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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.
| 651. |
If 10.98 × 10.98 + 10.98K + 0.02 × 0.02 is a perfect square, then find the value of 'K'. |
| A. | 0.2 |
| B. | 0.04 |
| C. | 0.02 |
| D. | 0.4 |
| Answer» C. 0.02 | |
| 652. |
If \((5\sqrt{5}x^3 - 3\sqrt{3}y^3) \div (\sqrt{5}x-\sqrt{3}y) = (Ax^2 + By^2+ Cxy)\), then the value of \((3A+ B- \sqrt{15} C)\) is: |
| A. | 8 |
| B. | 5 |
| C. | 3 |
| D. | 12 |
| Answer» D. 12 | |
| 653. |
If √y = √4 - √6, then find the value of y2 - 20y + 12. |
| A. | 4 |
| B. | 8 |
| C. | 10 |
| D. | 12 |
| Answer» C. 10 | |
| 654. |
If a - b = 10 and ab = -21, then what is the value of \({a^3} - {b^3}\)? |
| A. | 316 |
| B. | 370 |
| C. | 185 |
| D. | 158 |
| Answer» C. 185 | |
| 655. |
If \({\rm{x}} - \frac{1}{x} = 3\), then find the value of \({x^4} + \frac{1}{{{x^4}}}\). |
| A. | 123 |
| B. | 129 |
| C. | 119 |
| D. | 14 |
| Answer» D. 14 | |
| 656. |
A \(= \frac{{x - 1}}{{x + 1}}\), then the value of A - 1/A is: |
| A. | \(\frac{{ - 4(2x - 1)}}{{{x^2} - 1}}\) |
| B. | \(\frac{{{x^2} - 1}}{{ - 4(2x - 1)}}\) |
| C. | \(\frac{{{x^2} - 1}}{{ - 4(2x + 1)}}\) |
| D. | \(\frac{{ - 4x}}{{{x^2} - 1}}\) |
| Answer» E. | |
| 657. |
If x + y = 2z, then the value of \(\dfrac{x}{x-z}+\dfrac{z}{y-z}\) is |
| A. | 1 |
| B. | 2 |
| C. | xyz |
| D. | 0 |
| Answer» B. 2 | |
| 658. |
Given three numbers, first is twice the second and is half of the third. If the average of three numbers is 56, then difference of first and third number is |
| A. | 12 |
| B. | 24 |
| C. | 36 |
| D. | 48 |
| Answer» E. | |
| 659. |
If u + v = 10 and uv = 16, then find the value of (u2 - v2)/uv. |
| A. | 0 |
| B. | 15/8 |
| C. | 15/4 |
| D. | 15/2 |
| Answer» D. 15/2 | |
| 660. |
If \(x = \frac{{\sqrt 5 - \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}\) and y is the reciprocal of x, then what is the value of (x3 + y3)? |
| A. | 488 |
| B. | 504 |
| C. | 476 |
| D. | 472 |
| Answer» B. 504 | |
| 661. |
If x = (√2 + 1)/(√2 - 1), then what is the value of (x5 + x4 + x2 + x)/x3 ? |
| A. | 40 |
| B. | 37.5 |
| C. | 38 |
| D. | 20√2 |
| Answer» B. 37.5 | |
| 662. |
In a mobile circus party, there were 100 hens, 90 goats and 16 camels supervised by certain number of shepherds. If the total number of feet is 448 more than the number of heads, then how many shepherds were employed? |
| A. | 32 |
| B. | 30 |
| C. | 34 |
| D. | 28 |
| Answer» C. 34 | |
| 663. |
Jane won a lottery and gets 1/3rd of the winning amount and donates Rs. 6000 which is 1/6th of amount he got, find how much the lottery was worth. |
| A. | 36000 |
| B. | 18000 |
| C. | 54000 |
| D. | 108000 |
| Answer» E. | |
| 664. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 + 8x + 15 = 0II. y2 - 4y - 21 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or relationship between x and y cannot be established. |
| Answer» E. x = y or relationship between x and y cannot be established. | |
| 665. |
If x + y + z = 1, x2 + y2 + z2 = 2 and x3 + y3 + z3 = 3, then what is the value of xyz? |
| A. | 1/3 |
| B. | 1/6 |
| C. | 1/2 |
| D. | 1/4 |
| Answer» C. 1/2 | |
| 666. |
If \(\rm \vec{a} \ and\ \vec b\) are two vectors such that \(\rm | \vec{a}| = \frac{1}{\sqrt3} \ , |\vec b| = 2\) and \(\rm \vec{a}\times \vec{b}\) is a unit vector, then find the angle between \(\vec a \ and \ \vec b\) |
| A. | 30° |
| B. | 90° |
| C. | 45° |
| D. | 60° |
| Answer» E. | |
| 667. |
If y2 = y + 7, then what is the value of y3? |
| A. | 8y + 7 |
| B. | y + 14 |
| C. | y + 2 |
| D. | 4y + 7 |
| Answer» B. y + 14 | |
| 668. |
Let A = [aij], 1 ≤ i, j ≤ n with n ≥ 3 and aij = i. j. The rank of A is: |
| A. | 0 |
| B. | 1 |
| C. | n-1 |
| D. | n |
| Answer» C. n-1 | |
| 669. |
If x = 2 - √3 then the value of x3 – x-3 is: |
| A. | 30√2 |
| B. | -30√2 |
| C. | 30√3 |
| D. | -30√3 |
| Answer» E. | |
| 670. |
If x > 0 and x1 + x-1 ≤ 2, then what is the value of (x1 + x -1)1 + (x2 + x-2)2 + (x3 + x-3)3 + ⋯ (x11 + x -11)11 is : |
| A. | 4864 |
| B. | 4210 |
| C. | 4094 |
| D. | 5234 |
| Answer» D. 5234 | |
| 671. |
If x2 = y + z, y2 = z + x and z2 = x + y, then what is the value of \(\frac{1}{{x\; + \;1}} + \frac{1}{{y\; + \;1\;}} + \frac{1}{{z\; + \;1}}\;?\) |
| A. | -1 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 672. |
Find the value of (0.75 × 0.75 × 0.75 - 0.001) ÷ (0.75 × 0.75 + 0.075 + 0.01). |
| A. | 0.845 |
| B. | 2.312 |
| C. | 1.908 |
| D. | 0.65 |
| Answer» E. | |
| 673. |
If x + y + z = 360 and x : y : z = 4 : 3 : 2, then what is the value of y + z - x? |
| A. | 60 |
| B. | 80 |
| C. | 30 |
| D. | 40 |
| Answer» E. | |
| 674. |
If x2 + 9y2 = 6xy, then what is y : x equal to? |
| A. | 1 : 3 |
| B. | 1 : 2 |
| C. | 2 : 1 |
| D. | 3 : 1 |
| Answer» B. 1 : 2 | |
| 675. |
If a - b = 2 and ab = 15, then what is the value of a3 - b3? |
| A. | 152 |
| B. | 112 |
| C. | 108 |
| D. | 98 |
| Answer» E. | |
| 676. |
If x + y + z = 2, xy + yz + zx = -11, then the value of x3 + y3 + z3 – 3xyz is: |
| A. | 152 |
| B. | 70 |
| C. | 74 |
| D. | 148 |
| Answer» D. 148 | |
| 677. |
A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)? |
| A. | 35/3 |
| B. | 37/3 |
| C. | -105/11 |
| D. | -105/13 |
| Answer» D. -105/13 | |
| 678. |
A positive number which when increased by 17 is equal to 84 times the reciprocal of the number. The number is: |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 3 |
| Answer» B. 5 | |
| 679. |
Find the factors of (x2 + x - 42). |
| A. | (x + 14) (x - 3) |
| B. | (x + 6) (x - 7) |
| C. | (x - 6) (x + 7) |
| D. | (x - 14) (x + 3) |
| Answer» D. (x - 14) (x + 3) | |
| 680. |
If both a and b are rational numbers, find the values of a and b in the following equalities:\(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}\) |
| A. | a = -1, b = 2 |
| B. | a = 1, b = 2 |
| C. | a = 2, b = -1 |
| D. | a = -2, b = 1 |
| Answer» D. a = -2, b = 1 | |
| 681. |
If \(\rm \frac{{144}}{{0.144}} = \frac{{14.4}}{x}\), then the value of x is |
| A. | 0.0144 |
| B. | 144 |
| C. | 14.4 |
| D. | 1.44 |
| Answer» B. 144 | |
| 682. |
a, b, c are three natural numbers such that \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\), what are the values of a, b and c? |
| A. | 1, 2, 3 |
| B. | 1, 3, 5 |
| C. | 2, 3, 4 |
| D. | 2, 3, 6 |
| Answer» E. | |
| 683. |
If 16 - 3 (a - 7) = -14, then a = _____. |
| A. | 19 |
| B. | 17 |
| C. | 21 |
| D. | 13 |
| Answer» C. 21 | |
| 684. |
If \(\frac{{x + \sqrt {{x^2} - 1} }}{{x - \sqrt {{x^2} - 1} }} + \frac{{x - \sqrt {{x^2} - 1} }}{{x + \sqrt {{x^2} - 1} }} = 62\), then what is the value of x (x < 0)? |
| A. | -4 |
| B. | 0 |
| C. | 3 |
| D. | 16 |
| Answer» B. 0 | |
| 685. |
Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer:I. x2 + 2x = 0II. \(y + 4 + \frac{4}{y} = 0\) |
| 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» C. If x < y | |
| 686. |
if \(x = \frac{1}{{2 + \frac{1}{2}}}\) then \(\frac{1}{x}\) ? |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{3}{5}\) |
| C. | \(\frac{5}{2}\) |
| D. | \(\frac{2}{5}\) |
| Answer» D. \(\frac{2}{5}\) | |
| 687. |
Consider a 3 × 3 real symmetric matrix S such that two of its eigenvalues are a ≠ 0, b ≠ 0 with respective eigen vectors \(\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} {{y_1}}\\ {{y_2}}\\ {{y_3}} \end{array}} \right]\).If a ≠ b then x1y1 + x2y2 + x3y3 equals |
| A. | a |
| B. | b |
| C. | ab |
| D. | 0 |
| Answer» E. | |
| 688. |
In a Zoo, there are rabbits and pigeons. If heads are counted there are 200 in all and if legs are counted there are 580 in all. How many pigeons are there in the Zoo? |
| A. | 90 |
| B. | 110 |
| C. | 121 |
| D. | 130 |
| Answer» C. 121 | |
| 689. |
If (p + 2)(2q - 1) = 2pq - 10 and (p - 2)(2q - 1) = 2pq - 10, then what is the value of pq? |
| A. | - 10 |
| B. | -5 |
| C. | 5 |
| D. | 10 |
| Answer» D. 10 | |
| 690. |
Let \(\vec a,\vec b\;and\;\vec c\) be three mutually perpendicular vectors each of unit magnitude. If \(\vec A = \vec a + \vec b + \vec c,\;\vec B = \vec a - \vec b + \vec c\) and \(\vec C = \vec a - \vec b - \vec c,\) then which one of the following is correct? |
| A. | \(\left| {\vec A} \right| > \left| {\vec B} \right| > \left| {\vec C} \right|\) |
| B. | \(\left| {\vec A} \right| = \left| {\vec B} \right| \ne \left| {\vec C} \right|\) |
| C. | \(\left| {\vec A} \right| = \left| {\vec B} \right| = \left| {\vec C} \right|\) |
| D. | \(\left| {\vec A} \right| \ne \left| {\vec B} \right| \ne \left| {\vec C} \right|\) |
| Answer» D. \(\left| {\vec A} \right| \ne \left| {\vec B} \right| \ne \left| {\vec C} \right|\) | |
| 691. |
If a2 + b2 = 80 and a - b = 4, then ab = ?A. 20B. 24C. 28D. 32 |
| A. | C |
| B. | A |
| C. | D |
| D. | B |
| Answer» D. B | |
| 692. |
If a - b = 2 and ab = 8, then what is the value of (a3 - b3)? |
| A. | 65 |
| B. | 34 |
| C. | 43 |
| D. | 56 |
| Answer» E. | |
| 693. |
Consider a 3 × 3 real symmetric matrix A such that the two of its Eigen values are a ≠ 0 and b ≠ 0 with respective Eigen vectors \(\left[ {\begin{array}{*{20}{c}}{{x_1}}\\{{x_2}}\\{{x_3}}\end{array}} \right],\;\left[ {\begin{array}{*{20}{c}}{{y_1}}\\{{y_2}}\\{{y_3}}\end{array}} \right]\). If a ≠ b, then x1 y1 + x2 y2 + x3 y3 equals |
| A. | a |
| B. | b |
| C. | ab |
| D. | 0 |
| Answer» E. | |
| 694. |
If 3x + 2y = 12 and xy = 6, then 9x2 + 4y2 = ______. |
| A. | 36 |
| B. | 144 |
| C. | 72 |
| D. | 52 |
| Answer» D. 52 | |
| 695. |
If 5x2 + y2 + z2 + 5 = 2x (y + 2) + 4z, then the value of (4x + 2y - z) is: |
| A. | 0 |
| B. | \(\frac{{ - 1}}{2}\) |
| C. | \(\frac{1}{2}\) |
| D. | 1 |
| Answer» E. | |
| 696. |
If aî + ĵ + k̂, î + b ĵ + k̂, î + ĵ + ck̂ (a ≠ b ≠ c ≠ 1) are co-plananr, then the value of \(\frac {1}{1 - a}+\frac {1}{1 - b}+\frac {1}{1 - c}\) is |
| A. | -1 |
| B. | -1 / 2 |
| C. | 1 / 2 |
| D. | 1 |
| Answer» E. | |
| 697. |
If the roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c is |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 2 |
| Answer» B. -1 | |
| 698. |
If \(P = \left| {\begin{array}{*{20}{c}}6&1&0\\0&1&0\\0&0&2\end{array}} \right|and\;Q = \left| {\begin{array}{*{20}{c}}2&3&1\\0&5&1\\0&0&5\end{array}} \right|\)Then the product of determinant P and Q has the value |
| A. | 50 |
| B. | 80 |
| C. | 500 |
| D. | 600 |
| Answer» E. | |
| 699. |
If \(a^{\frac{1}{3}}=11\) then the value of a2 - 331a is |
| A. | 1331331 |
| B. | 1331000 |
| C. | 1334331 |
| D. | 1330030 |
| Answer» C. 1334331 | |
| 700. |
If the HCF of polynomialsf(x) = (x – 1) (x2 + 3x + a) andg(x) = (x + 2) (x2 + 2x + b) is (x2 + x – 2)then what are the values of a and b respectively? |
| A. | 2, 2 |
| B. | 2, -3 |
| C. | -1, -3 |
| D. | -2, -1 |
| Answer» C. -1, -3 | |