List of top Mathematics Questions asked in KEAM

$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to

The statement $p \rightarrow \left(\sim q\right)$ is equivalent to

If $z^2 + z + 1 = 0$ where $z$ is a complex number, then the value of $\left(z+ \frac{1}{z}\right)^{2} + \left(z^{2} + \frac{1}{z^{2}}\right)^{2} + \left(z^{3} + \frac{1}{z^{3}}\right)^{2} $ equals

$ \int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}} $ is equal to

The derivative of $ {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) $ with respect to $ {{\sin }^{-1}}(3x-4{{x}^{3}}) $ is

Let $a, a + r$ and $a + 2r$ be positive real numbers such that their product is $64$. Then the minimum value of $a + 2r$ is equal to

$\displaystyle \lim_{x \to 2} $ $\frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to

If $\int \frac{f\left(x\right)}{log\,cos\,x}dx=-log\left(log\,cos\,x\right)+C$, then $f\left(x\right)$ is equal to

$ \int{({{\sin }^{6}}x+{{\cos }^{6}}x+3{{\sin }^{2}}x \,{{\cos }^{2}}x)}dx $ is equal to

If the vectors $ \overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k} $ and $ \overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k} $ are coplanar, then the value of $\lambda$ is equal to

The roots of the equation $\begin{vmatrix}x-1&1&1\\ 1&x-1&1\\ 1&1&x-1\end{vmatrix} = 0 $ are

$ \int{\frac{{{x}^{3}}\sin [{{\tan }^{-1}}{{(x)}^{4}}]}{1+{{x}^{8}}}}dx $ is equal to:

$ \int_{-1}^{1}{\frac{17{{x}^{5}}-{{x}^{4}}+29{{x}^{3}}-31x+1}{{{x}^{2}}+1}}dx $ is

$ \underset{x\to 2}{\mathop{\lim }}\,\frac{{{x}^{100}}-{{2}^{100}}}{{{x}^{77}}-{{2}^{77}}} $ is equal to

If $y = x + \frac{1}{x}, x \ne 0$, then the equation $\left(x^{2}-3x+1\right)\left(x^{2}-5x+1\right)=6x^{2}$ reduces to

The value of $\sum\limits^{n}_{k=0}\left(i^{k}+i^{k+1}\right)$, where $i^2 = -1$, is equal to

$ \displaystyle\lim_{x\rightarrow0} \frac{1}{3-2^{\frac{1}{x}}}$ is equal to

The negation of $\left(p\vee\sim q\right)\wedge q$ is

Let $p$ : roses are red and q : the sun is a star. Then, the verbal translation of $ (-\text{ }p) \vee q $ is

If $ \tan \alpha =\frac{b}{a},a>b>0 $ and if $ 0

If z =$\frac{2-i}{i}$ = , then Re(z$^2$) + lm(z$^2$) is equal to

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

If $ {{x}^{2}}+4ax+2>0 $ for all values of $ x, $ then $a$ lies in the interval