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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.
| 1551. |
If a3 + b3 = 35 and ab = 6, then what is the value of a + b? |
| A. | 5 |
| B. | 8 |
| C. | 2 |
| D. | -8 |
| Answer» B. 8 | |
| 1552. |
If \(p + \frac{1}{p} = \sqrt {10} \), then find the value of \({p^4} + \frac{1}{{{p^4}}}\) |
| A. | 52 |
| B. | 60 |
| C. | 62 |
| D. | 65 |
| Answer» D. 65 | |
| 1553. |
If \(\vec a, \vec b\) are vectors such that \(|\vec a + \vec b| = \sqrt {29}\) and \(\vec a \times (2\hat i + 3\hat j + 4\hat k) = (2\hat i + 3\hat j + 4\hat k) \times \vec b\) then possible value of \((\vec a + \vec b).(-7\hat i + 2\hat j + 3\hat k)\) is |
| A. | 0 |
| B. | 3 |
| C. | 4 |
| D. | 8 |
| Answer» D. 8 | |
| 1554. |
If a + b + c = 6, a3 + b3 + c3 - 3 abc = 342,and a2 + b2 + c2 = 50, then what is the value of ab + bc + ca? |
| A. | 5 |
| B. | - 5 |
| C. | - 7 |
| D. | 8 |
| Answer» D. 8 | |
| 1555. |
If x2– √7x + 1 = 0, then (x3 + x - 3) = ? |
| A. | 3√7 |
| B. | 4√7 |
| C. | 7√7 |
| D. | 10√7 |
| Answer» C. 7√7 | |
| 1556. |
If two vectors \(\vec a = 3i + 4j - 7k\: and\: \vec b = pi - 6j + 3k\) are perpendicular, the value of P is |
| A. | 1 |
| B. | 0 |
| C. | 12 |
| D. | 15 |
| Answer» E. | |
| 1557. |
If \({x^4} + \frac{1}{{{x^4}}} = 14159\), then the value of \(x + \frac{1}{x}\) is: |
| A. | 11 |
| B. | 12 |
| C. | 9 |
| D. | 10 |
| Answer» B. 12 | |
| 1558. |
If the equations x2 + 5x + 6 = 0 and x2 + kx + 1 = 0 have a common root, then what is the value of k? |
| A. | -5/2 or -10/3 |
| B. | 5/2 or 10/3 |
| C. | 5/2 or -10/3 |
| D. | -5/2 or 10/3 |
| Answer» C. 5/2 or -10/3 | |
| 1559. |
According to Mr. Sharma’s will, half of his property goes to his wife and the rest is equally divided between his two sons, Ravi and Raj. Some years later, Ravi dies and leaves half of his property to his widow and rest to his brother Raj. When Raj dies, he leaves half of his property to his widow and remaining to his mother, who is still alive. The mother now owns 88,000 worth of the property. The total worth of the property of Mr. Sharma was |
| A. | Rs. 1,00,000 |
| B. | Rs. 1,24,000 |
| C. | Rs. 1,28,000 |
| D. | Rs. 1,32,000 |
| Answer» D. Rs. 1,32,000 | |
| 1560. |
P + Q = 2(P – Q), if Q = 10, what is the value of P?A.10B. 40C. 20D. 30 |
| A. | D |
| B. | C |
| C. | A |
| D. | B |
| Answer» B. C | |
| 1561. |
If 3x2 + ax + 4 is perfectly divisible by x – 8, then the value of a is: |
| A. | 24.5 |
| B. | -25.5 |
| C. | -24.5 |
| D. | 25.5 |
| Answer» D. 25.5 | |
| 1562. |
Find the value of x in the following expression:5 (5x – 4) = 16 (5x + 1) |
| A. | 4/5 |
| B. | -36/55 |
| C. | 5/4 |
| D. | -55/44 |
| Answer» C. 5/4 | |
| 1563. |
If a + b + c \(=2,\frac{1}{a} + \frac{1}{b}+\frac {1}{c}=0, ac=\frac{4}{b}\) and a3 + b3 + c3 = 28, find the value of a2 + b2 + c2 |
| A. | 8 |
| B. | 6 |
| C. | 10 |
| D. | 12 |
| Answer» B. 6 | |
| 1564. |
If 4(x + y) = 256 and (256)(x - y) = 4, then what is the value of x and y? |
| A. | 17/8, 15/8 |
| B. | 17/4, 15/4 |
| C. | 9/17, 15/17 |
| D. | 8/17, 8/15 |
| Answer» B. 17/4, 15/4 | |
| 1565. |
Expand: (4a + 3b + 2c)2 |
| A. | 16a2 + 9b2 + 4c2 + 24ab + 12bc + 16ca |
| B. | 16a2 + 9b2 + 4c2- 24ab - 12bc - 16ca |
| C. | 4a2 + 3b + 2c2 + 24ab + 12bc + 16ca |
| D. | 16a2 - 9b2 + 4c2 - 24ab + 12bc - 16ca |
| Answer» B. 16a2 + 9b2 + 4c2- 24ab - 12bc - 16ca | |
| 1566. |
If a and b are two positive integer such that a2 – b2 = 19 then value of a is |
| A. | 19 |
| B. | 20 |
| C. | 9 |
| D. | 10 |
| Answer» E. | |
| 1567. |
If \(\frac{{3\left( {{x^2} + 1} \right) - 7x}}{{3x}} = 6,\) x ≠ 0, then the value of \(\sqrt x + \frac{1}{{\sqrt x }}\;is:\) |
| A. | \(\sqrt {\frac{{11}}{3}}\) |
| B. | \(\sqrt {\frac{{25}}{3}}\) |
| C. | \(\sqrt {\frac{{31}}{3}}\) |
| D. | \(\sqrt {\frac{{35}}{3}}\) |
| Answer» D. \(\sqrt {\frac{{35}}{3}}\) | |
| 1568. |
If (x + y + z) = 12, xy + yz + zx = 44 and xyz = 48, then what is the value of x3 + y3 + z3? |
| A. | 104 |
| B. | 144 |
| C. | 196 |
| D. | 288 |
| Answer» E. | |
| 1569. |
Find the value of equation a3 + b3 + c3 - 3abc. if a2 + b2 + c2 = ab + bc + ca + 4 and a + b + c = 4. |
| A. | 0 |
| B. | 1 |
| C. | 16 |
| D. | 256 |
| Answer» D. 256 | |
| 1570. |
IF x = 3 + √8, find the value of \({x^3} + \frac{1}{{{x^3}}}\). |
| A. | 216 |
| B. | 198 |
| C. | 200 |
| D. | 196 |
| Answer» C. 200 | |
| 1571. |
If x + y + z = 13, x2 + y2 + z2 = 133 and x3 + y3 + z3 = 847, then the value of \(\sqrt[3]{{xyz}}\) is: |
| A. | -9 |
| B. | -6 |
| C. | 7 |
| D. | 8 |
| Answer» C. 7 | |
| 1572. |
If 2x + 3 = 9 then find the value of 3x + 2.A. 12B. 16C. 13D. 11 |
| A. | D |
| B. | C |
| C. | B |
| D. | A |
| Answer» B. C | |
| 1573. |
If a + 1/a = 5 then a3 + 1/a3 is |
| A. | 10 |
| B. | 140 |
| C. | 110 |
| D. | 80 |
| Answer» D. 80 | |
| 1574. |
In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.I. x2 = 81II. (y - 9)2 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | Either x = y or Relationship between x and y cannot be established |
| Answer» E. Either x = y or Relationship between x and y cannot be established | |
| 1575. |
If 2√2x3 – 3√3y3 = (√2 x – √3 y) (Ax2 + By2 + Cxy), then the value of A2 + B2 – C2 is∶ |
| A. | 11 |
| B. | 10 |
| C. | 19 |
| D. | 7 |
| Answer» E. | |
| 1576. |
Find the last of 23729 × 78900 |
| A. | 7 |
| B. | 3 |
| C. | 0 |
| D. | 8 |
| Answer» E. | |
| 1577. |
If one cup of ghee gives 1/5th of the required amount of fat, then, what is the amount of fat provided by 3 cups of ghee? |
| A. | 4/5 |
| B. | 3/5 |
| C. | 2/5 |
| D. | 1/5 |
| Answer» C. 2/5 | |
| 1578. |
If (b – 6) is one root of the quadratic equation x2 – 6x + b = 0, where b is an integer, then what is the maximum value of b2? |
| A. | 36 |
| B. | 49 |
| C. | 64 |
| D. | 81 |
| Answer» E. | |
| 1579. |
If 5/2(8x/3 – 1/2) + 13/2 = 2x/3, then what is the value of x? |
| A. | 7/8 |
| B. | 8/7 |
| C. | -8/7 |
| D. | -7/8 |
| Answer» E. | |
| 1580. |
If x + y + z = 10, xy + yz + zx = 25 and xyz = 100, then what is the value of (x3 + y3 + z3)? |
| A. | 540 |
| B. | 550 |
| C. | 450 |
| D. | 570 |
| Answer» C. 450 | |
| 1581. |
Let \({\rm{\vec \alpha }} = {\rm{\hat i}} + 2{\rm{\hat j}} - {\rm{\hat k}},{\rm{\;\vec \beta }} = 2{\rm{\hat i}} - {\rm{\hat j}} + 3{\rm{\hat k}}\) and \({\rm{\vec \gamma }} = 2{\rm{\hat i}} + {\rm{\hat j}} + 6{\rm{\hat k}}\) be three vectors. If \({\rm{\vec \alpha }}\) and \({\rm{\vec \beta }}\) are both perpendicular to the vector \({\rm{\vec \delta }}\) and \({\rm{\vec \delta }} \cdot {\rm{\vec \gamma }} = 10\) , then what is the magnitude of \({\rm{\vec \delta }}\) ? |
| A. | √3 units |
| B. | 2√3 units |
| C. | √3/2 units |
| D. | 1/√3 units |
| Answer» C. √3/2 units | |
| 1582. |
If 5x + 6(3 - 2x) = 4, then what is the value of x? |
| A. | 1 |
| B. | 3 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 1583. |
Consider the linear transformation T : R4 → R4 given by T(x, y, z, u) = (x, y, 0, 0) ∀ (x, y, z, u) ∈ R4. Then which one of the following is correct? |
| A. | Rank of T > Nullity of T |
| B. | Rank of T < Nullity of T |
| C. | Rank of T = Nullity of T = 3 |
| D. | Rank of T = Nullity of T = 2 |
| Answer» E. | |
| 1584. |
If x + y = 10 and xy = 4, then what is the value of x4 + y4? |
| A. | 8464 |
| B. | 8432 |
| C. | 7478 |
| D. | 6218 |
| Answer» C. 7478 | |
| 1585. |
If \({y^4}\; + \;\frac{1}{{{y^4}}}\; = \;223\;and\;y > 1\), then find the value of \({y^2}\; + \;\frac{1}{{{y^2}}}?\) |
| A. | 15 |
| B. | 14 |
| C. | 14.86 |
| D. | 16 |
| Answer» B. 14 | |
| 1586. |
If \(x^4 + \frac{1}{x^4} = \frac{257}{16}\) then find \(\frac{8}{13} (x^3 + \frac{1}{x^3})\), where x > 0. |
| A. | 5 |
| B. | 8 |
| C. | 4 |
| D. | 6 |
| Answer» B. 8 | |
| 1587. |
If x - 1/x = 11, then x3 - 1/x3 is: |
| A. | 1188 |
| B. | 1474 |
| C. | 1364 |
| D. | 1298 |
| Answer» D. 1298 | |
| 1588. |
A matrix is singular if and only if its has |
| A. | one as an eigenvalue |
| B. | two as an eigenvalue |
| C. | zero as an eigenvalue |
| D. | none of these |
| Answer» D. none of these | |
| 1589. |
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 + 12x + 35 = 0B. y2 + 17y + 72 = 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» B. if x ≥ y | |
| 1590. |
If a2 + b2 + c2 = 21, and a + b + c = 7, then (ab + bc + ca) is equal to∶ |
| A. | 14 |
| B. | 8 |
| C. | 12 |
| D. | 28 |
| Answer» B. 8 | |
| 1591. |
If \(x = \frac{{\left( {{a^2} - 25} \right)}}{{\left( {{a^2} - 36} \right)}},\frac{x}{y} = \frac{{a - 5}}{{a - 6}}\), then find the value of Y.A. \(\frac{{a + 6}}{{a + 5}}\)B. \(\frac{{{{\left( {a + 6} \right)}^2}}}{{{{\left( {a + 5} \right)}^2}}}\)C. \(\frac{{\left( {a + 5} \right)}}{{\left( {a + 6} \right)}}\)D. \(\frac{{\left( {a + 5} \right)}}{{{{\left( {a + 6} \right)}^2}}}\) |
| A. | C |
| B. | B |
| C. | D |
| D. | A |
| Answer» B. B | |
| 1592. |
If a3 + b3 = 5824 and a + b = 28, then (a - b)2 + ab equal to∶ |
| A. | 208 |
| B. | 180 |
| C. | 236 |
| D. | 152 |
| Answer» B. 180 | |
| 1593. |
Find the square root of \(\frac{{{x^2}}}{{{y^2}}}\; + \;\frac{{{y^2}}}{{{x^2}}} - 2\) |
| A. | \(\frac{x}{{2y}}\; + \;\frac{y}{{2x}}\) |
| B. | \(\frac{x}{y} - \frac{y}{x}\) |
| C. | \(\frac{{x - y}}{2}\) |
| D. | \(\frac{x}{y}\; + \;\frac{y}{x}\) |
| Answer» C. \(\frac{{x - y}}{2}\) | |
| 1594. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}}3&2&{ - 1}\\0&4&6\end{array}} \right]\) and \({\rm{B}} = \left[ {\begin{array}{*{20}{c}}1&0&2\\5&3&1\\6&4&2\end{array}} \right]\) Then the product of the matrices AB is |
| A. | \(\left[ {\begin{array}{*{20}{c}}4&7&5\\0&{12}&4\end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}}7&2&3\\{16}&{51}&{36}\end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}}7&2&6\\{56}&{36}&{16}\end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}}{16}&2&7\\{56}&6&{36}\end{array}} \right]\) |
| Answer» D. \(\left[ {\begin{array}{*{20}{c}}{16}&2&7\\{56}&6&{36}\end{array}} \right]\) | |
| 1595. |
If p(x) and q(x) are two polynomials, then which of the following one is the degree of {p(x) × q(x)}? |
| A. | Degree of p(x) × Degree of q(x) |
| B. | Degree of p(x) + Degree of q(x) |
| C. | Degree of p(x) - Degree of q(x) |
| D. | Degree of p(x) ÷ Degree of q(x) |
| Answer» C. Degree of p(x) - Degree of q(x) | |
| 1596. |
If 30x2 – 15x + 1 = 0, then what is the value of 25x2 + (36x2)–1? |
| A. | 65/12 |
| B. | \(6\frac{1}{4}\) |
| C. | 9/2 |
| D. | 55/12 |
| Answer» E. | |
| 1597. |
Factors of 23xy – 46x + 53y – 106 are: |
| A. | (y + 2)(23x + 54) |
| B. | (23x + 53)(y – 2) |
| C. | (y – 2)(23x + 54) |
| D. | (23x + 54y)(-46x – 108) |
| Answer» C. (y – 2)(23x + 54) | |
| 1598. |
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.Quantity 1: (y – 1/3)2 = 25/36Quantity 2: x2 – 3x/4 – 1/4 = 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» F. | |
| 1599. |
Obtain the eigen values of the matrix.\(A = \left[ {\begin{array}{*{20}{c}}1&2&{34}&{49}\\0&2&{43}&{94}\\0&0&{ - 2}&{104}\\0&0&0&{ - 1}\end{array}} \right]\) |
| A. | 1, -2, -1, 2 |
| B. | 1, 0, 0, 1 |
| C. | 1, 2, 1, 1 |
| D. | 1, 0, -1, 2 |
| Answer» B. 1, 0, 0, 1 | |
| 1600. |
If x = [√(a + 2b) + √(a - 2b)]/[√(a + 2b) - √(a - 2b)], then bx2 - ax + b is equal to (given that b ≠ 0) |
| A. | 0 |
| B. | 1 |
| C. | ab |
| D. | 2ab |
| Answer» B. 1 | |