MCQOPTIONS
Saved Bookmarks
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.
| 1501. |
If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of a3 + b3 is: |
| A. | 7760 |
| B. | 240 |
| C. | 8000 |
| D. | 8240 |
| Answer» B. 240 | |
| 1502. |
(a + b + c - d)2 - (a - b - c + d)2= ? |
| A. | 4a (b + c - d) |
| B. | 2a(b + c + d) |
| C. | 2a (b - c + d) |
| D. | 2a (b + c - d) |
| Answer» B. 2a(b + c + d) | |
| 1503. |
If x = 1 + √2 + √3, then the value of 2x4 – 8x3 – 5x2 + 26x – 28 is: |
| A. | 2√2 |
| B. | 3√3 |
| C. | 5√5 |
| D. | 6√6 |
| Answer» E. | |
| 1504. |
If x + 1/x = 2√3, then x2 + 1/x2 is equal to: |
| A. | 8 |
| B. | 16 |
| C. | 10 |
| D. | 12 |
| Answer» D. 12 | |
| 1505. |
If \(x + \frac{1}{x}=5,\) x ≠ 0 then the value of \(\frac{{{x^4} + \frac{1}{{{x^2}}}}}{{{x^2} - 3x + 1}}\) is equal to: |
| A. | 60 |
| B. | 65 |
| C. | 55 |
| D. | 50 |
| Answer» D. 50 | |
| 1506. |
In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer:I. x2 – 18x + 45 = 0II. y2 - 5y + 6 = 0 |
| 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 | |
| 1507. |
If 16a4 + 36a2b2 + 81b4 = 91 and 4a2 + 9b2 – 6ab = 13, then what is the value of 3ab? |
| A. | 5 |
| B. | –3 |
| C. | 3/2 |
| D. | –3/2 |
| Answer» E. | |
| 1508. |
Factorise:1 – 2xy – (x2 + y2) |
| A. | (1 + × - y)(1 + × + y) |
| B. | (1 + × - y)(1 – × + y) |
| C. | (1 + × + y)(1 – × + y) |
| D. | (1 + × + y) (1 – × – y) |
| Answer» E. | |
| 1509. |
For real a, b and c if a2 + b2 + c2 = ab + bc + ca, then find the value of (a + b + c)2 |
| A. | 9a2 |
| B. | 81a2 |
| C. | 27a2 |
| D. | 243a2 |
| Answer» B. 81a2 | |
| 1510. |
If x + y = 7, then what is the value of x3 + y3 + 21xy? |
| A. | 343 |
| B. | 49 |
| C. | 294 |
| D. | 288 |
| Answer» B. 49 | |
| 1511. |
Let \(A = \left[ {\begin{array}{*{20}{c}} 1&1&0\\ 0&1&0\\ 1&1&0\\ 0&0&1 \end{array}} \right]\) and \(B = \left[ {\begin{array}{*{20}{c}} 1&0&0&0\\ 0&1&1&0\\ 1&0&1&1\\ \end{array}} \right]\) Find the boolean product A ⊙ B of the two matrices. |
| A. | \(\left[ {\begin{array}{*{20}{c}} 1&1&1&0\\ 0&1&1&0\\ 1&1&1&0\\ 1&0&1&1 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} 1&1&0&1\\ 0&1&0&1\\ 1&1&1&0\\ 1&0&1&1 \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} 1&1&0&1\\ 0&1&1&0\\ 1&1&1&0\\ 1&0&1&1 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} 1&1&1&0\\ 0&1&1&0\\ 1&0&1&1\\ 1&0&1&1 \end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}} 1&1&0&1\\ 0&1&0&1\\ 1&1&1&0\\ 1&0&1&1 \end{array}} \right]\) | |
| 1512. |
If a + b + c = 8 and ab + bc + ca = 12, then a3 + b3 + c3 – 3abc is equal to∶ |
| A. | 144 |
| B. | 400 |
| C. | 224 |
| D. | 192 |
| Answer» D. 192 | |
| 1513. |
If x + (1/x) = √13, then what is the value of x5 - (1/x5)? |
| A. | 169 |
| B. | 169√3 |
| C. | 393 |
| D. | 507 |
| Answer» D. 507 | |
| 1514. |
If x2 + ax + b, when divided by x - 3, leaves a remainder of 22 and x2 + bx + a, when divided by x - 3, leaves a remainder of 24, then a + b = ? |
| A. | 7 |
| B. | 23 |
| C. | -7 |
| D. | -23 |
| Answer» B. 23 | |
| 1515. |
If x + 1/x = 8, then x2 + 1/x2 is equal to∶ |
| A. | 62 |
| B. | 68 |
| C. | 64 |
| D. | 66 |
| Answer» B. 68 | |
| 1516. |
Five points given by A, B, C, D, E are in a plane. Three forces \(\vec {AC},\; \vec {AD}\) and \(\vec {AE}\) act at A and three forces \(\vec {CB},\;\vec {DB},\;\vec {EB}\) act at B. Then their resultant force is: |
| A. | \(2 \vec {AC}\) |
| B. | \(3 \vec {AB}\) |
| C. | \(3 \vec {DB}\) |
| D. | \(2 \vec {BC}\) |
| Answer» C. \(3 \vec {DB}\) | |
| 1517. |
Find the product of the roots of the equation 6x2 + 3x + 12 = 0 |
| A. | -2 |
| B. | 3 |
| C. | -3 |
| D. | 2 |
| Answer» E. | |
| 1518. |
Expand (3x - 2y)2 |
| A. | 9x2 + 4y2 + 12xy |
| B. | 9x2 - 4y2 + 12xy |
| C. | 9x2 + 4y2 - 12xy |
| D. | 9x2 - 4y2 - 12xy |
| Answer» D. 9x2 - 4y2 - 12xy | |
| 1519. |
If the sum of two numbers is 10 and the sum of their reciprocals is 5/12 then what will be the numbers? |
| A. | 7, 3 |
| B. | 9, 1 |
| C. | 8, 2 |
| D. | 6, 4 |
| Answer» E. | |
| 1520. |
If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively? |
| A. | 1 : 9 |
| B. | 1 : 3 |
| C. | 3 : 1 |
| D. | 9 : 1 |
| Answer» B. 1 : 3 | |
| 1521. |
If a2 + b2 + c2 + 27 = 6(a + b + c), then what is the value of \(\sqrt[3]{{{a^3} + {b^3} - {c^3}}}?\) |
| A. | 1 |
| B. | 3 |
| C. | 9 |
| D. | 6 |
| Answer» C. 9 | |
| 1522. |
In x2 + 1 = 3x, then the value of 4[(x2 + x-2)(x2 + 5x + 1)]/x is: |
| A. | 213 |
| B. | 412 |
| C. | 224 |
| D. | 312 |
| Answer» D. 312 | |
| 1523. |
If a3 – b3 = 208 and a – b = 4, then (a + b)2 – ab is equal to: |
| A. | 32 |
| B. | 52 |
| C. | 38 |
| D. | 42 |
| Answer» C. 38 | |
| 1524. |
If the vector \({\rm{\vec k}}\) and \({\rm{\vec A}}\) are parallel to each other, then what is \({\rm{\vec k}} \times {\rm{\vec A}}\) equal to? |
| A. | \({{\rm{k}}^2}\overrightarrow {{\rm{A}}} \) |
| B. | \(\vec 0\) |
| C. | \(-{{\rm{k}}^2}\overrightarrow {{\rm{A}}} \) |
| D. | \({\rm{\vec A}}\) |
| Answer» C. \(-{{\rm{k}}^2}\overrightarrow {{\rm{A}}} \) | |
| 1525. |
If α and β are the roots of the equation ax2 + bx + c = 0, then the value of 1/(aα + b) + 1/(aβ + b) is |
| A. | a/bc |
| B. | b/ac |
| C. | c/ab |
| D. | 1/abc |
| Answer» C. c/ab | |
| 1526. |
If x is an even number, what is the consecutive odd number? |
| A. | x – 1 |
| B. | x + 1 |
| C. | x + 2 |
| D. | x – 2 |
| Answer» C. x + 2 | |
| 1527. |
If a = 2b = 8c and a + b + c = 13 then the value of \(\frac{{\sqrt {{a^2} + {b^2} + {c^2}} }}{{2c}}\) is: |
| A. | -5/6 |
| B. | 9/2 |
| C. | -9/2 |
| D. | 5/6 |
| Answer» C. -9/2 | |
| 1528. |
If a, b, c are positive real numbers such that a + b + c = 16, then abc will be greatest when: |
| A. | a ≠ b ≠ c |
| B. | a ≠ b = c |
| C. | a = b ≠ c |
| D. | a = b = c |
| Answer» E. | |
| 1529. |
If the sum as well as the product of the roots of the equation px2 - 6x + q = 0 is 6, then what is (p + q) equal to? |
| A. | 8 |
| B. | 7 |
| C. | 6 |
| D. | 5 |
| Answer» C. 6 | |
| 1530. |
If \(\frac{{3x - 1}}{x} + \frac{{5y - 1}}{y} + \frac{{7z - 1}}{z} = 0\), then what is the value of \(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}?\) |
| A. | -3 |
| B. | 0 |
| C. | 15 |
| D. | 21 |
| Answer» D. 21 | |
| 1531. |
If \(\vec a + \vec b + \vec c = \vec 0,\) then which of the following is/are correct?1. \(\vec a,\;\vec b,\;\vec c\) are coplanar.2. \(\vec a \times \vec b = \vec b \times \vec c = \vec c \times \vec a\)Select 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» D. Neither 1 nor 2 | |
| 1532. |
If a (a + b + c) = 45; b (a + b + c) = 75 and c (a + b + c) = 105, then find the value of a2 + b2 + c2. |
| A. | 90 |
| B. | 625 |
| C. | 225 |
| D. | 83 |
| Answer» E. | |
| 1533. |
Find the unit place digit in (192)102 + (193)103 |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | 5 |
| Answer» C. 3 | |
| 1534. |
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix AT A? Answer is |
| A. | Yes, it is always possible to get a unique solution for any 2 × 4 matrix A. |
| B. | No, it is not possible to get a unique solution for any 2 × 4 matrix A. |
| C. | Yes, can obtain a unique solution provided the matrix AT A is well conditioned |
| D. | Yes, can obtain a unique solution provided the matrix A is well conditioned. |
| Answer» C. Yes, can obtain a unique solution provided the matrix AT A is well conditioned | |
| 1535. |
If 2x2 + 2y2 = 4a, then find the value of 2a/ (x2 - a) + 2a/ (y2 - a). |
| A. | 0 |
| B. | 1 |
| C. | a |
| D. | 2a |
| Answer» B. 1 | |
| 1536. |
If x3 + 27 y3 + 64 z3 = 36xyz, then the relationship between x, y and z is |
| A. | x + 3y = 4z |
| B. | x + y + z = 0 |
| C. | x - 3y + 4z = 0 |
| D. | x + 3y + 4z = 0 |
| Answer» E. | |
| 1537. |
In my pocket, I have Rs. 25 consisting of only the denominations of 20 paise and 50 paise. There are total 80 coins in my pocket. The number of coins of the denomination of 50 paise is: |
| A. | 30 |
| B. | 25 |
| C. | 15 |
| D. | 20 |
| Answer» B. 25 | |
| 1538. |
If a3 – b3 = 91 and ab = 30, then what is the value of a – b? |
| A. | 1 |
| B. | 8 |
| C. | 4 |
| D. | 6 |
| Answer» B. 8 | |
| 1539. |
Find the roots of the following quadratic polynomial x2 - 2x - 15 |
| A. | 3, 5 |
| B. | -3, -5 |
| C. | -3, 5 |
| D. | 3, -5 |
| Answer» D. 3, -5 | |
| 1540. |
If 5 is one of the roots of y3 – 10y2 + 31y – 30 = 0, then the sum of the other two roots is: |
| A. | 0 |
| B. | -2 |
| C. | 6 |
| D. | 5 |
| Answer» E. | |
| 1541. |
A bag has Rs 43 in the form of 5-rupee, 50-paise and 10-paise coins in the ratio of 1 : 5 : 11. What is the total number of 50-paise coins? |
| A. | 5 |
| B. | 25 |
| C. | 50 |
| D. | 40 |
| Answer» C. 50 | |
| 1542. |
If any two columns of a determinant \(P = \left| {\begin{array}{*{20}{c}} 4&7&8\\ 3&1&5\\ 9&6&2 \end{array}} \right|\) are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? |
| A. | Absolute value remains unchanged but sign will change |
| B. | Both absolute value and sign will change |
| C. | Absolute value will change but sign will not change |
| D. | Both absolute value and sign will remain unchanged |
| Answer» B. Both absolute value and sign will change | |
| 1543. |
For an orthogonal matrix Q, the valid equality is |
| A. | QT = Q-1 |
| B. | Q = Q-1 |
| C. | QT = Q |
| D. | det(Q) = 0 |
| Answer» B. Q = Q-1 | |
| 1544. |
If 4(3x - 2) = 2(3x + 8), Then x = ?A. 1B. 2C. 3D. 4 |
| A. | B |
| B. | D |
| C. | C |
| D. | A |
| Answer» C. C | |
| 1545. |
If x + 1/x = 3, then the value of x3 + x-3. |
| A. | 52 |
| B. | 36 |
| C. | 27 |
| D. | 18 |
| Answer» E. | |
| 1546. |
If \(\vec a\) and \(\vec b\) are vectors in space, given by \(\vec a = \frac {\hat i - 2\hat j}{\sqrt 5}\) and \(\vec b = \frac {2\hat i + \hat j + 3\hat k}{\sqrt {14}}\) then the value of \(\left(2\vec a + \vec b\right)\left[\left(\vec a \times \vec b\right)\times \left(\vec a - 2\vec b\right)\right]\) is |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 1547. |
If x3 + y3 = 16 and x + y = 4, then find the value of x4 + y4 |
| A. | 26 |
| B. | 28 |
| C. | 36 |
| D. | 32 |
| Answer» E. | |
| 1548. |
If \(x + \frac{1}{x} = 4\), then what is the value of \({x^5} + \frac{1}{{{x^5}}}\) ? |
| A. | 52 |
| B. | 256 |
| C. | 1026 |
| D. | 724 |
| Answer» E. | |
| 1549. |
Find the value of y if 0.008x + 0.04y = 10 and 0.2(x - 1) + 0.4y = 24.8 |
| A. | 375 |
| B. | 275 |
| C. | 125 |
| D. | 195 |
| Answer» B. 275 | |
| 1550. |
If a + b = 8 and ab = 32/3, then (a3 + b3) is equal to∶ |
| A. | 256 |
| B. | 320 |
| C. | 384 |
| D. | 128 |
| Answer» B. 320 | |