List of top Mathematics Questions asked in KEAM

If $z = i^9 + i^{19}$ , then $z$ is equal to

Let $S_{1}$ be a square of side $5\,cm$. Another square $S_{2}$ is drawn by joining the midpoints of the sides of $S_{1}$ Square $S_{3}$ is drawn by joining the midpoints of the sides of $S_{2}$ and so on. Then (area of $S_{1}$ + area of $S_{2}$ + area of $S_{3}$ $+\ldots+$ area of $S_{10}$) =

The plane $ \overrightarrow{r}=s(\hat{i}+2\hat{j}-4\hat{k})+t(3\hat{i}+4\hat{j}-4\hat{k}) $ $ +(1-t)(2\hat{i}-7\hat{j}-3\hat{k}) $ is parallel to the line

$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ is equal to

If $ \alpha ,\beta ,\gamma $ are the cube roots of a negative number $p$, then for any three real numbers, $ x,y,z $ the value of $ \frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha } $ is

If one of the roots of the quadratic equation $ax^2 - bx + a = 0$ is $6$, then value of $\frac{ b}{ a}$ is equal to

If $ {{x}^{2}}-px+q=0 $ has the roots $ \alpha $ and $ \beta $ then the value of $ {{(\alpha -\beta )}^{2}} $ is equal to

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

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

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

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

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