List of top Mathematical Ability Questions on Algebra asked in APICET

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:

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:

The number of distinct prime factors in the product $(30)^7 \times (22)^5 \times (34)^{10}$ is:

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

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

If $\dfrac{\sqrt{13-\sqrt{11}}}{\sqrt{13+\sqrt{11}}} - \dfrac{\sqrt{13+\sqrt{11}}}{\sqrt{13-\sqrt{11}}} = x - \sqrt{y}$, then $(\sqrt{y})^x = ?$}

If $a = \sqrt{5} - \sqrt{3}$, then the value of $a^2 + 2a\sqrt{3} + 8$ is:

$(256)^{0.16} \times (256)^{0.09} = ?$}

$1 - \{1 + (x^2 - 1)^{-1}\}^{-1} = ?$}

If twice the square of a number is 45 more than 13 times of it, then what is the cube of that number?

If $x * y = \frac{1}{x} + \frac{1}{y}$ for all $x,y \in \mathbb{R} - \{0\}$, then $(5 * 2) * (3 * 5) =$ ?

Suppose $a, b, c$ are positive real numbers such that $2^a = 3^b = 6^{-c}$. Then $\frac{ab + bc + ca}{abc} =$ ?

If $\sqrt[4]{\,4\sqrt[4]{\,4\sqrt[4]{\,4\sqrt[4]{4}\,}\,}\,} = 2^{\frac{a}{b}}$, where $\frac{a}{b}$ is in the reduced form, then $a+b =$ ?

If $x = 3 + 2\sqrt{2}$, then the value of $\left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)$ is:

It is given that $(2^{32} + 1)$ is completely divisible by a whole number $w$. Which of the following numbers is completely divisible by this number $w$?