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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.
| 201. |
Find the value of x:\(\frac{2}{5}\left( x \right) + \frac{3}{{10}}\left( x \right) - \frac{3}{5}\left( x \right) = 521\) |
| A. | 5310 |
| B. | 5110 |
| C. | 5210 |
| D. | 5410 |
| Answer» D. 5410 | |
| 202. |
If \(\sqrt{x}+\frac{1}{\sqrt{x}}=\sqrt{7},\) then \({{x}^{3}}+\frac{1}{{{x}^{3}}}\) is equal to∶ |
| A. | 120 |
| B. | 130 |
| C. | 140 |
| D. | 110 |
| Answer» E. | |
| 203. |
If α and β are the roots of the quadratic equation (5 + √2) x2 - (4 + √5) x + (8 + 2√5) = 0, then the value of 2αβ/ (α + β) is: |
| A. | 7 |
| B. | 4 |
| C. | 2 |
| D. | 8 |
| Answer» C. 2 | |
| 204. |
If 2x + 3y = 14 and xy = 8, then the value of 8x3 + 27y3 is: |
| A. | 872 |
| B. | 768 |
| C. | 782 |
| D. | 728 |
| Answer» E. | |
| 205. |
One of the eigenvectors of the matrix \(\left[ {\begin{array}{*{20}{c}} { - 5}&2\\ { - 9}&6 \end{array}} \right]\) is |
| A. | \(\left\{ {\begin{array}{*{20}{c}} { - 1}\\ 1 \end{array}} \right\}\) |
| B. | \(\left\{ {\begin{array}{*{20}{c}} { - 2}\\ 9 \end{array}} \right\}\) |
| C. | \(\left\{ {\begin{array}{*{20}{c}} 2\\ { - 1} \end{array}} \right\}\) |
| D. | \(\left\{ {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right\}\) |
| Answer» E. | |
| 206. |
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. | 3 |
| B. | 2 |
| C. | -2 |
| D. | -3 |
| Answer» E. | |
| 207. |
If the price of 3 pens, 2 pencils and 4 erasers is Rs. 92 and the price of 8 pencils and 16 erasers is Rs. 68, then the price of 24 pens is |
| A. | Rs. 625 |
| B. | Rs. 500 |
| C. | Rs. 675 |
| D. | Rs. 600 |
| Answer» E. | |
| 208. |
If \((a^2 + b^2)^3 = (a^3 + b^3)^2\), then the value of \(\frac{a}{b} + \frac{b}{a}\) is |
| A. | 1 |
| B. | \(\frac{2}{3}\) |
| C. | \(\frac{3}{2}\) |
| D. | 6 |
| Answer» C. \(\frac{3}{2}\) | |
| 209. |
Express the given statement as an algebraic equation:Rahman adds 52 to a number ‘p’ and then multiplies the sum by 8. This gives the product as 628. |
| A. | (52 + p) = 628 × 8 |
| B. | 52 + 8p = 628 |
| C. | (p × 52) + 8 = 628 |
| D. | 8(p + 52) = 628 |
| Answer» E. | |
| 210. |
One of the factors of x3 - 3x2 + 3x - 2 is: |
| A. | x2 + x + 1 |
| B. | x2 - x + 1 |
| C. | x2 - x - 1 |
| D. | x2 + x - 1 |
| Answer» C. x2 - x - 1 | |
| 211. |
If x, y, z are three numbers such that x + y = 13, y + z = 15 and z + x = 16, then the value of \(\frac{{xy + xz}}{{xyz}}\) is: |
| A. | 36/5 |
| B. | 5/18 |
| C. | 18/5 |
| D. | 5/36 |
| Answer» C. 18/5 | |
| 212. |
One of the Eigen vectors of the matrix \(\left[ {\begin{array}{*{20}{c}} { - 5}&2\\ { - 9}&6 \end{array}} \right]\) |
| A. | \(\left[ {\begin{array}{*{20}{c}} { - 1}\\ 1 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} { - 2}\\ 9 \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} { 2}\\ -1 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} { 1}\\ 1 \end{array}} \right]\) |
| Answer» E. | |
| 213. |
Consider the following 2 × 2 matrix A where two elements are unknown and are marked by a and b. The eigenvalues of this matrix are -1 and 7. What are the values of a and b?\(A\; = \;\left( {\begin{array}{*{20}{c}} 1&4\\ b&a \end{array}} \right)\) |
| A. | a = 6, b = 4 |
| B. | a = 4, b = 6 |
| C. | a = 3, b = 5 |
| D. | a = 5, b = 3 |
| Answer» E. | |
| 214. |
If x2 + y2 + 2x + 1 = 0, then the value of x31 + y35 is |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» B. 0 | |
| 215. |
For the matrix \(X = \left[ {\begin{array}{*{20}{c}} 1&{ - 1}&1\\ 0&{ - 1}&1\\ 0&0&2 \end{array}} \right]\) the eigenvector corresponding to the eigenvalue -1 is |
| A. | (2, 1, 1) |
| B. | (1, -1, 1) |
| C. | (0, 0, 0) |
| D. | (1, 2, 0) |
| Answer» E. | |
| 216. |
If \(a^3 + b^3 = 20\) and a + b = 5, then find the value of a4 + b4 |
| A. | 26 |
| B. | 23 |
| C. | 25 |
| D. | 24 |
| Answer» C. 25 | |
| 217. |
7 pens and 5 pencils cost Rs. 16.90. Had been a purchase of 5 pens and 7 pencils, the expense would have been Rs. 2.60 less. If so, a pen costs∶ |
| A. | Rs. 1.65 |
| B. | Rs. 2.25 |
| C. | Rs. 1.95 |
| D. | Rs. 2.15 |
| Answer» D. Rs. 2.15 | |
| 218. |
For what values of 'k' does the equation kx(x – 2) + 6 = 0 have equal roots? |
| A. | 6 |
| B. | -2 |
| C. | 3, 2 |
| D. | 0, 6 |
| Answer» B. -2 | |
| 219. |
Let a two digit number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is |
| A. | 9 - k |
| B. | 10 - k |
| C. | 11 - k |
| D. | k - 1 |
| Answer» D. k - 1 | |
| 220. |
If (x2 + 1/16x2) = 19/2, then find the value of (2x – 1/2x).A. 6B. 12C. 32D. 41 |
| A. | B |
| B. | A |
| C. | C |
| D. | D |
| Answer» C. C | |
| 221. |
If a and b are two real numbers such that b > a, ab < 0, the sum of their squares is 458 and the difference between their squares is 120, then find the value of a - b. |
| A. | 30 |
| B. | -30 |
| C. | -4 |
| D. | 4 |
| Answer» C. -4 | |
| 222. |
If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = -7/12, then what is the value of a + c? |
| A. | 1/2 |
| B. | 5/12 |
| C. | 3/4 |
| D. | 1/4 |
| Answer» C. 3/4 | |
| 223. |
If x2 + 3x + 1 = 0, then what is the value of \({x^6}\; + \;\frac{1}{{{x^6}}}?\) |
| A. | 318 |
| B. | 322 |
| C. | 327 |
| D. | 324 |
| Answer» C. 327 | |
| 224. |
If a + b + c = 10 and ab + bc + ca = 32 then a3 + b3 + c3 – 3abc is equal to: |
| A. | 50 |
| B. | 60 |
| C. | 40 |
| D. | 70 |
| Answer» D. 70 | |
| 225. |
If \({{\rm{x}}^2} + \frac{1}{{{{\rm{x}}^2}}} = 2\), then what is the value of x6? |
| A. | 6 |
| B. | 0 |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 226. |
Eigen values of a 4 × 4 matrix [A] are given as 2, -3, 13 and 7. Then, what is the value of |det[A]| ? |
| A. | 25 |
| B. | 19 |
| C. | -546 |
| D. | 546 |
| Answer» E. | |
| 227. |
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 – 11x + 24 = 0II. y2 + 4y – 12 = 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» B. If x ≥ y | |
| 228. |
If x + 1/x = 5, then find the value of x2 + 1/x2 . |
| A. | 24 |
| B. | 23 |
| C. | 20 |
| D. | 19 |
| Answer» C. 20 | |
| 229. |
If \(\frac{1}{{x\; + \;2}} = \frac{3}{{y\; + \;3}} = \frac{{1331}}{{z\; + \;1331}} = \frac{1}{3}\), then what is the value of \(\frac{x}{{x\; + \;1}} + \frac{4}{{y\; + \;2}} + \frac{z}{{z\; + \;2662}}\) |
| A. | 0 |
| B. | 1 |
| C. | 3/2 |
| D. | 3 |
| Answer» D. 3 | |
| 230. |
If x – y = 4 and xy = 21, then the value of x2 + y2 is: |
| A. | 48 |
| B. | 58 |
| C. | 16 |
| D. | 26 |
| Answer» C. 16 | |
| 231. |
If 5√5 x3 + 2√2 y3 = (Ax + √2y)(Bx2 + 2y2 + Cxy), then what is the value of (A2 + B2 – C2)? |
| A. | 40 |
| B. | 15 |
| C. | 30 |
| D. | 20 |
| Answer» E. | |
| 232. |
(a - b)2 + 2ab = ? |
| A. | a2 - b2 |
| B. | a2 + b2 |
| C. | a2 - 4ab + b2 |
| D. | a2 - 2ab + b2 |
| Answer» C. a2 - 4ab + b2 | |
| 233. |
Find the value of x3 - y3, if x - y = 4 and xy = 12 |
| A. | 198 |
| B. | 208 |
| C. | 218 |
| D. | 228 |
| Answer» C. 218 | |
| 234. |
If x + (1/x) = 2, then what is the value of x64 + x121? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | –2 |
| Answer» D. –2 | |
| 235. |
If x2 - 3x + 2 is a factor of , x4 - px2 + q, then (p, q) = |
| A. | (5,2) |
| B. | (5,4) |
| C. | (-5,-4) |
| D. | (-5,4) |
| Answer» C. (-5,-4) | |
| 236. |
Consider the following assertions:I. Rank (ST) = Rank S = Rank TII. Rank (ST) = Rank S, if T is non-singularIII. Rank (ST) = Rank T, if T is non-singularWhere S, T : V → V are linear transformations of a finite dimensional vector space V. Which of these is/are correct? |
| A. | Only II |
| B. | Only I |
| C. | II and III |
| D. | I and II |
| Answer» B. Only I | |
| 237. |
If a + b + c = 11 and ab + bc + ca = 38, then a3 + b3 + c3 – 3abc is equal to∶ |
| A. | 44 |
| B. | 66 |
| C. | 55 |
| D. | 77 |
| Answer» E. | |
| 238. |
Find the value of \(\frac{(0.03)^2-(0.01)^2}{0.03-0.01}\) |
| A. | 0.4 |
| B. | 0.02 |
| C. | 0.04 |
| D. | 0.004 |
| Answer» D. 0.004 | |
| 239. |
If 65x - 33y = 97 and 33x - 65y = 1, then what is xy equal to? |
| A. | 2 |
| B. | 3 |
| C. | -2 |
| D. | -3 |
| Answer» B. 3 | |
| 240. |
If 5 is the zero of the polynomial f(x) = ax2 - (2a + 1)x - 5 then value of a is |
| A. | 2/3 |
| B. | - 4/5 |
| C. | 0 |
| D. | - 35 |
| Answer» B. - 4/5 | |
| 241. |
If x1.x2.x3 = 4(4 + x1 + x2 + x3), then what is the value of [1/(2 + x1)] + [1/(2 + x2)] + [1/(2 + x3)]? |
| A. | 1 |
| B. | 1/2 |
| C. | 2 |
| D. | 1/3 |
| Answer» C. 2 | |
| 242. |
If 9x/2 - (1/3)(5x/2 + 7) = -1/3, then what is the value of x? |
| A. | 6/11 |
| B. | -6/11 |
| C. | 11/6 |
| D. | -11/6 |
| Answer» B. -6/11 | |
| 243. |
If â, b̂ and ĉ are unit vectors and |â + b̂|2 = |b̂ + ĉ|2 = |ĉ + â|2 = 8, then |2â + b̂ + ĉ| is equal to |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | none of the above |
| Answer» D. none of the above | |
| 244. |
If \({\left( {{x^3} + \frac{1}{{{x^3}}} - k} \right)^2} + {\left( {x + \frac{1}{x} - p} \right)^2} = 0,\) where k and p are real numbers and x ≠ 0, then k/p is equal to: |
| A. | p2 + 1 |
| B. | p2 + 3 |
| C. | p2 - 1 |
| D. | p2 - 3 |
| Answer» E. | |
| 245. |
If (x - 6)3 + (x - 4)3 + (x - 5)3 = (3x - 15) (x - 4) (x - 6), then what is the value of x? |
| A. | 3 |
| B. | 7 |
| C. | 18 |
| D. | 5 |
| Answer» E. | |
| 246. |
If x2 + kx + k = 0 has two distinct real solutions, then the value of k will satisfy: |
| A. | k < 0 or k > 4 |
| B. | 0 < k < 4 |
| C. | k < 0 only |
| D. | k > 4 only |
| Answer» B. 0 < k < 4 | |
| 247. |
If 3x - [1/(3x)] = 9, then what is the value of x2 + [1/(81x2)]? |
| A. | 7 |
| B. | 83/9 |
| C. | 11 |
| D. | 121/9 |
| Answer» C. 11 | |
| 248. |
If a2 + b2 + c2 = 300 and ab + bc + ca = 50 then what is the value of a + b + c ? (Given that a, b and c are all positive) |
| A. | 15 |
| B. | 22 |
| C. | 20 |
| D. | 25 |
| Answer» D. 25 | |
| 249. |
If (a + b)2 – 2(a + b) = 80 and ab = 16, then what can be the value of 3a – 19b? |
| A. | -16 |
| B. | -14 |
| C. | -18 |
| D. | -20 |
| Answer» C. -18 | |
| 250. |
If vector space V have dimension dim V = n and let B and B’ are two basis of V then: |
| A. | B and B’ have less than n elements |
| B. | B and B’ have same number of elements n |
| C. | B and B’ will have distinct number of elements |
| D. | B and B’ have more than n elements |
| Answer» C. B and B’ will have distinct number of elements | |