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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.
| 1601. |
If a + b + c = 0, then \((\frac{2a^2}{3bc} + \frac{2b^2}{3ca} + \frac{2c^2}{3ab})\) is equal to: |
| A. | 3 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 1602. |
Mukesh has some cows and some hens in the shed. The total number of legs is 92 and total number of heads is 29. Find the total number of cows in shed: |
| A. | 19 |
| B. | 17 |
| C. | 14 |
| D. | 12 |
| Answer» C. 14 | |
| 1603. |
If \({x^2} - 2\sqrt 5 x + 1 = 0,\) then what is the value of \({x^5} + \frac{1}{{{x^5}}}\)? |
| A. | 406√5 |
| B. | 610√5 |
| C. | 408√5 |
| D. | 612√5 |
| Answer» C. 408√5 | |
| 1604. |
If 5x2 - 6x - 5 = 0, then find the value of \({\left( {x - \frac{1}{x}} \right)^2}\). |
| A. | 16/25 |
| B. | 64/25 |
| C. | 81/25 |
| D. | 36/25 |
| Answer» E. | |
| 1605. |
If x + y = 7 and xy = 10, then the value of (1/x3 + 1/y3) is: |
| A. | 0.453 |
| B. | 0.133 |
| C. | 0.543 |
| D. | 0.131 |
| Answer» C. 0.543 | |
| 1606. |
If x4 – 62x2 + 1 = 0, then a value of x3 + x-3 can be: |
| A. | 498 |
| B. | 389 |
| C. | 320 |
| D. | 488 |
| Answer» E. | |
| 1607. |
If \(x(3-\frac{2}{x}) = \frac{3}{x} \) then \(x^3 - \frac{1}{x^3} = ?\) |
| A. | \(2 \frac{1}{27}\) |
| B. | \(2\frac{11}{27}\) |
| C. | \(2 \frac{13}{27}\) |
| D. | \(2 \frac{8}{27}\) |
| Answer» E. | |
| 1608. |
If a + b = 10 and √[(a/b) - 13] = √[(-b/a) - 11], then what is the value of 3ab + 4a2 + 5b2? |
| A. | 450 |
| B. | 300 |
| C. | 600 |
| D. | 750 |
| Answer» C. 600 | |
| 1609. |
Find the roots of the following equation.5x2 - 6x - 2 = 0 |
| A. | \(\frac{{2 \pm 2\sqrt 5 }}{2}\) |
| B. | \(\frac{{3 \pm \sqrt {19} }}{5}\) |
| C. | \(\frac{{2 \pm \sqrt {15} }}{3}\) |
| D. | \(\frac{{2 \pm \sqrt {18} }}{4}\) |
| Answer» C. \(\frac{{2 \pm \sqrt {15} }}{3}\) | |
| 1610. |
For what value(s) of \(t, 25x^2 - 20x + t^2\) will be a perfect square? |
| A. | 2 |
| B. | -2 |
| C. | \(\pm2\) |
| D. | 1 |
| Answer» D. 1 | |
| 1611. |
Evaluate: 1299 × 1299 |
| A. | 1687401 |
| B. | 1683701 |
| C. | 1685701 |
| D. | 1538501 |
| Answer» B. 1683701 | |
| 1612. |
From Vadodara station, if we buy two tickets to station P and three tickets to station Q, the total cost is Rs. 77, but if we buy 3 tickets to station P and 5 tickets to station Q, the total cost is Rs. 124. The fare from Vadodara to P is: |
| A. | Rs. 13 |
| B. | Rs. 14 |
| C. | Rs. 18 |
| D. | Rs. 20 |
| Answer» B. Rs. 14 | |
| 1613. |
If \(x = \frac{4}{{2\sqrt 3 + 3\sqrt 2 }}\) then find the value of \(\left( {x + \frac{1}{x}} \right)\) |
| A. | \(\frac{{\left( {10\sqrt 3 + 15\sqrt 2 } \right)}}{{12}}\) |
| B. | \(\frac{{\left( {10\sqrt 3 - 15\sqrt 2 } \right)}}{{12}}\) |
| C. | \(\frac{{ - \left( {10\sqrt 3 - 33\sqrt 2 } \right)}}{{12}}\) |
| D. | \(\frac{{\left( {10\sqrt 3 + 33\sqrt 2 } \right)}}{{12}}\) |
| Answer» D. \(\frac{{\left( {10\sqrt 3 + 33\sqrt 2 } \right)}}{{12}}\) | |
| 1614. |
If 2x + (9/x) = 9, then what is the minimum value of x2 + (1/x2)? |
| A. | 95/36 |
| B. | 97/36 |
| C. | 86/25 |
| D. | 623/27 |
| Answer» C. 86/25 | |
| 1615. |
If the two roots of a quadratic equation are α, β where α + β = 8 and α – β = 2, then the equation is : |
| A. | x² – 8x + 15 = 0 |
| B. | x² + 8x – 15 = 0 |
| C. | x² – 8x – 15 = 0 |
| D. | x² + 8x + 15 = 0 |
| Answer» B. x² + 8x – 15 = 0 | |
| 1616. |
M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M2 are |
| A. | 4 and 9 |
| B. | 2 and 3 |
| C. | -2 and -3 |
| D. | 16 and 81 |
| Answer» E. | |
| 1617. |
30 dozen of nuts were bought for Rs. 14400 and another 32 packets of nuts (20 nuts in each packet) were bought for Rs. 57600. If the nuts are mixed and then sold in a packet of five for Rs. 432, then how much is the profit percentage? |
| A. | 25% |
| B. | 15% |
| C. | 20% |
| D. | 30% |
| Answer» D. 30% | |
| 1618. |
If x4 – 6x2 – 1 = 0, then the value of x6 – 5x2 + 5/x2 – 1/x6 + 5 is: |
| A. | 239 |
| B. | 204 |
| C. | 219 |
| D. | 209 |
| Answer» E. | |
| 1619. |
If 2x - 5y = 7z - 3y then, for xyz ≠ 0, \(\frac {8x^3 - 343z^3 - 8y^3}{xyz} \) |
| A. | 80 |
| B. | 82 |
| C. | 84 |
| D. | 86 |
| Answer» D. 86 | |
| 1620. |
Deepa goes to a post office to post-mail letters and parcels. The postal rates depicted are as below:Letter Weighting:i) 20 g or less – Rs. 5.00ii) Per every additional 20 g – Rs. 2.00Parcel Weighting:i) 50 g or less – Rs. 5.00ii) For every additional 50 g – Rs. 3.00Deepa wants to send two parcels weighing 250 g and 300 g respectively and two letters each to 20 g and 35 g respectively. How much postal charge does she have to pay? |
| A. | Rs. 48 |
| B. | Rs. 39 |
| C. | Rs. 49 |
| D. | Rs. 41 |
| Answer» D. Rs. 41 | |
| 1621. |
Let M4 = I, (where I denotes the identity matrix) and M ≠ I, M2 ≠ I and M3 ≠ I. Then, for any natural number k, M−1 equals: |
| A. | M4k + 1 |
| B. | M4k + 2 |
| C. | M4k + 3 |
| D. | M4k |
| Answer» D. M4k | |
| 1622. |
A fraction is such that the numerator is five less than the denominator. Also four times the numerator is one more than the denomination. Find the Fraction. |
| A. | \(\frac{2}{7}\) |
| B. | \(\frac{7}{12}\) |
| C. | \(\frac{3}{8}\) |
| D. | \(\frac{7}{7}\) |
| Answer» B. \(\frac{7}{12}\) | |
| 1623. |
In a two digit number the unit's digit is twice the ten's digit. If 27 is added to the number, the digit interchange their places, the number is: |
| A. | 24 |
| B. | 12 |
| C. | 36 |
| D. | 48 |
| Answer» D. 48 | |
| 1624. |
If \(a^2 + \frac{1}{a^2} = 98\), a > 0, then the value of \(a^3 + \frac{1}{a^3}\) will be: |
| A. | 960 |
| B. | 950 |
| C. | 970 |
| D. | 870 |
| Answer» D. 870 | |
| 1625. |
If the roots of the quadratic equation x2 - x ln (a2 - 3a + 2) + a2 - 4 = 0 are of opposite signs. |
| A. | a ∈ (-2, 2) |
| B. | a ∈ (-∞, -2) ∪ (2, ∞) |
| C. | a ∈ (-∞, 1) ∪ (2, ∞) |
| D. | a ∈ (-2, 1) |
| Answer» C. a ∈ (-∞, 1) ∪ (2, ∞) | |
| 1626. |
If \(x^4 + \frac{1}{x^4} = 194\), then the value of x3 + \(\frac{1}{x^3}\) is: |
| A. | 50 |
| B. | 46 |
| C. | 54 |
| D. | 52 |
| Answer» E. | |
| 1627. |
If x3 + 2x2 - ax - b is exactly divisible by (x2 - 1), then the values of a and b are: |
| A. | a = -1 and b = 2 |
| B. | a = 1 and b = - 2 |
| C. | a = 1 and b = 2 |
| D. | a = 2 and b = 2 |
| Answer» D. a = 2 and b = 2 | |
| 1628. |
If \(x + \frac{1}{x} = 8\), then find the value of \(\frac{5x}{x^2 +1 - 6x}\) |
| A. | 6 |
| B. | 6.5 |
| C. | 5 |
| D. | 2.5 |
| Answer» E. | |
| 1629. |
If X : Y : Z = 1 : 2 : 3 and, X2 + Y2 + Z2 = 224, then what is the value of X + Y + Z? |
| A. | 32 |
| B. | 24 |
| C. | 48 |
| D. | 36 |
| Answer» C. 48 | |
| 1630. |
If P \(\frac{{{x^3} + {y^3}}}{{{{\left( {x - y} \right)}^2} + 3xy}},\;Q = \frac{{{{\left( {x + y} \right)}^2} - 3xy}}{{{x^3} - {y^3}}}\) and R \( = \frac{{{{\left( {x + y} \right)}^2} + {{\left( {x - y} \right)}^2}}}{{{x^2} - {y^2}}}\), then what is the value of(P ÷ Q) × R? |
| A. | 2(x2 + y2) |
| B. | x2 + y2 |
| C. | 2xy |
| D. | 4xy |
| Answer» B. x2 + y2 | |
| 1631. |
If \(x^2 + \frac 1 {x^2} = 7,\) then the value of \(x^3 + \frac 1 {x^3}\) where x > 0 is equal to: |
| A. | 16 |
| B. | 18 |
| C. | 12 |
| D. | 15 |
| Answer» C. 12 | |
| 1632. |
A man has Rs. 312, the denominations of one rupee notes, five rupee notes and twenty rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has? |
| A. | 32 |
| B. | 28 |
| C. | 24 |
| D. | 36 |
| Answer» E. | |
| 1633. |
If a + b + c = 8, a2 + b2 + c2 = 30, and a3 + b3 + c3 = 134, then the value of (abc)-1 is: |
| A. | 6 |
| B. | 1/10 |
| C. | 1/6 |
| D. | 10 |
| Answer» C. 1/6 | |
| 1634. |
If a is between 0 and 1, which of the following statements is (are) true?(i) a2 - 1> 0(ii) a2 + 1 > 0(iii) a2 - a > 0 |
| A. | only (ii) |
| B. | (i) & (ii) |
| C. | (iii) only |
| D. | All three |
| Answer» B. (i) & (ii) | |
| 1635. |
If a - b = 4 and ab = -3, then what is the value of a3 - b3? |
| A. | 21 |
| B. | 28 |
| C. | 23 |
| D. | -20 |
| Answer» C. 23 | |
| 1636. |
A force of 78 grams acts at the point (2, 3, 5), the direction ratios of the line of action being 2, 2, 1. The magnitude of its moment about the line joining the origin to the point (12, 3, 4) is: |
| A. | 24 |
| B. | 136 |
| C. | 36 |
| D. | 0 |
| Answer» C. 36 | |
| 1637. |
If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is- |
| A. | 5 |
| B. | 15/8 |
| C. | 8/15 |
| D. | 16/3 |
| Answer» E. | |
| 1638. |
If (x – 1/x)2 = 3, then the value of x6 + 1/x6 equals |
| A. | 90 |
| B. | 100 |
| C. | 110 |
| D. | 120 |
| Answer» D. 120 | |
| 1639. |
If (x - 5)3 + (x - 6)3 + (x - 7)3 = 3 (x - 5) (x - 6) (x - 7), then what is the value of x? |
| A. | 6 |
| B. | 7 |
| C. | 5 |
| D. | 18 |
| Answer» B. 7 | |
| 1640. |
If a2 + b2 = 135 and ab = 7, (a > 0, b > 0) then the value of (a3 – b3) is: |
| A. | 1350 |
| B. | 1562 |
| C. | 1680 |
| D. | 1600 |
| Answer» C. 1680 | |
| 1641. |
If \(a× b=a+b+\sqrt{ab}\), then find the value of 4 × 9. |
| A. | 29 |
| B. | 49 |
| C. | 20 |
| D. | 19 |
| Answer» E. | |
| 1642. |
If A is a square matrix of order n the inverse A-1 exits, if ______. |
| A. | 1 is not an Eigen value of A |
| B. | 1 is an Eigen value of A |
| C. | 0 is not an Eigen value of A |
| D. | 0 is an Eigen value of A |
| Answer» D. 0 is an Eigen value of A | |
| 1643. |
Let \({\rm{\vec a}} = \hat i + 2{\rm{\hat j}} + 4{\rm{\hat k}},\;{\rm{\vec b}} = {\rm{\hat i}} + \lambda {\rm{\hat j}} + 4{\rm{\hat k}},{\rm{\;and\;\vec c}} = 2{\rm{\hat i}} + 4{\rm{\hat j}} + \left( {{\lambda ^2} - 1} \right){\rm{\hat k}}\) be coplanar vectors. Then the non-zero vector \({\rm{\vec a}} \times {\rm{\vec c}}\) is: |
| A. | \(- 10\hat i - 5{\rm{\hat j}}\) |
| B. | \(- 14\hat i - 5{\rm{\hat j}}\) |
| C. | \(- 14\hat i + 5{\rm{\hat j}}\) |
| D. | \(- 10\hat i + 5{\rm{\hat j}}\) |
| Answer» E. | |
| 1644. |
Find the value of a if the polynomials 2x3 + ax2 + 3x - 5 and x3 + x2 - 4x - a leave the same remainder when divided by (x - 1) |
| A. | a = -1 |
| B. | a = 1 |
| C. | a = 2 |
| D. | a = -2 |
| Answer» B. a = 1 | |
| 1645. |
If the total of half, one-third and one-fourth of a number is 12 greater than the number, then the number is |
| A. | 144 |
| B. | 154 |
| C. | 90 |
| D. | 174 |
| Answer» B. 154 | |
| 1646. |
If \(\frac{x}{5}=\frac{y}{8},\) then the value of \(\frac{x+5}{y+8}\) is equal to: |
| A. | \(\frac{7}{8}\) |
| B. | \(\frac{3}{5}\) |
| C. | \(\frac{5}{8}\) |
| D. | \(\frac{8}{5}\) |
| Answer» D. \(\frac{8}{5}\) | |
| 1647. |
If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + {1/(x – 4)}]? |
| A. | 3 |
| B. | 5 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 1648. |
If \(x + \frac 1 {2x} = 3,\) find the value of \(8x^3 + \frac 1 {x^3}.\) |
| A. | 186 |
| B. | 180 |
| C. | 164 |
| D. | 160 |
| Answer» C. 164 | |
| 1649. |
If x + y + z = 11, x2 + y2 + z2 = 133 and x3 + y3 + z3 = 881, then the value of ∛(xyz) is: |
| A. | -8 |
| B. | -6 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 1650. |
If \(\sqrt x - \frac{1}{{\sqrt x }} = \sqrt 5 ,\) then \({x^2} + \frac{1}{{{x^2}}}\) is equal to∶ |
| A. | 47 |
| B. | 49 |
| C. | 45 |
| D. | 51 |
| Answer» B. 49 | |