List of top Mathematics Questions asked in KEAM

The value of the determinant \( \begin{vmatrix} 1 & 1 & 1 \\ p & q & r \\ p & q & r+1 \end{vmatrix} \) is equal to:

The equation $5x^2 + y^2 + y = 8$ represents

If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$

The eccentricity of the ellipse $ \frac{\left(x-1\right)^{2}}{2} + \left(y + \frac{3}{4}\right)^{2} = \frac{1}{16}$ is

If $\sum_{k=0}^{18} \frac{k}{\binom{18}{k}} = a \sum_{k=0}^{18} \frac{1}{\binom{18}{k}}$, then the value of $a$ is equal to:

If the square of the matrix $\begin{pmatrix} a & b \\ a & -a \end{pmatrix}$ is the unit matrix, then $b$ is equal to:

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

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

If \( ^nC_2 + ^nC_3 = ^6C_3 \) and \( ^nC_x = ^nC_3, x \neq 3 \), then the value of \( x \) is equal to:

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 the coefficients of \( x^3 \) and \( x^4 \) in the expansion of \( (3+kx)^9 \) are equal, then the value of \( k \) is:

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

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

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

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

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

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