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.
| 1101. |
If a4 + 1 = [a2/b2](4b2 - b4 - 1) and b =1, then what is the value of a4 + b4? |
| A. | 2 |
| B. | 16 |
| C. | 32 |
| D. | 64 |
| Answer» B. 16 | |
| 1102. |
One-sixth of the trees in a garden are neem trees. Half of the trees are Ashoka trees and the remaining are eucalyptus trees. If the number of neem trees is five, then how many eucalyptus trees are there in the garden? |
| A. | 5 |
| B. | 10 |
| C. | 15 |
| D. | 20 |
| Answer» C. 15 | |
| 1103. |
A and B together have Rs. 1,500. If 1/4th of A’s amount is equal to 2/4th of B’s, then how much amount A has? |
| A. | Rs. 2,000 |
| B. | Rs. 5,000 |
| C. | Rs. 1,500 |
| D. | Rs. 1,000 |
| Answer» E. | |
| 1104. |
If \(\frac{{256}}{{0.256}} = \frac{{25.6}}{x}\) then what will be the value of x? |
| A. | 2.56 |
| B. | 25.6 |
| C. | 0.256 |
| D. | 0.0256 |
| Answer» E. | |
| 1105. |
If \(\sqrt 8x^6 + 3\sqrt 3y^6 = (Ax^2 + By^2) (Cx^4 + Dx^2y^2 + 3y^4)\), then the value of \(\frac{(C - D)}{A + B}\) is |
| A. | 2√2 |
| B. | √2 |
| C. | √3 |
| D. | 3√3 |
| Answer» C. √3 | |
| 1106. |
If x + y + z = 1, xy + yz + zx = -1 and xyz = -1 then the value of \(\sqrt[3]{{{x^3} + {y^3} + {z^3}}}\) is: |
| A. | – 1 |
| B. | – 2 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 1107. |
In a square matrix A = [aij], if aij = -aji for all i and j so that all the leading diagonal elements are zero, then the matrix is called |
| A. | Skew symmetric matrix |
| B. | Triangular matrix |
| C. | Symmetric matrix |
| D. | Null matrix |
| Answer» B. Triangular matrix | |
| 1108. |
Natu and Buchku each have a certain number of oranges. Natu says to Buchku,"If you give me 10 of your oranges, I will have twice the number of oranges left with you". Buchku replies,"If you give me 10 of your oranges, I will have the same number of oranges as left with you". What is the number of oranges with Natu and Buchku, respectively? |
| A. | 50, 20 |
| B. | 70, 50 |
| C. | 20, 50 |
| D. | 50, 70 |
| Answer» C. 20, 50 | |
| 1109. |
If 3x2 + kx + k = 0 has no solution, then the value of k will satisfy: |
| A. | 0 < k < 12 |
| B. | k > 12 |
| C. | k < 12 |
| D. | k > - 12 |
| Answer» B. k > 12 | |
| 1110. |
A jeweller makes a gold pendant. He uses 50 g of copper for making the piece. If the price for 1 kg of copper is Rs. 420, what is the cost of copper used in the jewellery? |
| A. | Rs. 20 |
| B. | Rs. 19 |
| C. | Rs. 21 |
| D. | Rs. 22 |
| Answer» D. Rs. 22 | |
| 1111. |
If 5x - (1/2) × (2x - 7) = 5.5, then what is the value of x? |
| A. | 3/2 |
| B. | 1/2 |
| C. | -1/2 |
| D. | -3/2 |
| Answer» C. -1/2 | |
| 1112. |
Determine k so that the equation x2 - 4x + k = 0, has two distinct real roots |
| A. | k = 4 |
| B. | k > 4 |
| C. | k < 4 |
| D. | k = 10 |
| Answer» D. k = 10 | |
| 1113. |
Given below are two quantities named A and B. 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.Quantity A: A group of 40 persons having boys and girls is further divided into two different groups, group A and group B. The number of boys in both groups is equal. The number of girls in group A is 8 and the total number of people in group B is 2 more than that of group A. Find the number of girls in group B.Quantity B: 16 |
| A. | Quantity A > Quantity B |
| B. | Quantity A < Quantity B |
| C. | Quantity A ≤ Quantity B |
| D. | Quantity A ≥ Quantity B |
| E. | Quantity A = Quantity B or no relation can be established |
| Answer» C. Quantity A ≤ Quantity B | |
| 1114. |
If a + b + c = 9 and ab + bc + ca = - 22, then the value of a3 + b3 + c3 - 3abc is: |
| A. | 783 |
| B. | 487 |
| C. | 1323 |
| D. | 1571 |
| Answer» D. 1571 | |
| 1115. |
If 2x - 3(x + 2) < 5 - 2x < - x + 2, then find the value of x. |
| A. | 2 |
| B. | 0 |
| C. | 10 |
| D. | 12 |
| Answer» D. 12 | |
| 1116. |
If a3 - b3 = 56 and ab = 8, then what is the value of a - b? |
| A. | 7 |
| B. | 6 |
| C. | 1 |
| D. | 2 |
| Answer» E. | |
| 1117. |
Out of the given options, for which value of k, 345k6 is divisible by 4 |
| A. | 6 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 1118. |
If x = (2√15)/(√3 + √5), then what is the value of (x + √5)/(x – √5) + (x + √3)/(x – √3) ? |
| A. | √5 |
| B. | √3 |
| C. | √15 |
| D. | 2 |
| Answer» E. | |
| 1119. |
If \(\frac{y}{{x}}=\frac{1}{{3}}\)then find the value of \(\frac{x^2+y^2}{{x^2-y^2}}\) |
| A. | 5/3 |
| B. | 2/5 |
| C. | 4/5 |
| D. | 5/4 |
| Answer» E. | |
| 1120. |
If x2 – 3x + 1 = 0, then the value of \((x^4 + \frac{1}{x^2}) \div (x^2+1)\) is: |
| A. | 9 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» D. 7 | |
| 1121. |
If x - 1/x = 3, then what is the value of x3 – 1/x3? |
| A. | 36 |
| B. | 21 |
| C. | 9 |
| D. | 27 |
| Answer» B. 21 | |
| 1122. |
If x2 + 1/x2 = 7/4 for x > 0 then what is the value of x4 + 1/x4? |
| A. | 1 |
| B. | 17/16 |
| C. | 15/16 |
| D. | 51/16 |
| Answer» C. 15/16 | |
| 1123. |
A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 1124. |
If 22x2 - ax + 2 = ax2 + 18x - 7 has only one (repeated) solution, then the positive integral solution of a is |
| A. | 3 |
| B. | 6 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 1125. |
If (x - 7)3 + (x - 8)3 + (x + 6)3 = 3 (x - 7)(x - 8) (x + 6), then what is the value of x? |
| A. | 6 |
| B. | 8 |
| C. | 10 |
| D. | 3 |
| Answer» E. | |
| 1126. |
If x2 - 4x + 4b = 0 has two real solutions, find the value of 'b'. |
| A. | b = 0 |
| B. | b ≤ 1 |
| C. | b = +1, -1 |
| D. | b ≥ 1 |
| Answer» C. b = +1, -1 | |
| 1127. |
If â is a unit vector in the xy-plane making an angle 30° with the positive x-axis, then what is â equal to? |
| A. | \(\rm \dfrac{\sqrt{3}\hat{i}+\hat{j}}{2}\) |
| B. | \(\rm \dfrac{\sqrt{3}\hat{i}-\hat{j}}{2}\) |
| C. | \(\rm \dfrac{\hat{i}+\sqrt{3}\hat{j}}{2}\) |
| D. | \(\rm \dfrac{\hat{i}-\sqrt{3}\hat{j}}{2}\) |
| Answer» B. \(\rm \dfrac{\sqrt{3}\hat{i}-\hat{j}}{2}\) | |
| 1128. |
A toy weighing 24 grams of an alloy of two metals is worth Rs 174/-, but if the weights of the two metals be interchanged, the toy would be worth Rs 162/-. If the price of one metal be Rs. 8 per gram, find the price of the other metal used to make the toy. |
| A. | Rs. 10/ gram |
| B. | Rs. 6/ gram |
| C. | Rs. 4/ gram |
| D. | Rs. 5/ gram |
| Answer» C. Rs. 4/ gram | |
| 1129. |
Factors of (1 - 3x2 + 3x4 - x6 ) are - |
| A. | (1 - x)2 (1 + x)4 |
| B. | (1 - x)3 (1 + x)3 |
| C. | (1 - x)4 (1 + x)2 |
| D. | (x - 1)3 (x + 1)3 |
| Answer» C. (1 - x)4 (1 + x)2 | |
| 1130. |
If \(x = \frac{{\sqrt 5 - \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}\) and y is reciprocal of x, then what is the value of \(\sqrt {\left( {{x^3} + {y^3}} \right)} ?\) |
| A. | 3√122 |
| B. | 5√122 |
| C. | √122 |
| D. | 2√122 |
| Answer» E. | |
| 1131. |
If \(\sqrt {10 - 2\sqrt {21} } + \sqrt {8 + 2\sqrt {15} } = \sqrt a + \sqrt b ,\) where a and b are positive integers, then the value of √(ab) is closet to: |
| A. | 4.6 |
| B. | 5.9 |
| C. | 6.8 |
| D. | 7.2 |
| Answer» C. 6.8 | |
| 1132. |
Consider the following system of linear equations,x1 + 2x2 = b1 2x1 + 4x2 = b2 3x1 + 7x2 = b3 3x1 + 9x2 = b4 Which one of the following conditions ensures that a solution exists for the above system? |
| A. | b2 = 2b1 and 6b1 – 3b3 + b4 = 0 |
| B. | b3 = 2b1 and 6b1 – 3b3 + b4 = 0 |
| C. | b2 = 2b1 and 3b1 – 6b3 + b4 = 0 |
| D. | b3 = 2b1 and 3b1 – 6b3 + b4 = 0 |
| Answer» B. b3 = 2b1 and 6b1 – 3b3 + b4 = 0 | |
| 1133. |
If a, b, c are three non-coplanar vectors, such that \(\left[ {\vec b \times \overrightarrow {c,} \vec c \times \overrightarrow {a,} \vec a \times \vec b} \right] = 2\left[ {\vec a,\vec b,\vec c} \right],\)then the value of \([\vec{a}, \vec{b}, \vec{c}]\)is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 1134. |
If (2x – 5)3 + (x + 2)3 + (3x – 9)3 = (2x – 5) (3x – 9) (3x + 6), then what is the value of x? |
| A. | 7 |
| B. | 2 |
| C. | 18 |
| D. | 5 |
| Answer» C. 18 | |
| 1135. |
Find the value of \(\frac{{{{\left( {0.22} \right)}^3} - {{\left( {0.11} \right)}^3}}}{{0.0484\; + \;0.0242\; + \;0.0121\;}}\) |
| A. | 9 |
| B. | 1.2 |
| C. | 2 |
| D. | 0.11 |
| Answer» E. | |
| 1136. |
If \(3\sqrt 3 {x^3} - 2\sqrt 2 {y^3} = \left( {\sqrt 3 x - \sqrt 2 y} \right)\left( {A{x^2} - Bxy + C{y^2}} \right)\), then the value of (A2 + B2 + C2) is: |
| A. | 17 |
| B. | 10 |
| C. | 1 |
| D. | 19 |
| Answer» E. | |
| 1137. |
If a3 + b3 = 28 and ab = 3, then what is the value of a + b? |
| A. | 2 |
| B. | 4 |
| C. | 9 |
| D. | 3 |
| Answer» C. 9 | |
| 1138. |
In a school, half of the students play badminton, one-fourth (1/4th) play volleyball, one-eighth (1/8th) play tennis, one-sixteenth (1/16th) play chess and the remaining go for swimming. If the number of students playing volleyball is 160, how many students play chess? |
| A. | 120 |
| B. | 80 |
| C. | 20 |
| D. | 40 |
| Answer» E. | |
| 1139. |
If x + y = 5, x3 + y3 = 35, then what is the positive difference between x and y? |
| A. | 0 |
| B. | 1 |
| C. | 5 |
| D. | 6 |
| Answer» C. 5 | |
| 1140. |
In quadratic equation cx2 + bx + c = 0 find the ratio b : c if the given equation has equal roots. |
| A. | 2 : 1 |
| B. | 4 : 1 |
| C. | 1 : 4 |
| D. | 1 : 2 |
| Answer» C. 1 : 4 | |
| 1141. |
Consider the following statements:1. The cross product of two unit vectors is always a unit vector.2. The dot product of two unit vectors is always unity.3. The magnitude of sum of two unit vectors is always greater than the magnitude of their difference.Which of the above statements are not correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 1142. |
A tetrahedron has vertices P (1, 2, 1), Q (2, 1, 3), R (-1, 1, 2) and O (0, 0, 0). The angle between the faces OPQ and PQR is |
| A. | \(co{s^{ - 1}}{\rm{}}\left( {\frac{7}{{31}}} \right)\) |
| B. | \(co{s^{ - 1}}{\rm{}}\left( {\frac{9}{{35}}} \right)\) |
| C. | \(co{s^{ - 1}}{\rm{}}\left( {\frac{19}{{35}}} \right)\) |
| D. | \(co{s^{ - 1}}{\rm{}}\left( {\frac{17}{{31}}} \right)\) |
| Answer» D. \(co{s^{ - 1}}{\rm{}}\left( {\frac{17}{{31}}} \right)\) | |
| 1143. |
Directions: In this question two equations numbered I and II are given. You have to solve both the equations and find out the correct option.I. x2 – x – 42 = 0II. y2 + y – 30 = 0 |
| A. | x > y |
| B. | x < y |
| C. | x ≥ y |
| D. | x ≤ y |
| E. | x = y or no relationship could be established |
| Answer» F. | |
| 1144. |
If 11a + 11b = 29282 find the value of (a + b)/4 |
| A. | 661.5 |
| B. | 663.5 |
| C. | 665.5 |
| D. | 667.5 |
| Answer» D. 667.5 | |
| 1145. |
If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2? |
| A. | -4 |
| B. | 2 |
| C. | -1 |
| D. | -6 |
| Answer» B. 2 | |
| 1146. |
Directions: In this question two equations numbered I and II are given. You have to solve both the equations and find out the correct option.I. x2 – 208 = 233II. y2 + 47 – 371 = 0 |
| A. | If x ≥ y |
| B. | If x ≤ y |
| C. | If x > y |
| D. | If x < y |
| E. | If relationship between x and y cannot be established or x = y. |
| Answer» F. | |
| 1147. |
If x2 + (1/x2) = 1 then what is the value of x48 + x42 + x36 + x30 + x24 + x18 + x12 + x6 + 1 ? |
| A. | -9 |
| B. | 0 |
| C. | 1 |
| D. | 9 |
| Answer» D. 9 | |
| 1148. |
If x2 - 3x + 1 = 0, then the value of \({x^{10}} + \frac{1}{{{x^{10}}}}\) is: |
| A. | 14408 |
| B. | 14638 |
| C. | 14642 |
| D. | 15127 |
| Answer» E. | |
| 1149. |
If the vectors \(a\hat i + \hat j + \hat k,\;\hat i + b\hat j + \hat k\) and \(\hat i + \hat j + c\hat k\;\left( {a,\;b,\;c \ne 1} \right)\) are coplanar, then the value of \(\frac{1}{{1 - a}} + \frac{1}{{1 - b}} + \frac{1}{{1 - c}}\) is equal to |
| A. | 1 |
| B. | 2 |
| C. | a + b + c |
| D. | abc |
| Answer» B. 2 | |
| 1150. |
Consider a matrix P whose only eigenvectors are the multiples of \(\left[ {\begin{array}{*{20}{c}}1\\4\end{array}} \right]\).Consider the following statements. (I) P does not have an inverse(II) P has a repeated eigenvalue(III) P cannot be diagonalizedWhich one of the following options is correct? |
| A. | Only I and III are necessarily true |
| B. | Only II is necessarily true |
| C. | Only I and II are necessarily true |
| D. | Only II and III are necessarily true |
| Answer» E. | |