List of top Mathematics Questions asked in KEAM

If $*$ is defined by $a*b$ = $a - b^2$ and $\oplus$ is defined by $\oplus$ = $a^2 + b$, where a and b are integers, then ($3 \oplus 4) * 5$ is equal to

Two finite sets $A $ and$ B $ have m and n elements respectively. If the total number of subsets of $A $ is 112 more than the total number of subsets of $B$, then the value of m is

For any two statements $p$ and $q$, the statement $\sim\left(p \vee q\right) \vee \left(\sim p \wedge q\right)$ the is equivalent to

The equation of the tangent to the curve $ y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x) $ at $ x=0 $ is:

Equation of the plane passing through the intersection of the planes $ x+y+z=6 $ and $ 2x+3y+4z+5=0 $ and the point $(1, 1, 1)$ is

The chord joining the points $(5, 5)$ and $(11, 227)$ on the curve $y =3x^{2}-11x-15$ is parallel to tangent at a point on the curve. Then the abscissa of the point is

Two distinct numbers $x$ and $y$ are chosen from $1,2,3,4,5$. The probability that the arithmetic mean of $x$ and $y$ is an integer is

If $\begin{bmatrix}1&x&1\end{bmatrix} \begin{bmatrix}1&3&2\\ 2&5&1\\ 15&3&2\end{bmatrix}\begin{bmatrix}1\\ 2\\ x\end{bmatrix} = 0 $, then x can be

The area of the plane region bounded by the curve $ x={{y}^{2}}-2 $ and the line $ y=-x $ is (in square units)

If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

$\int\frac{1}{\sin x\, \cos x}$ dx is equal to

If $A = \begin{pmatrix}1&5\\ 0&2\end{pmatrix}$ , then

If $|z + 1| < |z - 1|$ , then $z$ lies

If $a$ is positive and if $A$ and $G$ are the arithmetic mean and the geometric mean of the roots of $ {{x}^{2}}-2ax+{{a}^{2}}=0 $ respectively, then

If $a_1, a_2 , a_3 , a_4$ are in A.P., then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\frac{1}{\sqrt{a_{3}}+\sqrt{a_{4}}}=$

If $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+ $ $ bx+c=0,\text{ }\alpha \beta =3 $ and $a, b, c$ are in $A.P.$, then $ \alpha +\beta $ is equal to

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

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

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

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