List of top Questions asked in KEAM

The remainder when $2^{2016}$ is divided by $63$ is:

The total number of 7 digit positive integral numbers with distinct digits that can be formed using the digits 4, 3, 7, 2, 1, 0, 5 is:

If \( ^nP_4 = 5(^nP_3) \), then the value of \( n \) is equal to:

In an A.P., the $6^{\text{th}}$ term is $52$ and the $11^{\text{th}}$ term is $112$. Then the common difference is equal to:

If the $6^{\text{th}}$ term of a G.P. is $2$, then the product of the first $11$ terms of the G.P. is equal to:

If $a_1, a_2, a_3, a_4$ are in A.P., then $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \frac{1}{\sqrt{a_3} + \sqrt{a_4}} =$

If the product of five consecutive terms of a G.P. is $\frac{243}{32}$, then the middle term is:

Sum of the series \( 1(1) + 2(1+3) + 3(1+3+5) + 4(1+3+5+7) + \cdots + 10(1+3+5+7+\cdots+19) \) is equal to:

If $a_1, a_2, a_3, a_4$ are in A.P., then $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \frac{1}{\sqrt{a_3} + \sqrt{a_4}} =$

If the equation \( 2x^2 + (a+3)x + 8 = 0 \) has equal roots, then one of the values of \( a \) is:

If \( a \) and \( a^2 \) are the roots of \( x^2 - 6x + c = 0 \), then the positive value of \( c \) is

If \( \alpha \) and \( \beta \) are the roots of \( 4x^2 + 2x - 1 = 0 \), then \( \beta = \)

If the roots of the quadratic equation $mx^2 - nx + k = 0$ are $\tan 33^\circ$ and $\tan 12^\circ$, then the value of $\frac{2m + n + k}{m}$ is equal to:

If one root of $ax^2 - bx + a = 0$ is $6$, then $\frac{b}{a}$ is:

If $\frac{(1+i)(2+3i)(3-4i)}{(2-3i)(1-i)(3+4i)} = a + ib$, then $a^2 + b^2 =$

If $|z + 1| < |z - 1|$, then $z$ lies:

If $\left| z - \frac{3}{z} \right| = 2$, then the greatest value of $|z|$ is:

Let $z, w$ be two nonzero complex numbers. If $\bar{z} + i\overline{w} = 0$ and $\arg(zw) = \pi$, then $\arg z =$

If $z = \frac{2 - i}{i}$, then $\text{Re}(z^2) + \text{Im}(z^2)$ is equal to:

The principal argument of the complex number $z = \frac{1 + \sin \frac{\pi}{3} + i \cos \frac{\pi}{3}}{1 + \sin \frac{\pi}{3} - i \cos \frac{\pi}{3}}$ is:

The function $f : A \to B$ given by $f(x) = x, x \in A$, is one to one but not onto. Then:

Let $f(x) = x^3$ and $g(x) = 3^x$. The values of $a$ such that $g(f(a)) = f(g(a))$ are:

The domain of the function $f(x) = \begin{cases} \frac{x^2 - 9}{x - 3}, & \text{if } x \neq 3 \\ 6, & \text{if } x = 3 \end{cases}$ is:

If $A \setminus B = \{a, b\}$, $B \setminus A = \{c, d\}$ and $A \cap B = \{e, f\}$, then the set $B$ is equal to:

If $f\left(\frac{x + 1}{2x - 1}\right) = 2x,\ x \in \mathbb{N}$, then the value of $f(2)$ is equal to: