List of top Mathematical Ability Questions on Algebra asked in APICET

Consider the logical statements P, Q and R. Then $(\sim P \lor R) \lor (P \land (\sim R \lor Q))$ is equivalent to:

If $A = \{x \in \mathbb{N} : x^2 < 25\}$ and $B = \{x \in \mathbb{N} : x \text{ is even}, x \leq 10\}$, then $A \cap B$ is:

The four points (1,7), (4,2), (-1,-1), (-4,4) form a:

If $f(x) + 2f(1/x) = 5x + 2$, for a polynomial $f(x)$, then $f(3) = ?$

The equation of the straight line passing through the point (−1, 2) and perpendicular to the line $x + 3y = 4$ is:

The distance of the point (1, 6, 2) from the point of intersection of the line $(x-2)/3 = (y+1)/4 = (z-2)/12$ and the plane $x - y + z = 16$ is:

Suppose a, b, c are real numbers such that a:b:c = 3:2:4. Then $\sqrt{a^2 + 6b^2 + c^2}$ is equal to: }

If $|x - y| < 5$ and $|x - y| \geq 2$ , then the maximum integral value of y, such that x is always negative is:

$1/(2 \times 3) + 1/(3 \times 4) + ... + 1/(49 \times 50) = ?$

Which of the following arrangements of rational numbers in ascending order is correct?

$(a/b)^{x-1} = (b/a)^{x-3}$, then x = ? }

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 = $?

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

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