List of top Mathematics Questions asked in KEAM

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 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

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

The sum of the first 24 terms of the series 9+13+17+...... is equal to

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

If z₁ and z₂ are two different complex numbers with |z₂|=1, then \(|\frac{1-\bar{z_1}z_2}{z_1-z_2}|\)is equal to

The modulus of \((\frac{1+i}{1-i})^{75}-(\frac{1-i}{1+i})^{75}\)is

If \(z^4=7-5i\), then \(\text{Im}((\bar{z})^4)\) is equal to

The value of \(\left[ \frac{5i}{(1-i)(2-i)(3-i)} \right]^{50}\)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 ⊙ 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

Let A and B be subsets of the universal set U. If n(A) = 24 , n (A∩B)=8 and n(U) = 63, then n( A'∪B') 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