List of top Mathematics Questions asked in KEAM

$ \int{\frac{\sec x cosec x}{2\cot x-\sec x\cos ecx}}dx $ is equal to

$ \int{\frac{{{4}^{x+1}}-{{7}^{x-1}}}{{{28}^{x}}}}dx $ is equal to

$ \int{\frac{\cos x-\sin x}{1+2\sin x\cos x}}dx $ is equal to

The vectors of magnitude $a, 2a, 3a $ meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

If a straight line makes angles $\alpha , \beta , \gamma $ with the coordinate axes, then $\frac{1-\tan^{2} \alpha }{1+tan^{2} \alpha} +\frac{1}{sec 2 \beta} -2\sin^{2} \gamma =$

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

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 $ \frac{5{{z}_{2}}}{11{{z}_{1}}} $ is purely imaginary, then the value of $ \left[ \frac{2{{z}_{1}}+3{{z}_{2}}}{2{{z}_{1}}-3{{z}_{2}}} \right] $ is

$\displaystyle \lim_{x \to 0} $ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to

Let $p, q, r$ be three statements. Then $\sim (p \vee \left(q \wedge r\right))$ is equal to

The functions $f , g$ and $h$ satisfy the relations $f ^{'}\left(x\right)=g\left(x+1\right)$. Then $f ^{"}\left(2x\right)$ is equal to

If $y=\frac{x}{x+1}+\frac{x+1}{x},$ then $\frac{d^{2}y}{dx^{2}} $ at $x=1$ is equal to

$\int \frac{sec\,x\,dx}{\sqrt{cos\,2\,x}}$ is equal to

The solution set of the in equation $ \frac{x+11}{x-3}>0 $ is

The set of all real $ x $ satisfying the in equal $ \frac{3-|x|}{4-|x|}\ge 0 $

If $\left(1+x+x^{2}\right)^{n} =1+a_{1}x+a_{2}x^{2} +\cdots+a_{2n}x^{2n}$, $2a_{1} -3a_{2} +\cdots-\left(2n+1\right)a_{2n}$ is equal to

If $ A= \begin{bmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \\ \end{bmatrix} , $ then $ {{A}^{4}} $ is equal to