List of top Mathematics Questions asked in KEAM

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

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

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

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

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