List of top Mathematical Ability Questions asked in APICET

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:

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

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

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

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:

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 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 ____.

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

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

If $\theta = 30^\circ$, then the value of \[ \frac{\sin^2\theta - \cos 2\theta}{\sin 2\theta + \cos^2\theta} \] 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 equation of a line perpendicular to $3x - 4y = 7$ and passing through $(2,5)$ is:

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

If $\sin\theta = \frac{3}{5}$ and $\theta<90^\circ$, then \[ \frac{\tan\theta - 2\cos\theta}{3\sin\theta + \sec\theta} = ? \]}

Let $a$ be a real number and \[ f(x) = \begin{cases} -2\sin x, & x \le -\frac{\pi}{2} \\ 1 + a\sin x, & -\frac{\pi}{2}<x \le \frac{\pi}{2} \end{cases} \] If $f(x)$ is continuous, then the value of $a$ 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:

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle $30^\circ$ with it. The distance between the foot of the tree and the point where the top touches the ground is 8 m. Then the height of the tree is:

In a cricket match, the batsman Varun made 110 runs which includes 3 boundaries and 8 sixes. Then the percent of runs Varun scored by running between the wickets is approximately:

The last digit of the number $373^{336}$ is:

The value of $x$ in the expression \[ \left(\frac{2^{2x+1} \cdot 4^{x-2}}{8^{x-3}}\right) = 1024 \] is: