List of top Mathematics Questions asked in KEAM

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

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

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

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to

The domain of the function \(f(x) = (x^2-2x-63)^{\frac{3}{2}}\), x ∈ R is

Let A = {1,2,3,4,5} and let B={1,2,3,4}. If the relation R : A → B is given by (a, b) ∈ R if and only if a+b is even, then n(R) is equal to

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

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

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

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

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

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

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

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=

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

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 number of 3-digit numbers that can be formed from the digits 0, 2, 3, 5, 7 is (repetition is allowed)

If p and q are positive integers such that \(^{p+q}P_2=42\ and\ ^{p-q}P_2=20\), then the values of p and q respectively

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 clements is

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

The first term of a G.P. is 3 and the common ratio is 2. Then the sum of first eight terms of the G.P. is

If the 10^th and 12^th terms of an A.P. are respectively 15 and 21, then the common difference of the A.P. is

In an A.P. the difference between the last and the first terms is 632 and the common difference is 4. Then the number of terms in the A.P. is

If the first term of a G.P. is 1 and the sum of 3^rd and 5^th terms is 90, then the positive common ratio of the G.P. is