List of top Mathematics Questions asked in KEAM

The area of the triangle formed by the points $(2, 2), (5, 5), (6, 7)$ is equal to (in square units)

The coefficient of $ {{a}^{5}}{{b}^{6}}{{c}^{7}} $ in the expansion of $ {{(bc+ca+ab)}^{9}} $ is

Three numbers $x, y$ and $z $ are in arithmetic progression. If $x + y + z = - 3$ and $xyz= 8$, then $x^2 + y^2 + z^2$ is equal to

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

If $ |x|<1, $ then the coefficient of $ {{x}^{6}} $ in the expansion of $ {{(1+x+{{x}^{2}})}^{-3}} $ is

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is

If $ {{x}^{y}}.{{y}^{x}}=16, $ then $ \frac{dy}{dx} $ at (2, 2) is

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

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

Suppose $a, b$ and $c$ are real numbers such that $ \frac{a}{b}>1 $ and $ \frac{a}{c}<0 $ . Which one of the following is true?

If $\begin{pmatrix}2x+y&x+y\\ p-q&p+q\end{pmatrix}=\begin{pmatrix}1&1\\ 0&0\end{pmatrix}$ , then $(x, y, p, q) $ equals

If $r$ is a real number such that $ |r| < 1 $ and if $ a=5(1-r), $ then

If $C_{0}$, $C_{1}$, $C_{2}$, $C_{3}$, $\cdots$ are binomial coefficients in the expansion of $(1 + x)^n$, then $\frac{C_{0}}{3}- \frac{C_{1}}{4}+ \frac{C_{2}}{5}- \frac{C_{3}}{6}+ \cdots$ is equal to

If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is

Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals

If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to