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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.
| 351. |
If x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0, then what is the value of x3 + 8y3? |
| A. | 85 |
| B. | 65 |
| C. | 76 |
| D. | 95 |
| Answer» C. 76 | |
| 352. |
If the vectors 2î - 3ĵ, î + ĵ - k̂ and 3î - k̂ form the three co-terminous edges of a parallelepiped, then the volume of parallelepiped is: |
| A. | 8 |
| B. | 10 |
| C. | 4 |
| D. | 14 |
| Answer» D. 14 | |
| 353. |
If a school of fish weighs 3 kg and each fish in the school weighs 150g, then the number of fish in the school is____. |
| A. | 10 |
| B. | 20 |
| C. | 30 |
| D. | 15 |
| Answer» C. 30 | |
| 354. |
If (2x - 7)3 + (2x – 8)3 + (2x - 3)3 = 3 (2x - 7) (2x - 8) (2x - 3), then what is the value of x? |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | 4 |
| Answer» C. 1 | |
| 355. |
Mary sold squid for Rs. 80 per kg and earned Rs. 960 at the end of the day. How many kg of squid did she sell? |
| A. | 18 kg |
| B. | 12 kg |
| C. | 0.83 kg |
| D. | 14 kg |
| Answer» C. 0.83 kg | |
| 356. |
If p and q are the roots of the equation x2 - 15x + r = 0 and p – q = 1, then what is the value of r? |
| A. | 55 |
| B. | 56 |
| C. | 60 |
| D. | 64 |
| Answer» C. 60 | |
| 357. |
Find the unit vector in the direction of vector \(\rm \vec{a}= 3\hat i -4\hat j+12\hat k\) |
| A. | \(\rm \frac{3}{13} \hat i + \frac{4}{13} \hat j + \frac{12}{13} \hat k\) |
| B. | \(\frac{1}{9} \hat i - \frac{4}{9} \hat j + \frac{8}{9} \hat k\) |
| C. | \(\rm \frac{3}{13} \hat i - \frac{4}{13} \hat j + \frac{12}{13} \hat k\) |
| D. | \(\rm \frac{3}{13} \hat i + \frac{4}{13} \hat j - \frac{12}{13} \hat k\) |
| Answer» D. \(\rm \frac{3}{13} \hat i + \frac{4}{13} \hat j - \frac{12}{13} \hat k\) | |
| 358. |
If \(x = \frac{{\sqrt 3 \; + \;1}}{2};\) then find the value of 4x3 + 2x2 – 8x + 7. |
| A. | 10 |
| B. | 4 |
| C. | 8 |
| D. | 6 |
| Answer» B. 4 | |
| 359. |
If \(\sqrt x - \frac{1}{{\sqrt x }} = \sqrt 6 ,\) then \({x^2} + \frac{1}{{{x^2}}}\) is equal to: |
| A. | 54 |
| B. | 66 |
| C. | 62 |
| D. | 40 |
| Answer» D. 40 | |
| 360. |
If (9/5) (x/2 – 10/ 3) + 4x/5 = 7x/10, then what is the value of x? |
| A. | -6 |
| B. | 1/6 |
| C. | 6 |
| D. | -1/6 |
| Answer» D. -1/6 | |
| 361. |
Let \(\left| {\vec a} \right| \ne 0,\left| {\vec b} \right| \ne 0.\)\(\left( {\vec a + \vec b} \right).\left( {\vec a + \vec b} \right) = {\left| {\vec a} \right|^2} + {\left| {\vec b} \right|^2}\)Holds if and only if |
| A. | \(\vec a\) and \(\vec b\) are perpendicular |
| B. | \(\vec a\) and \(\vec b\) are parallel |
| C. | \(\vec a\) and \(\vec b\) are inclined at an angle of 45° |
| D. | \(\vec a\) and \(\vec b\) are anti-parallel |
| Answer» B. \(\vec a\) and \(\vec b\) are parallel | |
| 362. |
If the matrix\(\left[ {\begin{array}{*{20}{c}} 1&3&{\lambda + 2}\\ 2&4&8\\ 3&5&{10} \end{array}} \right]\) is singular, then λ equals |
| A. | -2 |
| B. | 2 |
| C. | 4 |
| D. | -4 |
| Answer» D. -4 | |
| 363. |
If AB + C = D, find A and C given that when B = 6, D = 30 and when B = 8, D = 36. |
| A. | A = 2, C = 6 |
| B. | A = 3, C = 12 |
| C. | A = 6, C = 3 |
| D. | A = 4, C = 3 |
| Answer» C. A = 6, C = 3 | |
| 364. |
If x + y + z = 10 and xy + yz + zx = 15, then find the value of x3 + y3 + z3 - 3xyz. |
| A. | 550 |
| B. | 525 |
| C. | 575 |
| D. | 660 |
| Answer» B. 525 | |
| 365. |
a and b are two natural numbers such that a2 - b2 is a prime number. Then the value of a2 - b2 is |
| A. | a - b |
| B. | a + b |
| C. | ab |
| D. | None of the above |
| Answer» C. ab | |
| 366. |
Let c1 … cn be scalars, not all zero, such that \(\mathop \sum \limits_{i = 1}^n {c_i}{a_i} = 0\) where ai are column vectors in Rn. Consider the set of linear equationsAx = bwhere A = \(\left[ {{a_1} \ldots {a_n}} \right]\;and\;b = \mathop \sum \limits_{i = 1}^n {a_i}\) The set of equations has |
| A. | a unique solution at x = Jn where Jn denotes a n-dimensional vector of all 1 |
| B. | no solution |
| C. | infinitely many solutions |
| D. | finitely many solutions |
| Answer» D. finitely many solutions | |
| 367. |
In the following questions two equations numbered I and II are given. You have to solve both the equations.I) x2 - 6x + 8 = 0II) y2 – 14 y + 48 = 0 |
| A. | if x < y |
| B. | if x ≤ y |
| C. | if x > y |
| D. | if x ≥ y |
| E. | if x = y or the relationship can not be established |
| Answer» B. if x ≤ y | |
| 368. |
If the value of x satisfies the equation \(\frac{{125 \times 4 - x \times 2}}{{x + 50}} = \frac{{200}}{x}\), then the sum of all the possible values of x is? |
| A. | 150 |
| B. | 200 |
| C. | 100 |
| D. | 250 |
| Answer» B. 200 | |
| 369. |
Match the items in columns I and II.Columns IColumns II(P) Singular matrix(1) Determinant is not defined(Q) Non-square matrix(2) Determinant is always one(R) Real symmetric matrix(3) Determinant is zero(S) Orthogonal matrix(4) Eigen values are always real (5) Eigen values are not defined |
| A. | P - 3 Q - 1 R - 4 S - 2 |
| B. | P - 2 Q - 3 R - 4 S – 1 |
| C. | P - 3 Q - 2 R - 5 S – 4 |
| D. | P - 3 Q - 4 R - 2 S - 1 |
| Answer» B. P - 2 Q - 3 R - 4 S – 1 | |
| 370. |
Factorize the following:(x2 - 6xy + 9y2) - 25 |
| A. | (x - 5)(x + 5) |
| B. | (x - y - 5)(x - y + 5) |
| C. | (x + 3y + 5)(x - 3y - 5) |
| D. | (x - 3y - 5)(x - 3y + 5) |
| Answer» E. | |
| 371. |
Find the square root of \(49{x^4} - \frac{{7{x^3}}}{2} + \frac{{673{x^2}}}{{16}} - \frac{{3x}}{2} + 9\) |
| A. | \(7{x^2} - \frac{{3x}}{7} + 3\) |
| B. | \(7{x^2} - \frac{{7x}}{3} + 3\) |
| C. | \(7{x^2} - \frac{{2x}}{3} + 3\) |
| D. | \(7{x^2} - \frac{x}{4} + 3\) |
| Answer» E. | |
| 372. |
A square matrix is real and symmetric. Its eigen values will be: |
| A. | imaginary |
| B. | real |
| C. | complex |
| D. | negative |
| Answer» C. complex | |
| 373. |
If xy = - 30 and x2 + y2 = 61, then find the value of (x + y). |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | 4 |
| Answer» D. 4 | |
| 374. |
If the factor of 3x4 - (a + 2)x3 - x2 - 4 is (x - 2), then the value of a is-A. 5B. -1C. 3D. 4 |
| A. | D |
| B. | A |
| C. | C |
| D. | B |
| Answer» D. B | |
| 375. |
If the value of \({(a + b - 3)^2} + {(b + c - 2)^2} + {(c + a - 5)^2} = 0\), then the value of \(\sqrt {{{(b + c)}^a} + {{(c + a)}^b}}\) is: |
| A. | 3 |
| B. | 1 |
| C. | 0 |
| D. | 2 |
| Answer» B. 1 | |
| 376. |
If (5x + 1)3 + (x – 3)3 + 8(3x – 4)3 = 6(5x + 1) (x – 3) (3x – 4), then x is equal to∶ |
| A. | 2/3 |
| B. | 5/6 |
| C. | 1/3 |
| D. | 3/4 |
| Answer» C. 1/3 | |
| 377. |
If x3 + 2x2 – 5x + k is divisible by x + 1, then what is the value of k? |
| A. | –6 |
| B. | –1 |
| C. | 0 |
| D. | 6 |
| Answer» B. –1 | |
| 378. |
Let A be a point on the line \(\vec r = \left( {1 - 3\mu } \right)\hat i + \left( {\mu - 1} \right)\hat j + \left( {2 + 5\mu } \right)\hat k\) and B(3, 2, 6) be a point in the space. Then the value of μ for which the vector \(\overrightarrow {AB}\) is parallel to the plane x – 4y + 3z = 1 is: |
| A. | 1/4 |
| B. | 1/8 |
| C. | 1/2 |
| D. | \(- \frac{1}{4}\) |
| Answer» B. 1/8 | |
| 379. |
A number is such that 8 times the sum of its digit equals the number. If 45 is subtracted from it the digits are reversed. What is the number? |
| A. | 23 |
| B. | 27 |
| C. | 32 |
| D. | 72 |
| Answer» E. | |
| 380. |
If \(\frac{a}{b} = \frac{2}{3}\),then the value of is: (5a3 − 2a2b) : (3ab2 − b3) is : |
| A. | 16 : 27 |
| B. | 32 : 29 |
| C. | 34 : 19 |
| D. | 27 : 16 |
| Answer» B. 32 : 29 | |
| 381. |
If a3 - b3 = 216 and a - b = 6, then (a + b)2 - ab is equal to: |
| A. | 42 |
| B. | 36 |
| C. | 38 |
| D. | 52 |
| Answer» C. 38 | |
| 382. |
If a + b = 3, then the value of a3 + 9ab + b3 is |
| A. | 9 |
| B. | 18 |
| C. | 0 |
| D. | None of the above |
| Answer» E. | |
| 383. |
(1068 × 486 × 928)2 will be a number that ends in digit____. |
| A. | 8 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 384. |
Find the nature of the roots of the equation 3x2+ 5x + 3 = 0. |
| A. | real and imaginary |
| B. | imaginary |
| C. | real and unequal |
| D. | real and equal |
| Answer» C. real and unequal | |
| 385. |
If x = 17 - 4√18, then find the value of √x + 1/√x? |
| A. | 7√2 |
| B. | 9 |
| C. | 22 |
| D. | 6 |
| Answer» E. | |
| 386. |
Let α, β be the roots of ax2 + bx + c = 0; γ, δ be the roots of px2 + qx + r = 0 ;& D1 , D2 the respective discriminants of these equations. If α, β, γ, δ are in A.P. Then find the value of D1 : D2 |
| A. | \(\frac{{{a^2}}}{{{p^2}}}\) |
| B. | \(\frac{{{a^2}}}{{{b^2}}}\) |
| C. | \(\frac{{{b^2}}}{{{q^2}}}\) |
| D. | \(\frac{{{c^2}}}{{{r^2}}}\) |
| Answer» B. \(\frac{{{a^2}}}{{{b^2}}}\) | |
| 387. |
Let \(\vec a, \vec b, \vec c\) be vector such that \(|\vec a| = 2, |\vec b|= 3, |\vec c| = 5\) and \(\vec a + \vec b + \vec c = 0\). The value of \(\rm \vec a.\vec b + \vec b.\vec c + \vec c.\vec a\) is? |
| A. | 38 |
| B. | -38 |
| C. | 19 |
| D. | -19 |
| Answer» E. | |
| 388. |
If x + y + z = 2, xy + yz + zx = -11 and xyz = -12, then what is the value of \(\sqrt {{x^3} + {y^3} + {z^3} - 2}\)? |
| A. | 12 |
| B. | 6 |
| C. | 8 |
| D. | 9 |
| Answer» C. 8 | |
| 389. |
If a2 + 4b2 + 49c2 + 18 = 2 (2b + 28c – a), then the value of (3a + 2b + 7c) is: |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 390. |
If (x2/yz) + (y2/zx) + (z2/ xy) = 3, then what is the value of (x + y + z)3? |
| A. | 0 |
| B. | 4 |
| C. | 2 |
| D. | 8 |
| Answer» B. 4 | |
| 391. |
If a + b = 10 and a2 + b2 = 58, then find ab |
| A. | 21 |
| B. | 24 |
| C. | 25 |
| D. | 16 |
| Answer» B. 24 | |
| 392. |
If one root of equation 5x2 + 13x + k = 0 is reciprocal of the other root, then the value of k is - |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 5 |
| Answer» E. | |
| 393. |
Find the 13/16 worth of land whose 9/7 worth be Rs. 10116. |
| A. | Rs. 6391.75 |
| B. | Rs. 6394.75 |
| C. | Rs. 6392.75 |
| D. | Rs. 6302.75 |
| Answer» D. Rs. 6302.75 | |
| 394. |
If a2 + b2 + c2 + 96 = 8(a + b – 2c), then √(ab – bc + ca) is equal to: |
| A. | 6 |
| B. | 2√3 |
| C. | 2√2 |
| D. | 4 |
| Answer» E. | |
| 395. |
If \(8{x^6} - 6\sqrt 6 {y^6} = (2{x^2} + A{y^2})(4{x^4} + B{x^2}{y^2} + C{y^4})\), then what is the value of (A2 - B2 + C2)? |
| A. | 18 |
| B. | 30 |
| C. | 36 |
| D. | 42 |
| Answer» B. 30 | |
| 396. |
If x2 + y2 + z2 + 2 = 2 (y – x), then value of x3 + y3 + z3 is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 397. |
α and β are the roots of the quadratic equation x2 - x - 1 = 0. What is the value of α8 + β8? |
| A. | 47 |
| B. | 54 |
| C. | 59 |
| D. | 68 |
| Answer» B. 54 | |
| 398. |
If x + y + z = 3 and xy + yz + zx = -18, then what is the value of x3 + y3 + z3 – 3xyz = ? |
| A. | 217 |
| B. | 191 |
| C. | 189 |
| D. | 187 |
| Answer» D. 187 | |
| 399. |
A vessel, full of water, weighs 24 kg. When the vessel is ¼ full, it weighs 9 kg. Find the weight of the empty vessel. |
| A. | 4 Kg |
| B. | 5 Kg |
| C. | 8 Kg |
| D. | 3 Kg |
| Answer» B. 5 Kg | |
| 400. |
If a3 - b3 = 98 and ab = 15, then what is the value of a - b? |
| A. | 1 |
| B. | 4 |
| C. | 2 |
| D. | 7 |
| Answer» D. 7 | |