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.
| 1701. |
If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc ? |
| A. | 189 |
| B. | 243 |
| C. | 361 |
| D. | 486 |
| Answer» C. 361 | |
| 1702. |
If the value of (a + b - 2)2 + (b + c - 5)2 + (c + a - 5)2 = 0, then the value of \(\sqrt {{{\left( {b + c} \right)}^a} + {{\left( {c + a} \right)}^b} - 1} \) is: |
| A. | 1 |
| B. | 0 |
| C. | 3 |
| D. | 2 |
| Answer» D. 2 | |
| 1703. |
If x3 + y3 = 9 and x + y = 3, then find the value of x2 + y2. |
| A. | 5 |
| B. | 6 |
| C. | 25 |
| D. | 3 |
| Answer» B. 6 | |
| 1704. |
If \(11\sqrt{n} = \sqrt{112} + \sqrt{343}\) then the value of n is |
| A. | 3 |
| B. | 11 |
| C. | 13 |
| D. | 7 |
| Answer» E. | |
| 1705. |
If \(\left| {\vec a + \vec b} \right| = \left| {\vec a - \vec b} \right|\), then which one of the following is correct? |
| A. | \(\vec a = \lambda \vec b\) for some scalar λ |
| B. | \(\vec a\) is parallel to \(\vec b\) |
| C. | \(\vec a\) is perpendicular to \(\vec b\) |
| D. | \(\vec a = \vec b = \vec 0\) |
| Answer» D. \(\vec a = \vec b = \vec 0\) | |
| 1706. |
If (x – 8)3 + (2x + 16)3 + (2x - 13)3 = 3 (x - 8) (2x + 16) (2x – 13) then find the value of x. |
| A. | 1 |
| B. | -1 |
| C. | 2 |
| D. | -2 |
| Answer» B. -1 | |
| 1707. |
Let a, b, x, y be real number such that a2 + b2 = 25, x2 + y2 = 169, and ax + by = 65. If k = ay - bx, then |
| A. | k = 0 |
| B. | \(k = \frac{5}{13}\) |
| C. | \(0< k \le \frac{5}{13}\) |
| D. | \(k > \frac{5}{13}\) |
| Answer» B. \(k = \frac{5}{13}\) | |
| 1708. |
If x and y are different positive integer numbers and 3x/y = 4 then find the minimum value of (3x + 4y). |
| A. | 6 |
| B. | 1 |
| C. | 24 |
| D. | 8 |
| Answer» D. 8 | |
| 1709. |
If \({x^2} + \frac{1}{{{x^2}}} = \frac{7}{4}\) for x > 0, then what is the value of \({x^3} + \frac{1}{{{x^3}}}\)? |
| A. | (3√3)/5 |
| B. | (3√15)/5 |
| C. | (3√15)/8 |
| D. | (3√5)/8 |
| Answer» D. (3√5)/8 | |
| 1710. |
If (3x + 1)3 + (x – 3)3 + (4 – 2x)3 + 6(3x + 1)(x – 3)(x – 2) = 0, then x is equal to: |
| A. | -1/2 |
| B. | -1 |
| C. | 1/2 |
| D. | 1 |
| Answer» C. 1/2 | |
| 1711. |
If a + b = 27 and a3 + b3 = 5427, then find ab |
| A. | 149 |
| B. | 135 |
| C. | 176 |
| D. | 143 |
| Answer» D. 143 | |
| 1712. |
If x2 + 16 = -4x, then what is the value of x3 - 64? |
| A. | 128 |
| B. | 0 |
| C. | 64 |
| D. | 256 |
| Answer» C. 64 | |
| 1713. |
A quadratic polynomial ax2 + bx + c = 0 is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b)? |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | -1 |
| Answer» B. 2 | |
| 1714. |
If \(x - \frac {-1} {x} = 5\) then \(x^2 + \frac {1} {x^2}\) is |
| A. | 5 |
| B. | 25 |
| C. | 27 |
| D. | 23 |
| Answer» E. | |
| 1715. |
If x4 + x2y2 + y4 = 273 and x2 – xy + y2 = 13, then the value of xy is: |
| A. | 6 |
| B. | 8 |
| C. | 10 |
| D. | 4 |
| Answer» E. | |
| 1716. |
A number is divided into three parts such that thrice the first part, six times the second part and eight times the third part are equal. If the first part is Rs. 1600, what is the third part? |
| A. | Rs. 900 |
| B. | Rs. 750 |
| C. | Rs. 450 |
| D. | Rs. 600 |
| Answer» E. | |
| 1717. |
If a – b = 5 and a2 + b2 = 45, then the value of ab is: |
| A. | 25 |
| B. | 10 |
| C. | 15 |
| D. | 20 |
| Answer» C. 15 | |
| 1718. |
If x/3 - [5/2(7x/5 - 4/3)] = -x/6, then what is the value of x? |
| A. | 10/9 |
| B. | -10/9 |
| C. | -9/10 |
| D. | 9/10 |
| Answer» B. -10/9 | |
| 1719. |
If the sum of the roots of a quadratic equation is 11 and the product of the roots is 30, then the equation is: |
| A. | x2- 11x + 30 = 0 |
| B. | x2- 11x - 30 = 0 |
| C. | x2 + 11x - 30 = 0 |
| D. | x2 + 11x + 30 = 0 |
| Answer» B. x2- 11x - 30 = 0 | |
| 1720. |
Find the product of (x + y)(x2 - xy + y2) |
| A. | y3 + y3 |
| B. | x3 + y3 |
| C. | x3 - y3 |
| D. | y2 + y2 |
| Answer» C. x3 - y3 | |
| 1721. |
If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solution, then the value of k is: |
| A. | 12 |
| B. | -12 |
| C. | 8 |
| D. | -16 |
| Answer» C. 8 | |
| 1722. |
If y2 + 3y - 18 ≥ 0, which of the following is true? |
| A. | y ≤ 3 or y ≥ 0 |
| B. | y > - 6 or y < 3 |
| C. | -6 ≤ y ≤ 3 |
| D. | y ≥ 3 or y ≤ - 6 |
| Answer» E. | |
| 1723. |
If (3x)/5 - (4/5)(10/3 - x/2) = - 2/3, then what is the value of x? |
| A. | - 2 |
| B. | 10 / 3 |
| C. | 2 |
| D. | - 10 / 3 |
| Answer» D. - 10 / 3 | |
| 1724. |
If the difference between the roots of x2 – px + q = 0 is 2, then the relation between p and q is: |
| A. | p = 4(q + 1)2 |
| B. | p = 4(q + 1) |
| C. | p2 = 4(q + 1) |
| D. | p2 = (q + 1) |
| Answer» D. p2 = (q + 1) | |
| 1725. |
If a2 + b2 = 45 and ab = 18, then the value of \(\frac{1}{a}+\frac{1}{b}\) is |
| A. | 5/7 |
| B. | 7/8 |
| C. | ±1/2 |
| D. | ±1/3 |
| Answer» D. ±1/3 | |
| 1726. |
If x + y = 10 and x2 + y2 = 68, then find xy |
| A. | 21 |
| B. | 24 |
| C. | 25 |
| D. | 16 |
| Answer» E. | |
| 1727. |
-If \(y - \frac{1}{y} = 4\), then find the value of \(\left( {{y^3} - \frac{1}{{{y^3}}}} \right)\) |
| A. | 64 |
| B. | 76 |
| C. | 88 |
| D. | 90 |
| Answer» C. 88 | |
| 1728. |
If x4 + 1/x4 = 2, and x is a positive quantity, then x is equal to: |
| A. | 1 |
| B. | 2 |
| C. | 1/2 |
| D. | 1/4 |
| Answer» B. 2 | |
| 1729. |
Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2î + 4ĵ - 5k̂ and î + 2ĵ + 3k̂ respectively. If \(\vec{a}\) is a unit vector parallel to \(\overrightarrow{AC}\), then \(\vec{a}\) is equal to: |
| A. | \(\dfrac{1}{3}(3\hat{i}-6\hat{j}-2\hat{k})\) |
| B. | \(\dfrac{1}{3}(3\hat{i}+6\hat{j}+2\hat{k})\) |
| C. | \(\dfrac{1}{7}(3\hat{i}-6\hat{j}-2\hat{k})\) |
| D. | \(\dfrac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\) |
| Answer» E. | |
| 1730. |
If John’s cat eats 1106 g of cat food in a week, then how much cat food does it eat in a day? |
| A. | 160 g |
| B. | 221 g |
| C. | 92 g |
| D. | 158 g |
| Answer» E. | |
| 1731. |
If a + 2b = 55 and a – 2b = - 13, find the value of b.A. 21B. 14C. 17D. 19 |
| A. | D |
| B. | A |
| C. | C |
| D. | B |
| Answer» D. B | |
| 1732. |
If (x / 6) - (2 / 3)(5 - x / 2) = -1 / 3, then what is the value of x? |
| A. | 6 |
| B. | -6 |
| C. | 3 |
| D. | -3 |
| Answer» B. -6 | |
| 1733. |
If (p2 + q2)/(r2 + s2) = (pq)/(rs), then what is the value of (p - q)/(p + q) in terms of r and s? |
| A. | (r + s)/(r - s) |
| B. | (r - s)/(r + s) |
| C. | (r + s)/(rs) |
| D. | (rs)/(r - s) |
| Answer» C. (r + s)/(rs) | |
| 1734. |
If a + b + c = 5 and ab + bc + ca = 4, then a3 + b3 + c3 – 3abc is equal to: |
| A. | 72 |
| B. | 62 |
| C. | 65 |
| D. | 68 |
| Answer» D. 68 | |
| 1735. |
If 19x2 = 1002– 902, then find the value of x.A. 10B. 9C. 11D. 12 |
| A. | C |
| B. | A |
| C. | D |
| D. | B |
| Answer» C. D | |
| 1736. |
If a + b = 10 and 3/7 of ab = 9, then the value of a3 + b3 is: |
| A. | 350 |
| B. | 370 |
| C. | 270 |
| D. | 360 |
| Answer» C. 270 | |
| 1737. |
If l and m are the roots of the equation 4x2 + 3x + 7, then \(\frac{1}{l} + \frac{1}{m} = \;?\) |
| A. | \(\frac{3}{7}\) |
| B. | \( - \frac{3}{7}\) |
| C. | \( - \frac{7}{3}\) |
| D. | \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)\(\frac{7}{3}\) |
| Answer» C. \( - \frac{7}{3}\) | |
| 1738. |
If (x + y)3 + 8 (x - y)3 = (3x + Ay) (3x2 + Bxy + Cy2), then the value of A + B + C is: |
| A. | 3 |
| B. | 2 |
| C. | 4 |
| D. | 0 |
| Answer» E. | |
| 1739. |
If \(\vec a = \left( \hat i + \hat j + \hat k \right),\; \vec a \cdot \vec b = 1\) and \(\vec a \times \vec b = \hat j - \hat k\) then \(\vec b\) is: |
| A. | î + ĵ + k̂ |
| B. | 2ĵ - k̂ |
| C. | î |
| D. | 2î |
| Answer» D. 2î | |
| 1740. |
Find the value of x, if the given matrix \(\left[ {\begin{array}{*{20}{c}} 1&2&5\\ 2&x&{10}\\ 3&1&{ - 2} \end{array}} \right]\) is singular |
| A. | 4 |
| B. | - 4 |
| C. | \(\frac{1}{4}\) |
| D. | \(- \frac{1}{4}\) |
| Answer» B. - 4 | |
| 1741. |
If α, β are the roots of x2 – x + 2 = 0 then α2β + αβ2 |
| A. | 1 |
| B. | -2 |
| C. | -1 |
| D. | 2 |
| Answer» E. | |
| 1742. |
If a + b = 1, then a4 + b4 – a3 – b3 – 2a2b2 + ab is equal to: |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 0 |
| Answer» E. | |
| 1743. |
If \({x^2} + \frac{1}{{{x^{2}}}} = 23\), then the value of \({x^4} + \frac{1}{{{x^4}}}\) is |
| A. | 429 |
| B. | 629 |
| C. | 527 |
| D. | 526 |
| Answer» D. 526 | |
| 1744. |
If (3x + 1)3 + (x - 3)3 + (2x - 4)3 = 3 (3x + 1) (x - 3) (2x - 4), then x is equal to: |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | -13 |
| Answer» D. -13 | |
| 1745. |
If \(\frac{x}{y} + \frac{y}{x} = 2\), then value of \(\frac{{{x^2}\; + \;{y^2}}}{{xy\; + \;{y^2}}}\) is equal to |
| A. | 0 |
| B. | 1/2 |
| C. | 1/4 |
| D. | 1 |
| Answer» E. | |
| 1746. |
Ayesha has only Rs. 5 and Rs. 10 coins with her. If the total number of coins she has is 25 and the amount of money with her is Rs. 160, then the number of Rs. 5 and Rs. 10 coins with her are: |
| A. | 18 and 7 respectively |
| B. | 10 and 15 respectively |
| C. | 15 and 10 respectively |
| D. | 20 and 5 respectively |
| Answer» B. 10 and 15 respectively | |
| 1747. |
Let z ϵ C be such that |z|<1. If \({\rm{\omega }} = \frac{{5 + 3{\rm{z}}}}{{5\left( {1 - {\rm{z}}} \right)}}\), then: |
| A. | 5 Re(ω) > 4 |
| B. | 4 Im(ω) > 5 |
| C. | 5 Re(ω) > 1 |
| D. | 5 Im(ω) > 1 |
| Answer» D. 5 Im(ω) > 1 | |
| 1748. |
If a + 1/a = 3, then the value of (a6 + 1/a6) is equal to: |
| A. | 319 |
| B. | 322 |
| C. | 780 |
| D. | 730 |
| Answer» C. 780 | |
| 1749. |
Expand (2x - y + 3z)2 |
| A. | 4x2 + y2 + 9z2 + 4xy + 6yz + 12xz |
| B. | 4x2 + y2 + 9z2 + 4xy + 6yz - 12xz |
| C. | 4x2 + y2 + 9z2 - 4xy - 6yz + 12xz |
| D. | 4x2 + y2 + 9x2 + 4xy - 6yz + 12xz |
| Answer» D. 4x2 + y2 + 9x2 + 4xy - 6yz + 12xz | |
| 1750. |
If a + b = 11 and ab = 15, then a2 + b2 is equal to: |
| A. | 90 |
| B. | 91 |
| C. | 93 |
| D. | 92 |
| Answer» C. 93 | |