List of top Mathematics Questions asked in KEAM

In an A.P. there are 18 terms and the last three terms of the A.P. are 67, 72, 77. Then the first term of the A.P. is

If -1+7i, -1+xi and 3+3i are the three vertices of an isosceles triangle which is right angled at -1+xi, then the value of x is equal to

The principal argument of the complex number \(z=\frac{8+4i}{1+3i}\) is equal to

The minimum value of |z+1|+|z-2| is equal to

Let f: R→R be defined by f(x) = cos x. Then

Let \(f(x) =   \begin{cases}     x+2       & for\ x\lt\ 1 \\     4x-1  & for\ 1\leq x \leq3 \\ x^2+5 & for\ x\gt3   \end{cases}\). Then

A bag contains 5 yellow, 3 green, 2 blue and 7 white balls. If 4 balls are chosen at random, then the probability that none of them are white is

If $sin\alpha +sin \beta = \frac{\sqrt6}2$ and $cos \alpha + cos\beta = \frac{\sqrt2}2$ then $coas(\alpha - \beta)$ is equa; to

Let \(f(x)=6\sqrt{x^5}^3\). If \(f'(x)=ax^p\), where a and p are constants, then the value of p is equal to

For any two positive rational numbers m and n, a binary operation * is defined by \(m*n=\frac{m+n}{3}\), then \(\frac{7}{2}*\frac{5}{2}\) is equal to

The term independent of x in the binomial expansion of \((x+\frac{2}{x^3})^{20}\) is

The general solution of the differential equation 4xy+12x+(2x²+3)y' = 0 is

If \(\frac{z}{i}=11-13i\), then \(z+\bar z\) is equal to

Let X be the set {1, π, {42, √2}, {1,3}}. Which of the following statement(s) is/are true? Ρ : π ∈X , Q :{1,3} ⊆ X , R : {1,7} ⊆ X 

The matrix \(\begin{bmatrix} -2&1&0\\3&4&1\\-4&\lambda&0 \end{bmatrix}\) is non-singular for \(\lambda\ne\)

Let \(\begin{vmatrix} x-1&2&1\\2&x-1&2\\1&x+2&x-1 \end{vmatrix}=ax^3+bx^2+cx+d\), where a,b,c and d are constants. Then the value of d is

If the inequality -13 ≤ x ≤ 5 is expressed in the form |x-a|≤b, then the values of a and b are respectively

The solution set of the inequality 5(4x+6) <25x+10 is

Let \(A+B=\begin{bmatrix} 4&1&4\\1&4&4 \end{bmatrix}\)and \(B=\begin{bmatrix} 1&0&-2\\-1&3&0 \end{bmatrix}\), then A=

If \(AB=\begin{bmatrix} 4&3\\5&4 \end{bmatrix}\) and \(A^{-1}=\begin{bmatrix} 3&-2\\-1&1 \end{bmatrix}\), then B=

If x²² is in the (r+1)th term of the binomial expansion of (3x³-x²)⁹, then the value of r is equal to

The value of the determinant \(\begin{vmatrix} 4&4^2&4^3\\3&3^2&3^3\\2&2^2&2^3 \end{vmatrix}\)is

If \(\begin{vmatrix} 1&2&1\\0&x&-3\\2&-1&x \end{vmatrix}=0\), then the value of x are

The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is

A covid-19 vaccination reduces the probability of getting covid-19 infection from 0.4 to 0.1. In a city, 45% people are vaccinated. Then the probability that a non-vaccinated person chosen at random in the city gets covid-19 infection is