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.
| 551. |
A bucket full of water weighs 25 kg. And a bucket half full of water weighs 14 kg. If so, what is the net weight of the bucket? |
| A. | 1.5 Kg. |
| B. | 3 Kg. |
| C. | 11 Kg. |
| D. | 5.5 Kg. |
| Answer» C. 11 Kg. | |
| 552. |
If \(\vec u = a\hat i + \;2\hat j - \;\hat k\;and\;\vec v = 3\hat j + 4\hat k\) are two vectors such that \(\left| {\vec u + \;\vec v} \right| \le 10\) then a = ? |
| A. | \(\pm 2\sqrt 3\) |
| B. | \(\pm\sqrt 3\) |
| C. | \(\pm 2\sqrt 5\) |
| D. | \(\pm \sqrt 5\) |
| Answer» D. \(\pm \sqrt 5\) | |
| 553. |
If a + b + c = 7 and ab + bc + ca = –6, then the value of a3 + b3 + c3 – 3abc is: |
| A. | 469 |
| B. | 472 |
| C. | 463 |
| D. | 479 |
| Answer» B. 472 | |
| 554. |
ABCD is a parallelogram and P is the point of intersection of the diagonals. If O is the origin, then \(\overrightarrow {{\rm{OA}}} + \overrightarrow {{\rm{OB}}} + \overrightarrow {{\rm{OC}}} + \overrightarrow {{\rm{OD}}} \) is equal to |
| A. | \(4{\rm{\;}}\overrightarrow {{\rm{OP}}} \) |
| B. | \(2{\rm{\;}}\overrightarrow {{\rm{OP}}} \) |
| C. | \(\overrightarrow {{\rm{OP}}} \) |
| D. | Null vector |
| Answer» B. \(2{\rm{\;}}\overrightarrow {{\rm{OP}}} \) | |
| 555. |
Pranita got 30 marks more in Math than what she got in Science. Her Math marks are 60% of the sum of her Math and Science marks. What are her Science marks? |
| A. | 90 |
| B. | 150 |
| C. | 120 |
| D. | 60 |
| Answer» E. | |
| 556. |
If x + 2 and x - 1 are the factors of x3 + 10x2 + mx + n, then the values of m and n are respectively |
| A. | 5 and -3 |
| B. | 17 and -8 |
| C. | 7 and -18 |
| D. | 23 and -19 |
| Answer» D. 23 and -19 | |
| 557. |
For a given matrix P = \(\left[ {\begin{array}{*{20}{c}} {4+ 3i}&-i\\ { i}&{4 - 3i} \end{array}} \right]\), where \(i = \sqrt { - 1}\), the inverse of matrix P is |
| A. | \(\frac{1}{{24}}\left[ {\begin{array}{*{20}{c}} {4 - 3i}&i\\ { - i}&{4 + 3i} \end{array}} \right]\) |
| B. | \(\frac{1}{{25}}\left[ {\begin{array}{*{20}{c}} i&{4 - 3i}\\ {4 + 3i}&{ - i} \end{array}} \right]\) |
| C. | \(\frac{1}{{24}}\left[ {\begin{array}{*{20}{c}} {4 + 3i}&{ - i}\\ i&{4 - 3i} \end{array}} \right]\) |
| D. | \(\frac{1}{{25}}\left[ {\begin{array}{*{20}{c}} {4 + 3i}&{ - i}\\ i&{4 - 3i} \end{array}} \right]\) |
| Answer» B. \(\frac{1}{{25}}\left[ {\begin{array}{*{20}{c}} i&{4 - 3i}\\ {4 + 3i}&{ - i} \end{array}} \right]\) | |
| 558. |
If the following equations are consistent, then value of k is4x – 3y + 1 = 0kx – 8y + 10 = 0x + y – 5 = 0 |
| A. | -6 |
| B. | 7 |
| C. | 6 |
| D. | -7 |
| Answer» C. 6 | |
| 559. |
Division by zero during forward elimination steps in Naïve Gaussian Elimination of the set of equation [A] [X] = [C] implies the coefficient matrix [A] |
| A. | is invertible |
| B. | is non-singular |
| C. | may be singular or non-singular |
| D. | is singular |
| Answer» D. is singular | |
| 560. |
If \(n + \frac{n}{2} + \frac{n}{4} + \frac{n}{8} = 45\), then find the value of ‘n’ which will satisfy the equation. |
| A. | 16 |
| B. | 24 |
| C. | 36 |
| D. | 48 |
| Answer» C. 36 | |
| 561. |
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line is |
| A. | y = -0.5 x + 1 |
| B. | y = x – 0.5 |
| C. | y = 0.5x - 1 |
| D. | y = 2x + 1 |
| Answer» E. | |
| 562. |
If (x + y) = 5 and xy = 4, then x3 + y3 is equal to:‐ |
| A. | 113 |
| B. | 65 |
| C. | 105 |
| D. | 109 |
| Answer» C. 105 | |
| 563. |
Let the Eigenvector of the matrix \(\left[ {\begin{array}{*{20}{c}} 1&2\\ 0&2 \end{array}} \right]\) be written in the form \(\left[ {\begin{array}{*{20}{c}} 1\\ a \end{array}} \right]\) and \(\left[ {\begin{array}{*{20}{c}} 1\\ b \end{array}} \right]\). What is the value of (a + b)? |
| A. | 0 |
| B. | \(\frac{1}{2}\) |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 564. |
If x + 1/x = 3√2, then x2 + 1/x2 is equal to: |
| A. | 22 |
| B. | 16 |
| C. | 26 |
| D. | 14 |
| Answer» C. 26 | |
| 565. |
If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2? |
| A. | k1 = 6, k2 = -1 |
| B. | k1 = 1, k2 = -6 |
| C. | k1 = 1, k2 = 6 |
| D. | k1 = -6, k2 = 1 |
| Answer» C. k1 = 1, k2 = 6 | |
| 566. |
If \(\sqrt x - \frac{1}{{\sqrt x }}\; = \;3\sqrt 2\) , then \({x^2} + \frac{1}{{{x^2}}}\) is equal to: |
| A. | 398 |
| B. | 402 |
| C. | 324 |
| D. | 326 |
| Answer» B. 402 | |
| 567. |
If a + b + c = 13 and ab + bc + ca = 54, then a3 + b3 + c3 – 3abc is equal to: |
| A. | 182 |
| B. | 793 |
| C. | 91 |
| D. | 273 |
| Answer» D. 273 | |
| 568. |
If 8x2 + y2 – 12x – 4xy + 9 = 0, then the value of (14x – 5y) is: |
| A. | 3 |
| B. | 9 |
| C. | 6 |
| D. | 5 |
| Answer» D. 5 | |
| 569. |
If \(x = 5 - \frac{1}{x},\) what is the value of \({x^5} + \frac{1}{{{x^5}}}\) ? |
| A. | 625 |
| B. | 3125 |
| C. | 2525 |
| D. | 2500 |
| Answer» D. 2500 | |
| 570. |
(a + b – c + d)2 – (a – b + c – d)2 = ? |
| A. | 2a (a + b – c) |
| B. | 4a (b + d – c) |
| C. | 2a (b + c – d) |
| D. | 4a (b – d + c) |
| Answer» C. 2a (b + c – d) | |
| 571. |
If 1 – 64x3 – 12x + px2 = (1 – 4x)3 then the value of p is: |
| A. | -48 |
| B. | 16 |
| C. | 48 |
| D. | -12 |
| Answer» D. -12 | |
| 572. |
If a = -7, b = 5 and c = 2, then find the value of a3 + b3 + c3. |
| A. | -210 |
| B. | -180 |
| C. | 180 |
| D. | 210 |
| Answer» B. -180 | |
| 573. |
If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 7, then what is the value of x3 + y3 + z3 - 3xyz? |
| A. | 49 |
| B. | 343 |
| C. | 1029 |
| D. | 2401 |
| Answer» C. 1029 | |
| 574. |
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 – 3 = 0II. y2 + 6y + 8 = 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» F. | |
| 575. |
How many times does the number 3 occur in unit's place for numbers ranging from 1 to 100?A. 20B. 11C. 10D. 19 |
| A. | B |
| B. | D |
| C. | A |
| D. | C |
| Answer» E. | |
| 576. |
If \(\vec a = \hat i + \hat j + \hat k,\;\vec b= 2\hat i - 4\hat k,\;\vec c=\hat i + λ \hat j + 3\hat k\) are coplanar, then the value of λ is: |
| A. | 5/2 |
| B. | 3/5 |
| C. | 7/3 |
| D. | 5/3 |
| Answer» E. | |
| 577. |
1800 chocolates were distributed among the students of a class. Each student got twice as many chocolates as the number of students in the class. Calculate the number of students in the class. |
| A. | 30 |
| B. | 40 |
| C. | 60 |
| D. | 90 |
| Answer» B. 40 | |
| 578. |
If \(a^2 + \frac{2}{a^2}=16\), then find the value of \(\frac{72a^2}{a^4+2+8a^2}\) |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» B. 4 | |
| 579. |
If x – 1/x = 7, then what is the value of (x3 – 1/x3)? |
| A. | 350 |
| B. | 336 |
| C. | 343 |
| D. | 364 |
| Answer» E. | |
| 580. |
If α and β be two roots of a quadratic equation, then quadratic equation will be: |
| A. | x2 - (α + β)x - αβ = 0 |
| B. | x2 - (α + β)x - β = 0 |
| C. | x2 - (α + β)x + αβ = 0 |
| D. | x2 + (α + β)x + αβ = 0 |
| Answer» D. x2 + (α + β)x + αβ = 0 | |
| 581. |
Let \(\sqrt 3 \hat i + {\rm{\hat j}},{\rm{\hat i}} + \sqrt 3 {\rm{\hat j}},{\rm{\;and\;\beta \hat i}} + \left( {1 - \beta } \right){\rm{\hat j}}\) respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \(\frac{3}{{\sqrt 2 }}\), then the sum of all possible values of β is: |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» E. | |
| 582. |
If x2 + ax + b, when divided by x + 3, leaves a remainder of -1 and x2 + bx + a, when divide by x - 3, leaves a remainder of 39, then a + b = ? |
| A. | -14 |
| B. | -38 |
| C. | 14 |
| D. | 38 |
| Answer» D. 38 | |
| 583. |
If a - b = -1 and ab = 6, then what is the value of a3 - b3? |
| A. | 33 |
| B. | -19 |
| C. | 18 |
| D. | 35 |
| Answer» C. 18 | |
| 584. |
If \(\sqrt x + \frac{1}{{\surd x}} = \sqrt 6 ,\) then \({x^2} + \frac{1}{{{x^2}}}\) is equal to∶ |
| A. | 16 |
| B. | 62 |
| C. | 36 |
| D. | 14 |
| Answer» E. | |
| 585. |
If \(x^2-\frac{1}{x^2}=14\), what is the value of \(x^2+\frac{1}{x^2}\) ? |
| A. | 10√2 |
| B. | -10√2 |
| C. | 2√10 |
| D. | -2√10 |
| Answer» B. -10√2 | |
| 586. |
Let \(\rm \vec a =\hat i +\hat j +\hat k,\; \vec b =\hat i -\hat j + \hat k\) and c = î - ĵ - k̂ be three vectors. A vector \(\rm \vec v\) in the plane of \(\rm \vec a\) and \(\rm \vec b\) whose projection on \(\rm \frac {\vec c} {|\vec c|}\) is \(\frac 1 {\sqrt 3},\) is |
| A. | 3î - ĵ + 3k̂ |
| B. | î - 3ĵ + 3k̂ |
| C. | 5î - 2ĵ + 5k̂ |
| D. | 2î - ĵ + 3k̂ |
| Answer» B. î - 3ĵ + 3k̂ | |
| 587. |
If a + b + c = 2, a2 + b2 + c2 = 26, then the value of a3 + b3 + c3 – 3abc is: |
| A. | 74 |
| B. | 71 |
| C. | 78 |
| D. | 69 |
| Answer» B. 71 | |
| 588. |
If on subtracting 28 from a number, what remains is one-third of the number. What is 50% of the number? |
| A. | 23 |
| B. | 24 |
| C. | 21 |
| D. | 36 |
| Answer» D. 36 | |
| 589. |
Let A be an n × n matrix with rank r(0 < r < n). Then Ax = 0 has p independent solutions, where p is |
| A. | r |
| B. | n |
| C. | n - r |
| D. | n + r |
| Answer» D. n + r | |
| 590. |
Find a positive value of x for which the given equation \(\frac{x^2 - 9}{5 + x^2} = -\frac{5}{9}\) is satisfied. |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 4 |
| Answer» C. 1 | |
| 591. |
If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR? |
| A. | 9 |
| B. | 8 |
| C. | 12 |
| D. | 6 |
| Answer» D. 6 | |
| 592. |
If (2x + 3y + 4)(2x + 3y – 5) is equal to (ax2 + by2 + 2hxy + 2gx + 2fy + c), then what is the value of {3(g – f – c)/ab} ? |
| A. | \(\dfrac{41}{24}\) |
| B. | 1 |
| C. | \(\dfrac{31}{24}\) |
| D. | \(\dfrac{25}{24}\) |
| Answer» B. 1 | |
| 593. |
If the difference between a number and its reciprocal is 5, then what is the sum of the square of the number and its reciprocal? |
| A. | 25 |
| B. | 26 |
| C. | 27 |
| D. | 28 |
| Answer» D. 28 | |
| 594. |
Let the superscript T represent the transpose operation. Consider the function \(f(x) = \frac{1}{2} x^T Qx-r^Tx\), where x and r are n × 1 vectors and Q is a symmetric n × n matrix. the stationery point of f(x) is |
| A. | r |
| B. | Q-1 r |
| C. | \(\frac{r}{r^Tr}\) |
| D. | QTr |
| Answer» C. \(\frac{r}{r^Tr}\) | |
| 595. |
1595 is the sum of the square of three consecutive odd numbers. Find the numbers |
| A. | 19, 21, 23 |
| B. | 17, 19, 21 |
| C. | 21, 23, 25 |
| D. | 23, 25, 27 |
| Answer» D. 23, 25, 27 | |
| 596. |
If factors of polynomial 5x3 + 4x2 - 60x + k = 0 is 2 < x < 5, then which of the option is true. |
| A. | -144 < k < 9 |
| B. | -5 < k < 5 |
| C. | -3 < k < 7 |
| D. | -5 < k < 6 |
| Answer» B. -5 < k < 5 | |
| 597. |
Divide 960 into 2 parts such that one exceeds the other by 26 |
| A. | 534, 426 |
| B. | None of the above |
| C. | 474, 486 |
| D. | 467, 493 |
| Answer» E. | |
| 598. |
25a2 – 9 is factored as: |
| A. | (5a – 3)2 |
| B. | (5a + 3) (5a – 3) |
| C. | (25a + 1) (a – 9) |
| D. | (5a + 1) (5a – 9) |
| Answer» C. (25a + 1) (a – 9) | |
| 599. |
Directions: Given below are two quantities named I and II. 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.In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.Quantity I: 2x2 - 22x + 48 = 0Quantity II: y2 - 20y + 96 = 0 |
| A. | Quantity I ≤ Quantity II |
| B. | Quantity I > Quantity II |
| C. | Quantity I ≥ Quantity II |
| D. | Quantity I < Quantity II |
| E. | Quantity I = Quantity II |
| Answer» B. Quantity I > Quantity II | |
| 600. |
A 3 × 3 matrix is such that, \({P^3} = P\). Then the eigenvalues of \(P\;\) are |
| A. | 1, 2, −1 |
| B. | \(1,\;0.5 + j0.866,\;0.5 - j0.866\) |
| C. | \(1,\; - 0.5 + j0.866,\; - 0.5 - j0.866\) |
| D. | 0, 1, −1 |
| Answer» E. | |