MCQOPTIONS
Saved Bookmarks
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.
| 301. |
If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other, then which of the following is correct? |
| A. | a = c |
| B. | ac = 1 |
| C. | b = c |
| D. | a = b |
| Answer» B. ac = 1 | |
| 302. |
If \(y = \sqrt 3 - \sqrt 2\), then find the value of \(\left( {\frac{1}{{{y^3}}} - {y^3}} \right)\) |
| A. | 11 |
| B. | 11√2 |
| C. | 22 |
| D. | 22√2 |
| Answer» E. | |
| 303. |
If \(P = \frac{{{x^4} - 8x}}{{{x^3} - {x^2} - 2x}},\;Q = \frac{{{x^2} + 2x + 1}}{{{x^2} - 4x - 5}}\) and \(R = \frac{{2{x^2} + 4x + 8}}{{x - 5}}\), then (P × Q) ÷ R is equal to: |
| A. | 1 |
| B. | 4 |
| C. | 1/2 |
| D. | 2 |
| Answer» D. 2 | |
| 304. |
If \(\overrightarrow a \) and \(\overrightarrow b\) are two unit vectors inclined to x - axis at angles 30° and 120°, then \(\left| {\overrightarrow a + \overrightarrow b } \right|\) equals |
| A. | \(\sqrt {\frac{2}{3}} \) |
| B. | \(\sqrt 2 \) |
| C. | √3 |
| D. | 2 |
| Answer» C. √3 | |
| 305. |
If the product of two eigen values of the matrix \(\begin{bmatrix} 6 & -2 & 2 \\\ -2 & 3 & -1 \\\ 2 & -1 & 3 \end{bmatrix}\) is 16, then third eigen value is |
| A. | 2 |
| B. | -2 |
| C. | 36 |
| D. | 6 |
| Answer» B. -2 | |
| 306. |
Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a makes with vectors b and o respectively and \(a \times \left( {b \times c} \right) = \frac{1}{2}\;b\), then |α – β| is equal to |
| A. | 30° |
| B. | 45° |
| C. | 90° |
| D. | 60 |
| Answer» B. 45° | |
| 307. |
If x2 = y + z, y2 = z + x and z2 = x + y, x, y, z ≠ 0, then the value of \(\sqrt {\frac{1}{{1\; + \;x}}\; + \;\frac{1}{{1\; + \;y}}\; + \;\frac{1}{{1\; + \;z}}}\) is |
| A. | 2 |
| B. | 0 |
| C. | -2 |
| D. | 1 |
| Answer» E. | |
| 308. |
If x and y are positive integers such that x2 – y2 = 13, then the possible value of x2 + y2 will be |
| A. | 90 |
| B. | 85 |
| C. | 72 |
| D. | 65 |
| Answer» C. 72 | |
| 309. |
One of the factors of a2 - 4a - 12 is |
| A. | a - 6 |
| B. | a + 6 |
| C. | a - 3 |
| D. | None of the above |
| Answer» B. a + 6 | |
| 310. |
A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those friends who attended the picnic is |
| A. | 8 |
| B. | 12 |
| C. | 16 |
| D. | 20 |
| Answer» B. 12 | |
| 311. |
If the roots of the equation a (b – c) x2 + b (c – a) x + c (a – b) = 0 are equal, then which one of the following is correct? |
| A. | 2b = a + c |
| B. | b2 = ac |
| C. | 2/b = 1/a + 1/c |
| D. | 1/b = 1/a + 1/c |
| Answer» D. 1/b = 1/a + 1/c | |
| 312. |
If p + q = 7, pq = 5, then the value of p3 + q3 is: |
| A. | 448 |
| B. | 64 |
| C. | 238 |
| D. | 34 |
| Answer» D. 34 | |
| 313. |
Let p and q be the roots of the quadratic equation x2 - (α - 2) x - α - 1 = 0. What is the minimum possible value of p2 + q2? |
| A. | 0 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» E. | |
| 314. |
Forces of magnitude 5, 3, 1 units acts in directions 6i + 2j + 3k, 3i -2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced the point (2, -1, -3) to (5, -1, 1). The total work done by the force is |
| A. | 21 units |
| B. | 5 units |
| C. | 33 units |
| D. | 105 units |
| Answer» D. 105 units | |
| 315. |
If (-1/2) × (x - 5) + 3 = -5/2, then what is the value of x? |
| A. | 16 |
| B. | 4 |
| C. | -6 |
| D. | -4 |
| Answer» B. 4 | |
| 316. |
Find the roots of the following equation:4x2 + 4x - 3 = 0 |
| A. | -3 / 2, 1 / 2 |
| B. | -3 / 2,-1 / 2 |
| C. | 3 / 2, 1 / 2 |
| D. | 3 / 2,-1 / 2 |
| Answer» B. -3 / 2,-1 / 2 | |
| 317. |
If three vectors 2î - ĵ + k̂, î + 2ĵ - 3k̂ and 3î + λĵ + 5k̂ are co-planar, then λ is: |
| A. | -1 |
| B. | -2 |
| C. | -3 |
| D. | -4 |
| Answer» E. | |
| 318. |
If a3 - b3 = 210 and a - b = 5, then (a2 + b2) + ab is equal to: |
| A. | 52 |
| B. | 42 |
| C. | 32 |
| D. | 38 |
| Answer» C. 32 | |
| 319. |
If (a2 - b2) ÷ (a + b) = 25, find (a - b). |
| A. | 15 |
| B. | 18 |
| C. | 25 |
| D. | 30 |
| Answer» D. 30 | |
| 320. |
If a + b = 10 and b + c = 20 and c + a = 30 then what is the value of a + b + c = ? |
| A. | 50 |
| B. | 40 |
| C. | 35 |
| D. | 30 |
| Answer» E. | |
| 321. |
If a is greater than b by 2 and b is greater than c by 10 and a + b + c = 130, then value of (b + c) - a is: |
| A. | 28 |
| B. | 32 |
| C. | 34 |
| D. | 44 |
| Answer» D. 44 | |
| 322. |
If a3 + b3 + c3 – 3abc = 0, then find the value of (a2/bc + b2/ac – 3).A. –c2/abB. –c2/bcC. –c3/baD. –c/a |
| A. | B |
| B. | D |
| C. | A |
| D. | C |
| Answer» D. C | |
| 323. |
Find the coefficient of x2 in the quadratic equation x – 2x2 + 4 |
| A. | -2 |
| B. | 1 |
| C. | -1 |
| D. | 0 |
| Answer» B. 1 | |
| 324. |
If \(\rm \vec A = 4\hat i +3\hat j+ \hat k\) and \(\rm \vec B = 2\hat i -\hat j+2 \hat k\), then the unit vector N̂ perpendicular to the vectors \(\rm \vec A\) and \(\rm \vec B\), such that \(\rm \vec A\), \(\rm \vec B\) and N̂ form a right handed system, is: |
| A. | \(\rm \frac{1}{\sqrt{185}}\left(7\hat{i}-6\hat{j}-10\hat{k}\right)\) |
| B. | \(\rm \frac{1}{7}\left(6\hat{i}+2\hat{j}+3\hat{k}\right)\) |
| C. | \(\rm \frac{1}{\sqrt{21}}\left(2\hat{i}+4\hat{j}-\hat{k}\right)\) |
| D. | \(\rm \frac{1}{\sqrt{21}}\left(-2\hat{i}-4\hat{j}+\hat{k}\right)\) |
| Answer» B. \(\rm \frac{1}{7}\left(6\hat{i}+2\hat{j}+3\hat{k}\right)\) | |
| 325. |
If \(\vec a + 2\vec b + 3\vec c = \vec 0\) and \(\vec a \times \vec b + \vec b \times \vec c + \vec c \times \vec a = \lambda \left( {\vec b \times \overrightarrow {c\;} } \right),\) then what is the value of λ? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 326. |
If x, y, z are three integers such that x + y = 8, y + z = 13 and z + x = 17, then the value of x2/yz is: |
| A. | 0 |
| B. | 18/11 |
| C. | 1 |
| D. | 7/5 |
| Answer» C. 1 | |
| 327. |
If \(x + \;\frac{1}{x} = 5\), then what is the value of \({x^5} + \frac{1}{{{x^5}}}?\) |
| A. | 1875 |
| B. | 2525 |
| C. | 2530 |
| D. | 3120 |
| Answer» C. 2530 | |
| 328. |
If \(\vec a,\; \vec b\) and \(\vec c\) are the position vectors of the vertices A, B, C of a triangle ABC, then the area of the triangle ABC is |
| A. | \(\frac 1 2 |\vec a \times \vec b + \vec b \times \vec c + \vec c \times \vec a|\) |
| B. | \(|\vec a \times \vec b|\) |
| C. | \(\frac 1 2 |\vec a \times \vec b - \vec b \times \vec c \times -\vec c \times \vec a|\) |
| D. | \(|\vec a \times (\vec b \times \vec c)|\) |
| Answer» B. \(|\vec a \times \vec b|\) | |
| 329. |
If x = 3a and y = 2b, then x2 + 4y2 – 9a2 – 16b2 + 4xy – 24ab is equal to: |
| A. | 3 |
| B. | 6 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 330. |
Find the unit place digit in the given expression: (153)144 – (115)123–(111)510 + (216)25 |
| A. | 1 |
| B. | 5 |
| C. | 6 |
| D. | 3 |
| Answer» B. 5 | |
| 331. |
If A and B are the roots of the equation Ax2 - A2x + AB = 0, then what is the value of A and B respectively? |
| A. | 1, 0 |
| B. | 1, 1 |
| C. | 0, 2 |
| D. | 0, 1 |
| Answer» B. 1, 1 | |
| 332. |
If a and b are integers of opposite signs such that (a + 3)2 : b2 = 9 : 1 and (a - 1)2 : (b - 1)2 = 4 : 1, then the ratio a : b is? |
| A. | 9 : 4 |
| B. | 81 : 4 |
| C. | 1 : 4 |
| D. | 25 : 4 |
| Answer» E. | |
| 333. |
If \(x + y = \sqrt{3}\) and \(x-y=\sqrt{2}\), then the value of \(8xy(x^2 + y^2)\) is |
| A. | 6 |
| B. | \(\sqrt{6}\) |
| C. | 5 |
| D. | \(\sqrt{5}\) |
| Answer» D. \(\sqrt{5}\) | |
| 334. |
If b + c = ax, c + a = by, a + b = cz, then the value of \(\frac{1}{9}\left[ {\frac{1}{{x\; + \;1}} + \frac{1}{{y + 1}}\; + \;\frac{1}{{z\; + \;1}}} \right]\) is: |
| A. | 1 |
| B. | 1/3 |
| C. | 0 |
| D. | 1/9 |
| Answer» E. | |
| 335. |
If (2x + 3)3 + (x - 8)3 + (x + 13)3 = (2x + 3) (3x - 24) (x + 13), then what is the value of x? |
| A. | -2 |
| B. | -2.5 |
| C. | 1 |
| D. | -1.3 |
| Answer» B. -2.5 | |
| 336. |
Let A and B two n × n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.I. rank(AB) = rank(A) rank(B)II. det(AB) = det(A) det(B)III. rank(A + B) ≤ rank(A) + rank(B)IV. det(A + B) ≤ det(A) + det(B)Which of the above statements are TRUE? |
| A. | I and II only |
| B. | I and IV only |
| C. | II and III only |
| D. | III and IV only |
| Answer» D. III and IV only | |
| 337. |
Find the value of \(27{a^3} + \frac{1}{{{a^3}}}\), if \(9{a^2} + \frac{1}{{{a^2}}} = 43\) |
| A. | 240 |
| B. | 280 |
| C. | 320 |
| D. | 360 |
| Answer» C. 320 | |
| 338. |
If a = 355, b = 356, c = 357, then find the value of a3 + b3 + c3 - 3abc. |
| A. | 3206 |
| B. | 3202 |
| C. | 3204 |
| D. | 3208 |
| Answer» D. 3208 | |
| 339. |
Find the missing value.x2 + 7x + 12 = _____(x + 4) |
| A. | x - 4 |
| B. | x - 3 |
| C. | x + 3 |
| D. | x + 4 |
| Answer» D. x + 4 | |
| 340. |
If α and β are the roots of the equation x2 - x + 3 = 0, then what is the value of α4 + β4? |
| A. | 7 |
| B. | 9 |
| C. | 11 |
| D. | 13 |
| Answer» B. 9 | |
| 341. |
If sum of the roots of a quadratic equations is 1 and product of the roots is – 20. Find the quadratic equation. |
| A. | X2 – X – 20 = 0 |
| B. | X + X + 20 = 0 |
| C. | X2 + X – 20 = 0 |
| D. | X2 – X + 20 = 0 |
| Answer» B. X + X + 20 = 0 | |
| 342. |
If x2 - 7x + 1 = 0, then what is the value of \(x + \frac{1}{x}?\) |
| A. | 7 |
| B. | 3 |
| C. | 51 |
| D. | 47 |
| Answer» B. 3 | |
| 343. |
Multiply :\((5x^2-8xy+6y^2-3) by (3xy)\) |
| A. | \(15x^3y-24x^2y+18yx^3-9xy\) |
| B. | \(15x^2y-24x^2y^2-18xy^2-9xy\) |
| C. | \(15x^3y-24x^2y^2+18xy^3-9xy\) |
| D. | \(15x^2y+24x^2y^2+18x^2y-9xy\) |
| Answer» D. \(15x^2y+24x^2y^2+18x^2y-9xy\) | |
| 344. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 - 7x + 10 = 0II. y2 + 8y + 15 = 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» B. x < y | |
| 345. |
In the expansion of (2x + y )3 - (2x - y)3, the coefficient of x2y is: |
| A. | 24 |
| B. | 18 |
| C. | 12 |
| D. | 16 |
| Answer» B. 18 | |
| 346. |
If a + 1/b = b + 1/c = c + 1/a (where a ≠ b ≠ c), then abc is equal to |
| A. | + 1 |
| B. | – 1 |
| C. | + 1 & – 1 |
| D. | None of the options |
| Answer» D. None of the options | |
| 347. |
If \(A = \frac{1 + 2x}{1 - 2x} \) and \(B = \frac{1-2x}{1+2x}\), then the value of \(\frac{A+B}{A-B}\) is: |
| A. | \(x + \frac{1}{4x}\) |
| B. | \(x - \frac{1}{4x}\) |
| C. | \(\frac{1}{4x} - x\) |
| D. | \(x^2 + \frac{1}{4x^2}\) |
| Answer» B. \(x - \frac{1}{4x}\) | |
| 348. |
If \(x + \frac{1}{{16x}} = 3\), then the value of \(16{x^3} + \frac{1}{{256{x^3}}}\) is∶ |
| A. | 432 |
| B. | 441 |
| C. | 414 |
| D. | 423 |
| Answer» E. | |
| 349. |
If a square matrix A is real and symmetric, then the eigen values |
| A. | are always real |
| B. | are always real and positive |
| C. | are always real and non-negative |
| D. | occur in complex conjugate pairs |
| Answer» B. are always real and positive | |
| 350. |
Given that (a2 + b2) = 60, then find the value of (a + b)2 + (a – b)2.A. 90B. 120C. 140D. 150 |
| A. | C |
| B. | A |
| C. | D |
| D. | B |
| Answer» E. | |