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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.
| 401. |
If x - 1/x = 10, then find the value of \(\frac{{{x^4} + 1}}{{{x^2}}}\) |
| A. | 98 |
| B. | 100 |
| C. | 102 |
| D. | 106 |
| Answer» D. 106 | |
| 402. |
If x + y = 14; x3 + y3 = 1064, and xy = 40, then the value of (x - y)2 is: |
| A. | 36 |
| B. | 64 |
| C. | 81 |
| D. | 100 |
| Answer» B. 64 | |
| 403. |
If x – 1 = 5 + 2√6, then what is the value of √(x – 1) + 1/√(x – 1)? |
| A. | 2√3 |
| B. | 3√2 |
| C. | 2√2 |
| D. | 3√3 |
| Answer» B. 3√2 | |
| 404. |
If (a – b) = 4 and ab = 2, then (a3 – b3) is equal to∶ |
| A. | 80 |
| B. | 92 |
| C. | 84 |
| D. | 88 |
| Answer» E. | |
| 405. |
If (x + y)1/3 + (y + z)1/3 = -(z + x)1/3, then (x3 + y3 + z3) can be expressed as: |
| A. | 3xyz |
| B. | 1/8xyz |
| C. | 3/8(x + y) (y + z) (z + x) |
| D. | (x + y) (y + z) (z + x) |
| Answer» D. (x + y) (y + z) (z + x) | |
| 406. |
If \(\frac{x}{5}=\frac{x-1}{6}\) then X = ______. |
| A. | 5 |
| B. | 3 |
| C. | 4 |
| D. | -5 |
| Answer» E. | |
| 407. |
A quadratic polynomial in x leaves remainder 4, 4 and 0 respectively. when divided by (x - 1), (x - 2) and x - 3Find the quadratic polynomial: |
| A. | -2x2 + 6x + 5 |
| B. | -2x2 + 6x |
| C. | -2x2 + 6x - 5 |
| D. | -2x2 + 6x + 3 |
| Answer» C. -2x2 + 6x - 5 | |
| 408. |
If (x2 + 1/x2) = 6, then find the value of (10x – 10/x) |
| A. | ± 15 |
| B. | ± 20 |
| C. | ± 30 |
| D. | ± 40 |
| Answer» C. ± 30 | |
| 409. |
If \(X - \frac{1}{x}\) = 8, find the value of X4 + \(\frac{1}{X^4}\) |
| A. | 4355 |
| B. | 4356 |
| C. | 4352 |
| D. | 4354 |
| Answer» E. | |
| 410. |
If a2 + b2 = 99 and ab = 11, (a > 0, b > 0) then the value of (a3 + b3) is: |
| A. | 1100 |
| B. | 968 |
| C. | 1250 |
| D. | 1080 |
| Answer» C. 1250 | |
| 411. |
If (x)3/4 = (x)2, then what number should replace 'x'? |
| A. | 4 |
| B. | 2 |
| C. | 1 |
| D. | 6 |
| Answer» B. 2 | |
| 412. |
Find the value of x if 3x + 2 = 23. |
| A. | 7 |
| B. | 2 |
| C. | 6 |
| D. | 5 |
| Answer» B. 2 | |
| 413. |
If √x + 1/√x = 3, x > 0, then x2 (x2 – 47) = ? |
| A. | 0 |
| B. | -2 |
| C. | -1 |
| D. | 2 |
| Answer» D. 2 | |
| 414. |
A’s score is 2 times that of B and the sum of scores of A and C are 150. If the score of B is 36, then what is the score of C? |
| A. | 78 |
| B. | 72 |
| C. | 36 |
| D. | 150 |
| Answer» B. 72 | |
| 415. |
If 40√5x3 - 3√3y3 = (2√5x - √3y)(Ax2 + Bxy + cy2), then what is the value of √(B2 + C2 - A)? |
| A. | 11 |
| B. | 9 |
| C. | 8 |
| D. | 7 |
| Answer» E. | |
| 416. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 6x2 + 5x + 1 = 0II. 2y2 – y – 1 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or the relationship between x and y cannot be established. |
| Answer» F. | |
| 417. |
Find the quadratic equation whose roots are \(\frac{2}{3}\) and \(-\frac{1}{2}\): |
| A. | 6x2 + x + 2 = 0 |
| B. | 6x2 - x - 2 = 0 |
| C. | 16x2 - x + 2 = 0 |
| D. | 16x2 + x - 2 = 0 |
| Answer» C. 16x2 - x + 2 = 0 | |
| 418. |
If the roots of the equation px2 + x + r = 0 are reciprocal to each other, then which one of the following is correct? |
| A. | p = 2r |
| B. | p = r |
| C. | 2p = r |
| D. | p = 4r |
| Answer» C. 2p = r | |
| 419. |
For the matrix \(A = \left[ {\begin{array}{*{20}{c}} 5&3\\ 1&3 \end{array}} \right]\), ONE of the normalized eigen vectors is given as |
| A. | \(\left( {\begin{array}{*{20}{c}} {\frac{1}{2}}\\ {\frac{{\sqrt 3 }}{2}} \end{array}} \right)\) |
| B. | \(\left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 2 }}}\\ {\frac{{ - 1}}{{\sqrt 2 }}} \end{array}} \right)\) |
| C. | \(\left( {\begin{array}{*{20}{c}} {\frac{3}{{\sqrt {10} }}}\\ {\frac{{ - 1}}{{\sqrt {10} }}} \end{array}} \right)\) |
| D. | \(\left( {\begin{array}{*{20}{c}} {\frac{1}{{\sqrt 5 }}}\\ {\frac{2}{{\sqrt 5 }}} \end{array}} \right)\) |
| Answer» C. \(\left( {\begin{array}{*{20}{c}} {\frac{3}{{\sqrt {10} }}}\\ {\frac{{ - 1}}{{\sqrt {10} }}} \end{array}} \right)\) | |
| 420. |
In a certain gear train, the driver has 18 teeth while the follower has 8 teeth. For every 16 turns of the driver, the follower turns ______ times. |
| A. | 18 |
| B. | 8 |
| C. | 36 |
| D. | 9 |
| Answer» D. 9 | |
| 421. |
If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc? |
| A. | 121 |
| B. | 168 |
| C. | 300 |
| D. | 770 |
| Answer» E. | |
| 422. |
If x + y = 1, and x2y2 – 2xy = 12, then the value of \(\sqrt {{x^4} + {y^4}}\) is: |
| A. | 8 |
| B. | 6 |
| C. | 3 |
| D. | 5 |
| Answer» E. | |
| 423. |
If 3x2 + ax + 4 is perfectly divisible by x – 5, then the value of a is: |
| A. | -12 |
| B. | -5 |
| C. | -15.8 |
| D. | -15.6 |
| Answer» D. -15.6 | |
| 424. |
If a3 + b3 = 152 and a + b = 8, then what is the value of ab? |
| A. | 2 |
| B. | 11 |
| C. | -10 |
| D. | 15 |
| Answer» E. | |
| 425. |
If (x – 1) and (x + 3) are the factors of x2 + ax + b, then find the values of 'a' and 'b' respectively. |
| A. | -2, -3 |
| B. | 2, -3 |
| C. | -2, 3 |
| D. | 2, 3 |
| Answer» C. -2, 3 | |
| 426. |
If (x + a) is a common factor of x2 - (2 + √2)x + 2√2 and x2 - 2√2x + 2, then the value of \(\sqrt {\left( {5\sqrt 2 - a} \right)3\surd 2} \) is ∶ |
| A. | 4 |
| B. | 2 |
| C. | 8 |
| D. | 6 |
| Answer» E. | |
| 427. |
If a + 1/b = 1 and b + 1/c = 1, then the value of c + 1/a is |
| A. | 0 |
| B. | 2 |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 428. |
Find the sum of the cubes of the roots of the equation x3 - 6x2 + 11x - 6 = 0 |
| A. | 31 |
| B. | 32 |
| C. | 35 |
| D. | 36 |
| Answer» E. | |
| 429. |
If a - b = 4 and a3 - b3 = 88, then find the value of a2 - b2. |
| A. | \(8\sqrt{6}\) |
| B. | \(6\sqrt{6}\) |
| C. | \(7\sqrt{2}\) |
| D. | \(9\sqrt{6}\) |
| Answer» B. \(6\sqrt{6}\) | |
| 430. |
A sum of Rs. 8,200 was divided among A, B and C in such a way that A has Rs. 500 more than B, and C has Rs. 300 more than A. How much was A's share (in Rs.)? |
| A. | 2,800 |
| B. | 2,300 |
| C. | 3,100 |
| D. | 2,000 |
| Answer» B. 2,300 | |
| 431. |
If \(A=\begin{bmatrix} 1 & 2 &2 \\ 2& 1 &-2 \\ a&2 &b \end{bmatrix}\) is a matric such that AAT = 9I3, then what are the values of a and b? |
| A. | a = 2 and b = -1 |
| B. | a = 2 and b = 1 |
| C. | a = -2 and b = -1 |
| D. | a = -2 and b = 1 |
| Answer» D. a = -2 and b = 1 | |
| 432. |
Rajiv scored 20% marks in an exam and failed by 11 marks. If he scored 50% marks, then he gets 4 marks more than passing marks. What is the passing marks for the exam? |
| A. | 21 |
| B. | 33 |
| C. | 50 |
| D. | 45 |
| Answer» B. 33 | |
| 433. |
For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows:\(s\left( {P,\;Q} \right) = \mathop \sum \limits_{i = 1}^n \left( {p\left[ i \right].Q\left[ i \right]} \right)\)Let L be a set of 10-dimensional non-zero vectors such that for every pair of distinct vectors P, Q ∈ L, s(P, Q) = 0. What is the maximum cardinality possible for the set L ? |
| A. | 100 |
| B. | 10 |
| C. | 9 |
| D. | 11 |
| Answer» C. 9 | |
| 434. |
If √(3x2 - 7x - 30) - √(2x2 - 7x - 5) = x - 5 has α and β as its roots, then the value of αβ is |
| A. | -15 |
| B. | -5 |
| C. | 0 |
| D. | 5 |
| Answer» B. -5 | |
| 435. |
If 8x/3 + [7(5 - 2x/3)]/2 = 1/2, then what is the value of x? |
| A. | -17 |
| B. | 51 |
| C. | -51 |
| D. | 17 |
| Answer» D. 17 | |
| 436. |
Consider a transformation T: R3 → R2 where R3 and R2 represent three and two-dimensional real column vectors respectively. Also, T(x) = Ax for some matrix A and for each x in R3. How many rows and columns do A have and what is it's maximum possible rank? |
| A. | Rows: 3; Columns : 2; Rank : 3 |
| B. | Rows : 3; Columns : 2; Rank : 2 |
| C. | Rows : 2; Columns : 3; Rank : 2 |
| D. | Rows : 2; Columns : 3; Rank : 3 |
| Answer» D. Rows : 2; Columns : 3; Rank : 3 | |
| 437. |
If \(X=\dfrac{1}{1+\dfrac{1}{1+X}}\) and \(y=\dfrac{2}{2+\dfrac{1}{1+y}}\), then which of the following can be the value of X + Y? |
| A. | (-√5 - √17 + 3)/4 |
| B. | (2√5 + √17 - 3)/4 |
| C. | (-√5 + √17 + 1)/4 |
| D. | (√5 + √17 - 1)/4 |
| Answer» C. (-√5 + √17 + 1)/4 | |
| 438. |
If a - (1/a) = b, b - (1/b) = c and c - (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)? |
| A. | -3 |
| B. | -6 |
| C. | -1 |
| D. | -9 |
| Answer» B. -6 | |
| 439. |
If \(a + \frac{1}{a} = - 6\), find the value of \({{\rm{a}}^3} + \frac{1}{{{a^3}}}\) |
| A. | 216 |
| B. | -198 |
| C. | -216 |
| D. | 198 |
| Answer» C. -216 | |
| 440. |
If x – 1/x = 2√2, then x2 + 1/x2 is equal to∶ |
| A. | 16 |
| B. | 12 |
| C. | 11 |
| D. | 10 |
| Answer» E. | |
| 441. |
A = 1200 – X where X is a real number. A > 0 and A is divisible by 3, 5, 7 and 11. The sum of the two largest possible value of X is: |
| A. | 45 |
| B. | 55 |
| C. | –1110 |
| D. | –1065 |
| Answer» E. | |
| 442. |
A man has 3 sons, 2 daughters and a wife. They divided a sum of Rs. 19000 among themselves such that each daughter got 1.5 times the amount received by each son and his wife received 600 less than each son. What is the total amount (in Rs) received by the 3 sons together? |
| A. | 2800 |
| B. | 3600 |
| C. | 5600 |
| D. | 8400 |
| Answer» E. | |
| 443. |
If 2x - y = 5, then (2x - 3)3 - (y + 2)3 is equal to |
| A. | 0 |
| B. | 25 |
| C. | 40 |
| D. | 125 |
| Answer» B. 25 | |
| 444. |
Find the sum of roots and product of roots for the quadratic equation 2x2 – 5x – 4 = 0 |
| A. | \(\frac{5}{2}, -2\) |
| B. | 5, – 4 |
| C. | \(\frac{-5}{2}, 2\) |
| D. | – 5, 4 |
| Answer» B. 5, – 4 | |
| 445. |
2/5 of a number exceeds 2/7 of the same number by 40. Find the number. |
| A. | 250 |
| B. | 280 |
| C. | 320 |
| D. | 350 |
| Answer» E. | |
| 446. |
If x4 – 79x2 + 1 = 0, then a value of x3 + x–3 can be: |
| A. | 798 |
| B. | 720 |
| C. | 789 |
| D. | 702 |
| Answer» E. | |
| 447. |
If x – y = 3, then what is the value of x3 – y3 – 9xy? |
| A. | 3 |
| B. | 9 |
| C. | 18 |
| D. | 27 |
| Answer» E. | |
| 448. |
If x2 - 12x + 33 = 0, then what is the value of (x - 4)2 + [1/ (x - 4)2]? |
| A. | 16 |
| B. | 14 |
| C. | 18 |
| D. | 20 |
| Answer» C. 18 | |
| 449. |
A system of equations is said to be inconsistent if |
| A. | they have one solution |
| B. | they have no solution |
| C. | they have one or more solution |
| D. | none of these |
| Answer» C. they have one or more solution | |
| 450. |
If 9x2 + 16y2 = 24xy, then \(\frac{x}{y} = \) |
| A. | 4/3 |
| B. | 9/16 |
| C. | 3/16 |
| D. | 9/4 |
| Answer» B. 9/16 | |