List of top Mathematics Questions asked in KEAM

If the first term of a G.P. is 3 and the sum of second and third terms is 60, then the common ratio of the G.P. is

If n^th term of a series is n+(-1)^n-1, n = 1,2,3,..., then the sum of first 40 terms of the series 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 minimum value of |z+1|+|z-2| is equal to

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

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 \(\lambda\ne\)

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

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

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 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

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

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