List of top Mathematical Ability Questions

If $\frac{2^{\frac{1}{3}} + 27a^{\frac{5}{3}}}{(\frac{a}{3})^{-\frac{1}{3}} + 3a^{\frac{2}{3}}} = 2 - ka^{\frac{1}{3}} + 9a^{\frac{2}{3}}$, then $k = $?

Two trains 100m and 150m long, moving at $30~m/s$ and $20~m/s.$, cross each other. The time taken by the trains to cross each other is:

Two trains $T_{1}$ and $T_{2}$ start at the same time from stations P and Q to reach stations Q and P. After passing each other, they take 12 hours and 3 hours to reach their destinations. If the fastest train is 48kmph, what is the speed of the other train?

A finishes a work in twice the time of B and thrice the time of C. Together they take 2 days. Individual times are?

If $3^{x-y} = 27$ and $3^{x+y} = 243$, then find (x, y).

Two products sold at 300 each: one at 20% profit, one at 20% loss. Total Profit/Loss?

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other die is:

The probability that in 10 throws of a fair die, a score which is a multiple of 3 is obtained in 8 of the throws is:

Median of the following discrete data is: \[ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,......,10,10,10,10,10,10,10,10,10,10 \]

If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

A box contains 6 red balls and 4 blue balls. If two balls are drawn at random, then the probability that they are of the same colour is:

Second central moment (Variance) for the first $n$ natural numbers is ____.

The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?

If the mean and median are 28.33 and 28 respectively, then the mode is ____.

The cumulative frequency table of marks is given. Then, the number of students scoring between 20 and 40 is: \[ \begin{array}{c|ccccc} {Marks} & \le 10 & \le 20 & \le 30 & \le 40 & \le 50 \\ \hline {Frequency} & 5 & 12 & 26 & 37 & 50 \end{array} \]

The median of the frequency distribution is: \[ \begin{array}{c|cccc} x & 1 & 2 & 3 & 4\\ \hline f & 2 & 4 & 1 & 3 \end{array} \]

The equation of a line perpendicular to $3x - 4y = 7$ and passing through $(2,5)$ is:

The value of $\displaystyle \lim_{x \to \infty} \frac{x^3 + x^2 - 5}{3x^3 + 7}$ is:

If $3A - B = \begin{bmatrix} 1 & 2 & -1\\ 0 & 1 & -2\\ -1 & 1 & 4 \end{bmatrix} $ and $A^{-1} = \begin{bmatrix} 1 & 2 & 1\\ 0 & 1 & -1\\ 0 & 0 & 1 \end{bmatrix}$, then $B = ?$

The XNOR is the combination of ____.

The value of the determinant \[ \begin{vmatrix} 50 & 15 & 3\\ 51 & 17 & 7\\ 27 & 9 & 6 \end{vmatrix} \] is:

The triangle whose vertices are $(5,7), (2,7)$ and $(5,2)$ is a _____ triangle.

If $\theta = 30^\circ$, then the value of \[ \frac{\sin^2\theta - \cos 2\theta}{\sin 2\theta + \cos^2\theta} \] is:

A rectangle has dimensions $15 \times 20$ cm$^2$. Its width is decreased by 5% while its length is increased such that its area remains unchanged. Then the percentage increase in its length is?

In an office, $\frac{1}{3}$ of the employees are women. $\frac{1}{2}$ of the women are married and $\frac{1}{3}$ of the married women have children. If $\frac{3}{4}$ of the men are married and $\frac{2}{3}$ of the married men have children, then the part of employees without children is: