List of top Mathematics Questions asked in KEAM

Let $x_{1},x_{2},\cdots,x_{n}$ be in an $A.P$. If $x_{1}+x_{4}+x_{9}+x_{11}+x_{20}+x_{22}+x_{27}+x_{30}=272, $ then $x_{1}+x_{2}+x_{3}+\cdots+x_{30}$ is equal to

If $a + 1, 2a + 1, 4a - 1$ are in arithmetic progression, then the value of $a$ is

$\displaystyle \int^{\sqrt{\pi}/2}_0$ $2x^{3} sin\left(x^{2}\right) dx =$dx is equal to

If $ {{a}_{1}},{{a}_{2}},.....,{{a}_{n}} $ are in AP with common difference $ d\ne 0, $ then $ (\sin d) $ $ [\sec {{a}_{1}}\sec {{a}_{2}}+ $ $ \sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}] $ is equal to

Let $A$ and $B$ be two events such that $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right).$ If $0 < P\left(A\right)< 1$ and $0 < P\left(B\right)< 1$ , then $P\left(A\cup B\right)^{'}=$

$\int\frac{3 ^{x}}{\sqrt{1-9 ^{x}}}dx\quad$is equal to

If one root of the equation $ l{{x}^{2}}+mx+n=0 $ is $ \frac{9}{2} $ $ (l,m $ and n are positive integers) and $ \frac{m}{4n}=\frac{l}{m}, $ then $ \frac{1}{x}+\frac{1}{y} $ is equal to

If the sum to first $n$ terms of the $A.P. 2,4,6,...$ is $240$, then the value of $n$ is

The coefficient of $x^5$ in the expansion of $(1 + x^2)^5(1 + x)^4$ is

The solution set of $\frac{x+3}{x-2} \le\,2$ is

Which one of the following is not a statement?

If $a =\hat{ i }+2 \hat{ j }+2 \hat{ k },| b |=5$ and the angle between $a$ and $b$ is $\pi / 6$, then the area of the triangle formed by these two vectors as two sides is

The value of The value of $\frac{2(\cos \, 75^{\circ} + i \, \sin \, 75^{\circ})}{0.2(\cos \, 30^{\circ} + i \, \sin \, 30^{\circ})}$ is

The value of the determinant $ \left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right| $ is equal to

The value of $ \frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ } $ is equal to

Let $S(n)$ denote the sum of the digits of a positive integer n. e.g. $S(178)=1+$ $7+8=16 .$ Then, the value of $S(1)+S(2)+S(3)+\ldots+S(99)$ is

$ \int{(x+1){{(x+2)}^{7}}}(x+3)dx $ is equal to

$ \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