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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.
| 1451. |
If ab + bc + ca = 0, then the value of \(\frac{{\left( {{b^2} - ca} \right)\left( {{c^2} - ab} \right) + \left( {{a^2} - bc} \right)\left( {{c^2} - ab} \right) + \left( {{a^2} - bc} \right)\left( {{b^2} - ca} \right)}}{{\left( {{a^2} - bc} \right)\left( {{b^2} - ca} \right)\left( {{c^2} - ab\;} \right)}}\) is |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 1452. |
Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin. What is \(\overrightarrow {{\rm{OA}}} + \overrightarrow {{\rm{OB}}} + \overrightarrow {{\rm{OC}}} + \overrightarrow {{\rm{OD}}}\) equal to? |
| A. | \(2\;\overrightarrow {OP} \) |
| B. | \(4\;\overrightarrow {OP}\) |
| C. | \(6\;\overrightarrow {OP} \) |
| D. | \(8\;\overrightarrow {OP} \) |
| Answer» C. \(6\;\overrightarrow {OP} \) | |
| 1453. |
If a = 1 + √3, b = 1 – √3, then what is the value of a2 + b2? |
| A. | 4 |
| B. | 8 |
| C. | 0 |
| D. | 2 |
| Answer» C. 0 | |
| 1454. |
A two digit number is such that the product of its digits is 12. When 36 is added to the number, the digits interchange their places. Find the number: |
| A. | 62 |
| B. | 60 |
| C. | 26 |
| D. | 20 |
| Answer» D. 20 | |
| 1455. |
If a3 + b3 + c3 - 3abc = 126, a + b + c = 6, then the value of (ab + bc + ca) is: |
| A. | 8 |
| B. | 7 |
| C. | 5 |
| D. | 9 |
| Answer» D. 9 | |
| 1456. |
If x4 + 2x3 + ax2 + bx + 9 is a perfect square, where a and b are positive real numbers, then the value of a and b are |
| A. | a = 5, b = 6 |
| B. | a = 6, b = 7 |
| C. | a = 7, b = 6 |
| D. | a = 7, b = 8 |
| Answer» D. a = 7, b = 8 | |
| 1457. |
If a2 + b2 + c2 = 16, x2 + y2 + z2 = 25 and ax + by + cz = 20, then the value of \(\frac{{a + b + c}}{{x + y + z}}\) |
| A. | 3/5 |
| B. | 5/3 |
| C. | 4/5 |
| D. | 5/4 |
| Answer» D. 5/4 | |
| 1458. |
Divide (-12x + 48) / (x - 4), when x ≠ 4 |
| A. | -12 |
| B. | (x - 4) |
| C. | 12(x - 4) |
| D. | 12(x) / (x - 4) |
| Answer» B. (x - 4) | |
| 1459. |
If α and β are roots of the equation x2 – x – 1 = 0, then the equation whose roots are α/β and β/α is: |
| A. | x2 + 3x – 1 = 0 |
| B. | x2 + x – 1 = 0 |
| C. | x2 – x + 1 = 0 |
| D. | x2 + 3x + 1 = 0 |
| Answer» E. | |
| 1460. |
Find the unit place digit in 71 × 72 × 73 × 74 × 76 × 77 × 78 × 79. |
| A. | 2 |
| B. | 0 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 1461. |
If a3 + b3 + c3 - 3abc = 250 and a + b + c = 10, then what is the value of ab + bc + ca? |
| A. | 20 |
| B. | 25 |
| C. | 24 |
| D. | 15 |
| Answer» C. 24 | |
| 1462. |
If 27(x + y)3 - 8(x - y)3 = (x + 5y)(Ax2 + By2 + Cxy), then what is the value of (A + B - C)? |
| A. | 13 |
| B. | 16 |
| C. | 18 |
| D. | 11 |
| Answer» C. 18 | |
| 1463. |
If a + b = 5 and 3a + 2b = 20, then (3a + b) will be |
| A. | 10 |
| B. | 25 |
| C. | 20 |
| D. | 15 |
| Answer» C. 20 | |
| 1464. |
If \(x\left(3 - \frac 2 x\right) = \frac 3 x,\) then the value of \(x^3 - \frac 1 {x^3}\) is equal to: |
| A. | \(\frac {62}{27}\) |
| B. | \(\frac {52}{27}\) |
| C. | \(\frac {61}{27}\) |
| D. | \(\frac {8}{27}\) |
| Answer» B. \(\frac {52}{27}\) | |
| 1465. |
If x2 - 7x = -12, What is the vale of x? |
| A. | -3 or -4 |
| B. | 3 or 4 |
| C. | 3 or -4 |
| D. | Cannot be determined |
| Answer» C. 3 or -4 | |
| 1466. |
a × a × a × b × b × b can be expressed as: |
| A. | 3ab |
| B. | abba |
| C. | (ab)3 |
| D. | (ab)3 + 3 |
| Answer» D. (ab)3 + 3 | |
| 1467. |
If the expression (px3 - 8x2 - qx + 1) is completely divisible by the expression (3x2- 4x + 1), then what will be the value of p and q respectively? |
| A. | (21/4, 15/8) |
| B. | (6, 1) |
| C. | (33/4, 5/4) |
| D. | (1, 6) |
| Answer» D. (1, 6) | |
| 1468. |
\(\left( {4{x^2} + 4x - 3} \right) = \;?\) |
| A. | (2x - 1)(2x - 3) |
| B. | (2x + 1)(2x - 3) |
| C. | (2x + 3)(2x + 1) |
| D. | (2x - 1)(2x + 3) |
| Answer» E. | |
| 1469. |
A particle is displaced from the point whose position vector is \(\hat i + 3 \hat j\) to the point whose position vector is \(5 \hat i + 9 \hat j\) under the action of the force \(\vec F = 2\vec i + 3\vec j\). Find the work done by the force \(\vec F\). |
| A. | 26 |
| B. | 36 |
| C. | 49 |
| D. | None of these |
| Answer» B. 36 | |
| 1470. |
If the polynomial x6 + px5 + qx4 - x2 - x - 3 is divisible by (x4 - 1), then the value of p2 + q2 is |
| A. | 1 |
| B. | 9 |
| C. | 10 |
| D. | 13 |
| Answer» D. 13 | |
| 1471. |
Let \(\left[ {\vec a} \right] = {\rm{\hat i}} + {\rm{\hat j}} + \sqrt 2 \widehat {{\rm{k\;}}},\;\vec b = {{\rm{b}}_1}{\rm{\hat i}} + {{\rm{b}}_2}{\rm{\hat j}} + \sqrt 2 \widehat {{\rm{k\;}}}{\rm{\;and\;}}\vec c = 5{\rm{\hat i}} + {\rm{\hat j}} + \sqrt 2 \widehat {{\rm{k}}}\) be three vectors such that the projection vector of \(\vec b{\rm{\;on\;}}\vec a{\rm{\;is\;}}\vec a{\rm{.\;If\;}}\vec a + \vec b\)is perpendicular to \(\vec c,{\rm{\;then\;}}\left| {\vec b} \right|\) is equal to: |
| A. | \(\sqrt {32}\) |
| B. | 6 |
| C. | \(\sqrt {22}\) |
| D. | 4 |
| Answer» C. \(\sqrt {22}\) | |
| 1472. |
If \(\frac{{8x}}{{2{x^2}\; + \;7x - 2}} = 1,x > 0,\) then what is the value of \({x^3} + \frac{1}{{{x^3}}}\)? |
| A. | \(\frac{3}{8}\sqrt {17}\) |
| B. | \(\frac{3}{4}\sqrt {17}\) |
| C. | \(\frac{5}{8}\sqrt {17}\) |
| D. | \(\frac{5}{4}\sqrt {17} \) |
| Answer» D. \(\frac{5}{4}\sqrt {17} \) | |
| 1473. |
If \({\rm{\vec a}} = 2{\rm{\hat i}} + 3{\rm{\hat j}} + 4{\rm{\hat k}}\) and \({\rm{\vec b}} = 3{\rm{\hat i}} + 2{\rm{\hat j}} - {\rm{\lambda \hat k}}\) perpendicular, then what is the value of λ |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 1474. |
Let A and B be matrices of order 3. Which of the following is true? |
| A. | (AB)-1 = A-1B-1 |
| B. | (AB)-1 = AB-1 |
| C. | (BA)-1 = B-1 |
| D. | (BA)-1 = A-1B-1 |
| Answer» E. | |
| 1475. |
Ram spent Rs. 564 to buy pens and pencils. If each pen costs Rs. 7 and each pencil Rs. 3, and if the total number of pens and pencils bought was 108, how many pens did he buy? |
| A. | 65 |
| B. | 48 |
| C. | 60 |
| D. | 30 |
| Answer» D. 30 | |
| 1476. |
A two-digit number is such that the product of its digit is 12. When 36 is added to the number, the digits get reversed. What is the number? |
| A. | 43 |
| B. | 26 |
| C. | 34 |
| D. | 62 |
| Answer» C. 34 | |
| 1477. |
If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2? |
| A. | 196 |
| B. | 194 |
| C. | 206 |
| D. | 182 |
| Answer» C. 206 | |
| 1478. |
If x2 + 4y2 + z2 - 4x - 2z + 5 = 0, then find the value of \(\frac{{{y^{15}}\; + \;{x^5}}}{{{z^{14}}}}\). |
| A. | 32 |
| B. | 46 |
| C. | 58 |
| D. | 60 |
| Answer» B. 46 | |
| 1479. |
If 3x2 - 5x + 1 = 0, then the value of \((x^2+\frac{1}{9x^2})\) is: |
| A. | (5/3) |
| B. | (4/3) |
| C. | (19/9) |
| D. | (7/2) |
| Answer» D. (7/2) | |
| 1480. |
A singular matrix is a square matrix with: |
| A. | all elements with value as zero |
| B. | main diagonal elements as unity and other with value as zero |
| C. | associated determinant as zero |
| D. | all conjugate terms |
| Answer» D. all conjugate terms | |
| 1481. |
If x + (1/x) = 5, then what is the value of x8 + (1/x8)? |
| A. | 623 |
| B. | 627 |
| C. | 277727 |
| D. | 12102 |
| Answer» D. 12102 | |
| 1482. |
Find the direction cosines of the vector î + 2ĵ - k̂. |
| A. | \(\frac{1}{\sqrt 6}, \frac{2}{\sqrt 6}, \frac{-1}{\sqrt 6}\) |
| B. | \(\frac{1}{\sqrt 4}, \frac{2}{\sqrt 4}, \frac{-1}{\sqrt 4}\) |
| C. | \(\frac{-1}{\sqrt 4}, \frac{-2}{\sqrt 4}, \frac{1}{\sqrt 4}\) |
| D. | None of these. |
| Answer» B. \(\frac{1}{\sqrt 4}, \frac{2}{\sqrt 4}, \frac{-1}{\sqrt 4}\) | |
| 1483. |
Given below are two quantities 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.Find the value of x.Quantity A: x4 + a × x4 – a = x2 + a × x2 – aQuantity B: 4x2 – 4x + 1 = 0 |
| A. | Quantity A > Quantity B |
| B. | Quantity A < Quantity B |
| C. | Quantity A ≤ Quantity B |
| D. | Quantity A ≥ Quantity B |
| E. | Quantity A = Quantity B or no relation can be established |
| Answer» F. | |
| 1484. |
If\({\rm{\;x}} + \frac{4}{{\rm{x}}} = 4,\)then find the value of x6 + 1 |
| A. | 51 |
| B. | 65 |
| C. | 78 |
| D. | 82 |
| Answer» C. 78 | |
| 1485. |
If P(t) is a polynomial of degree n ≥ 1 and (t - 2) is a factor of P(t), then P(2) is - |
| A. | 0 |
| B. | (t - 2) |
| C. | 2 |
| D. | Can not be determined |
| Answer» B. (t - 2) | |
| 1486. |
Expand: (W - 9)2 |
| A. | (W2 - 9w + 81) |
| B. | (W2 - 9w + 18) |
| C. | (W2 - 18w + 81) |
| D. | (W2 - 18w - 81) |
| Answer» D. (W2 - 18w - 81) | |
| 1487. |
If \(\vec r\) = xî + yĵ + zk̂, then what is \(\vec r\) . (î + ĵ + k̂ ) equal to? |
| A. | x |
| B. | x + y |
| C. | –(x + y + z) |
| D. | (x + y + z) |
| Answer» E. | |
| 1488. |
Let A and B be non–singular square matrices of the same order. Consider the following statements.I. (AB)T = ATBTII. (AB)-1 =B-1A-1III. adj(AB) = (adj.1)(adj.2)IV. ρ(A2)= ρ(1) ρ(2)V. |AB| = |A|.|B|Which of the above statements are false? |
| A. | I, III & IV |
| B. | IV & V |
| C. | I & II |
| D. | All of these |
| Answer» B. IV & V | |
| 1489. |
If the sum of 60% of a fractional number and the number's square root is 5 greater than one fifth of the number, then the number is |
| A. | 6.25 |
| B. | 0.25 |
| C. | 12.25 |
| D. | 2.25 |
| Answer» B. 0.25 | |
| 1490. |
Five years ago, a woman's age was the square of her son's age. Ten years later, her age will be twice that of her son's age. Find the present age of the women. |
| A. | 25 years |
| B. | 24 years |
| C. | 20 years |
| D. | 30 years |
| Answer» E. | |
| 1491. |
If a carriage of 910 kg, for 70 km. cost Rs. 45, what will be the cost of a carriage of 940 kg for a distance of 63 km at half the former rate? |
| A. | Rs. 20.91 |
| B. | Rs. 21 |
| C. | Rs. 55 |
| D. | Rs. 12.56 |
| Answer» B. Rs. 21 | |
| 1492. |
If A is Square Matrix of order 3, then product of A and its transpose is |
| A. | Unit Matrix |
| B. | Zero Matrix |
| C. | Identity Matrix |
| D. | Symmetric Matrix |
| Answer» E. | |
| 1493. |
Find the solution set of \({\left( {x - \frac{a}{b}} \right)^2} = \frac{{{a^2}}}{{{b^2}}}.\) |
| A. | 0, -2a/b |
| B. | 0, 2a/b |
| C. | a/b, b/a |
| D. | a/b, -a/b |
| Answer» C. a/b, b/a | |
| 1494. |
If \({\rm{\vec d}} = {\rm{x\hat i}} + {\rm{y\hat j}} + {\rm{z\hat k}}\), then which of the following equations is/are correct?1. y – x = 42. 2z – 3 = 0Select the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 1495. |
A + B = 8, A – B = 4 then A2 – B2 = ? |
| A. | 16 |
| B. | 28 |
| C. | 32 |
| D. | 12 |
| Answer» D. 12 | |
| 1496. |
Find the nature of roots of 2x2 – 15x + 28. |
| A. | Both negative |
| B. | Both positive |
| C. | Not real |
| D. | One positive, other negative |
| Answer» C. Not real | |
| 1497. |
If \(x + \frac{1}{x} = 3\), then the value of \({x^5} + \frac{1}{{{x^5}}}\) is |
| A. | 133 |
| B. | 143 |
| C. | 123 |
| D. | None of the above |
| Answer» D. None of the above | |
| 1498. |
If x + y = 12 and xy = 27, x > y, then the value of (x3 – y3) is: |
| A. | 720 |
| B. | 724 |
| C. | 710 |
| D. | 702 |
| Answer» E. | |
| 1499. |
If 4x2 + y2 = 40 and xy = 6, (x > 0, y > 0) then the value of 2x + y is |
| A. | 4 |
| B. | 24 |
| C. | 8 |
| D. | 16 |
| Answer» D. 16 | |
| 1500. |
Consider the following in respect of two non-singular matrices A and B of same order:a. Det (A+ B) = det A + det Bb. (A + B)-1 = A-1 + B-1Which of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |