts into 4 children. Gift received by the first child, twice the gift which came in the other child's part, three times the gifts which came in the third child's part and four times the gift of the fourth child, all are equal. How many gifts are available to both the first and the second? |
| A. | 412 |
| B. | 312 |
| C. | 612 |
| D. | 512 |
| Answer» D. 512 | |
| 468. |
On dividing x4 + 2x3 + 8x2 + 12x + 18 by a polynomial g(x), the quotient and remainder are x2 + 2x + 3 and 2x + 3 respectively, then g(x) is: |
| A. | x2 – 3x + 10 |
| B. | x2 + 5 |
| C. | x2 - 3 |
| D. | x2 + 3X - 5 |
| Answer» C. x2 - 3 | |
| 469. |
If 5x3 + 5x2 – 6x + 9 is divided by (x + 3), then the remainder is |
| A. | 135 |
| B. | -135 |
| C. | -63 |
| D. | 63 |
| Answer» D. 63 | |
| 470. |
If (s - a) + (s - b) + (s - c) = s, then the value of [(s - a)2 + (s - b)2 + (s - c)2 + s2] / (a2 + b2 + c2) will be |
| A. | 3 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» C. 0 | |
| 471. |
If a + b + c = 6 and ab + bc + ca = 4, then a3 + b3 + c3 - 3abc is equal to: |
| A. | 144 |
| B. | 148 |
| C. | 154 |
| D. | 160 |
| Answer» B. 148 | |
| 472. |
Rajeev was to earn Rs. 500 and a free holiday for seven weeks’ work. He worked for only 5 weeks and earned Rs. 50 and a free holiday. What was the value of the holiday? |
| A. | Rs. 1,075 |
| B. | Rs. 1,850 |
| C. | Rs. 1,550 |
| D. | Rs. 1,675 |
| Answer» B. Rs. 1,850 | |
| 473. |
If (a2 - b2) ÷ (a + b) = 25, find (a - b). |
| A. | 15 |
| B. | 18 |
| C. | 25 |
| D. | 30 |
| Answer» D. 30 | |
| 474. |
A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25 paise coins is- |
| A. | 120 |
| B. | 124 |
| C. | 144 |
| D. | 200 |
| Answer» C. 144 | |
| 475. |
If 4x – 5y = –37 and 7x + y = –16, then x – y = ______ |
| A. | –8 |
| B. | 8 |
| C. | 2 |
| D. | –2 |
| Answer» B. 8 | |
| 476. |
Find the unit place digit in (194)102 + (294)103. |
| A. | 0 |
| B. | 6 |
| C. | 8 |
| D. | 2 |
| Answer» B. 6 | |
| 477. |
If \(A = \left[ {\begin{array}{*{20}{c}}1&5\\6&2\end{array}} \right]\) and \(B = \left[ {\begin{array}{*{20}{c}}3&7\\8&4\end{array}} \right].A{B^T}\) is equal to |
| A. | \(\left[ {\begin{array}{*{20}{c}}{38}&{28}\\{32}&{56}\end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}}3&{40}\\{42}&8\end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}}{43}&{27}\\{34}&{50}\end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}}{38}&{32}\\{28}&{56}\end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}}3&{40}\\{42}&8\end{array}} \right]\) | |
| 478. |
2x - 3y is a factor of: |
| A. | 4x2 + 9y2 – 12xy |
| B. | 4x2 + 9y2 + 12xy |
| C. | 8x3 + 27y3 |
| D. | 4x2 + 36y2 + 12xy |
| Answer» B. 4x2 + 9y2 + 12xy | |
| 479. |
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. x2 – 36x + 324 = 0B. y2 – 42y + 441 = 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» D. if x ≤ y | |
| 480. |
A tiger weighs 280 kg. If a blue whale weighs 1,40,000 kg, then how many tigers are needed to be put together to weigh the same as that of a whale? |
| A. | 140 |
| B. | 400 |
| C. | 500 |
| D. | 200 |
| Answer» D. 200 | |
| 481. |
Given below are two algebraic equation named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.Quantity A: x2 – 7x + 12 = 0Quantity B: y2 – 13y + 42 = 0 |
| A. | Quantity 1 > Quantity 2 |
| B. | Quantity 1 < Quantity 2 |
| C. | Quantity 1 ≤ Quantity 2 |
| D. | Quantity 1 ≥ Quantity 2 |
| E. | Either Quantity 1 = Quantity 2 or no relation can be established. |
| Answer» C. Quantity 1 ≤ Quantity 2 | |
| 482. |
If in a right-angled triangle ABC, hypotenuse AC = p, then what is \(\overrightarrow {AB} \cdot \overrightarrow {AC} + \overrightarrow {BC} \; \cdot \overrightarrow {BA} + \overrightarrow {CA} \cdot \overrightarrow {CB} \) equal to? |
| A. | p2 |
| B. | 2p2 |
| C. | \(\frac{{{p^2}}}{2}\) |
| D. | p |
| Answer» B. 2p2 | |
| 483. |
If sin A + cos A = p and sin3A + cos3A = q, then which one of the following is correct? |
| A. | p3 – 3p + q = 0 |
| B. | q3 – 3p + 2p = 0 |
| C. | p3 – 3p + 2q = 0 |
| D. | p3 + 3p + 2q = 0 |
| Answer» D. p3 + 3p + 2q = 0 | |
| 484. |
If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9? |
| A. | 18 |
| B. | -9 |
| C. | -27 |
| D. | -18 |
| Answer» C. -27 | |
| 485. |
If f(x) = (1/x) – 1/ (x + 1), then what is the value of f(1) + f(2) + f(3) + - - - + f(10)? |
| A. | 9/10 |
| B. | 10/11 |
| C. | 11/12 |
| D. | 12/13 |
| Answer» C. 11/12 | |
| 486. |
If x + 3y - 2z/4 = 6, x + (2/3)(2y + 3z) = 33 and (1/7)(x + y + z) + 2z = 9, then what is the value of 46x + 131y? |
| A. | 414 |
| B. | 364 |
| C. | 384 |
| D. | 464 |
| Answer» B. 364 | |
| 487. |
If x2 + 1/x2 = 98 (x>0), then the value of x3 + 1/x3 is |
| A. | 970 |
| B. | 1030 |
| C. | – 970 |
| D. | – 1030 |
| Answer» B. 1030 | |
| 488. |
Let \(\sum {u_n}\) be a series of positive terms and let \(\begin{array}{*{20}{c}} {{\rm{lim}}u_n^{1/n}}\\ {n \to \infty } \end{array} = l\), then, which among the following does not express the condition for the Cauchy’s nth root test? |
| A. | If l > 1, ∑un diverges |
| B. | If l < 1, ∑un converges |
| C. | If l = 0, the series neither converges nor diverges |
| D. | If l = 1, the test fails and the series may either converge or diverge |
| Answer» D. If l = 1, the test fails and the series may either converge or diverge | |
| 489. |
In an exam, a candidate attempts 20 questions and scores 72 marks. If 5 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer, then how many questions were answered correctly by him? |
| A. | 18 |
| B. | 17 |
| C. | 16 |
| D. | 15 |
| Answer» D. 15 | |
| 490. |
Find the roots of the following equationx2 + 12x - 36 = 0 |
| A. | 6(1 + √2), -6(√2 - 1) |
| B. | -6(1 + √2), 6(√2 - 1) |
| C. | 9(1 + √2), -9(√2 - 1) |
| D. | 6(1 + √2), 6(√2 - 1) |
| Answer» C. 9(1 + √2), -9(√2 - 1) | |
| 491. |
If a3 + b3 = 416 and a + b = 16, then (a – b)2 + ab is equal to: |
| A. | 32 |
| B. | 22 |
| C. | 24 |
| D. | 26 |
| Answer» E. | |
| 492. |
If (x - y) = 7, then what is the value of (x - 15)3 - (y - 8)3? |
| A. | 0 |
| B. | 343 |
| C. | 392 |
| D. | 2863 |
| Answer» B. 343 | |
| 493. |
If a2 + b2 = 82 and ab = 9, then a possible value of a3 + b3 is: |
| A. | 750 |
| B. | 730 |
| C. | 830 |
| D. | 720 |
| Answer» C. 830 | |
| 494. |
If (a2 - 1)/a = 5, then what is the value of (a6 - 1)/a3? |
| A. | 125 |
| B. | -125 |
| C. | 140 |
| D. | -140 |
| Answer» D. -140 | |
| 495. |
Choose the CORRECT set of functions, which are linearly dependent. |
| A. | sin x, sin2x and cos2x |
| B. | cosx, sinx and tan x |
| C. | cos2x, sin2x and cos2x |
| D. | cos2x, sinx and cosx |
| Answer» D. cos2x, sinx and cosx | |
| 496. |
If a2 + b2 = 45, a + b = 9, then a – b = ? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 2 |
| Answer» B. 4 | |
| 497. |
If \(p + \dfrac{1}{p}=8\), then \(p^3 + \dfrac{1}{p^3}=\)_____. |
| A. | 532 |
| B. | 468 |
| C. | 488 |
| D. | 486 |
| Answer» D. 486 | |
| 498. |
If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of q is: |
| A. | 4 |
| B. | 12 |
| C. | 3 |
| D. | 49/4 |
| Answer» E. | |
| 499. |
If equation 20x + 5y + 11 = 0 and 50x – ky – 9 = 0 has no solution, then the value of k is: |
| A. | - 18 |
| B. | 12.5 |
| C. | -12.5 |
| D. | 18 |
| Answer» D. 18 | |
| 500. |
If the sum of digits of a number is 9 and the difference between the digit at ten’s place and unit’s place is 1, then the two-digit number is: |
| A. | 18 |
| B. | 63 |
| C. | 54 |
| D. | 72 |
| Answer» D. 72 | |