List of top Mathematics Questions asked in KEAM

If $ A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right], $ then the value of the determinant $ |{{A}^{2009}}-5{{A}^{2008}}| $ is

If \(f(x) = \sin x e^{\sin x}\), find \(f'(x)\)

If \(tan(x - y) = \frac{4}{5}\), \(\tan(x + y) = \frac{6}{5}\), then \(\tan(2x) =\)

If \(f(x)\) is continuous in \(\mathbb{R}\),

\[f(x) = \begin{cases} \frac{3x^2 - 12}{x - 2}, & x \neq 2 \\k, & x = 2 \end{cases}\]

 find \(k\).

If \( |x + 3| < 2 \), then \( x \) lies in
If \( 1, a, b, c, 16 \) is in G.P., then \( \sqrt[3]{abc} = \)
Evaluate \( \int \sin x \cdot \sin 2x \, dx \)
Distance between two foci of the hyperbola \( x^2 - 4y^2 = 16 \) is
P(A) = 0.4, P(B/A) = 0.9. Then P(A ∩ B) is
Evaluate \( \int_1^3 [x - 1] \, dx \)
The $100^{th}$ term of the sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \dots$, is
If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is
If $ {{x}^{y}}.{{y}^{x}}=16, $ then $ \frac{dy}{dx} $ at (2, 2) is
Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to
If t$_5$, t$_{10}$ and t$_{25}$ are 5$^{th}$, 10$^{th}$, and 25$^{th}$ terms of an A.P. respectively, then the value of $\begin{vmatrix}t_{5}&t_{10}&t_{25}\\ 5&10&25\\ 1&1&1\end{vmatrix}$ is equal to
If $\left(1+ax\right)^{n} =1+6x+\frac{27}{2}x^{2}+\cdots+a^{n}\, x^{n}$, then the values of $a$ and $n$ are respectively
If $|x - 3| < 2x + 9$ then $x$ lies in the interval
Let $s_n = \cos \left(\frac{n\pi}{10}\right), n=1,2,3,\ldots$ Then the value of $\frac{s_{1}s_{2}\ldots s_{10}}{s_{1}+s_{2}+\ldots+s_{10}}$ is equal to
If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to
If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to
If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are
If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to
If $X=\{1,2,3, \ldots, 10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\{4\}$ is
$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to