List of top Mathematics Questions asked in KEAM

The value of \( \left( i^{18} + \left(\frac{1}{i}\right)^{25} \right)^3 \) is equal to

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

If \( z = e^{i4\pi/3} \), then \( (z^{192} + z^{194})^3 \) is equal to

If \( a \) and \( b \) are real numbers and \( (a + ib)^{11} = 1 + 3i \), then \( (b + ia)^{11} \) is equal to

If \( \alpha \neq \beta \), \( \alpha^2 = 5\alpha - 3 \), \( \beta^2 = 5\beta - 3 \), then the equation having \( \frac{\alpha}{\beta} \) and \( \frac{\beta}{\alpha} \) as its roots is

The focus of the parabola \( y^2 - 4y - x + 3 = 0 \) is

If the conjugate of a complex number \( z \) is \( \frac{1}{i - 1} \), then \( z \) is

The value of \( \frac{2(\cos 75^\circ + i \sin 75^\circ)}{0.2(\cos 30^\circ + i \sin 30^\circ)} \) is

In AP, \( a_k=5k+1 \). Find sum of first 100 terms

If \( \begin{vmatrix} x & 2 & x 2 & x & 6 x & x & 6 \end{vmatrix} = ax^4 + bx^3 + cx^2 + dx + e \), then \( 5a+4b+3c+2d+e \) is equal to

Evaluate \( \begin{vmatrix} 1 & a & b+c 1 & b & c+a 1 & c & a+b \end{vmatrix} \)

If \( f(x)=\begin{vmatrix} \frac{1}{2x} & \frac{1}{x-1} & \frac{1}{x} \\ 3x(x-1) & (x-1)(x-2) & x(x-1) \end{vmatrix} \), then \( f(50) \) is

Find equation of plane passing through (1,2,3), (-1,4,2), (3,1,1)

If \( \Delta(x)=\begin{vmatrix} 1 & \cos x & 1-\cos x \\ 1+\sin x & \cos x & 1+\sin x-\cos x \\ \sin x & \sin x & 1 \end{vmatrix} \), then \( \int_0^{\pi/2} \Delta(x)\,dx \)

Coin tossed and die rolled: probability of head and 3

If \( A=\begin{bmatrix}2x & 0 x & x \end{bmatrix} \) and \( A^{-1}=\begin{bmatrix}1 & 0 -1 & 2 \end{bmatrix} \), find \(x\)

If determinant of matrix is zero, then system is

If \( A = \begin{bmatrix} 1 & 2 & 3 0 & 1 & 4 5 & 6 & 0 \end{bmatrix} \), then the sum of the diagonal elements of \( A^{-1} \) is

If \( A = \begin{bmatrix} 2 & 1 3 & 2 \end{bmatrix} \), then \( A^{-1} \) is

If \( x = A\cos 4t + B\sin 4t \), then \( \frac{d^2x}{dt^2} = \)

If set \( S \) has 10 elements and \( A=\{(x,y):x,y\in S, x\ne y\} \), number of elements in \( A \)

The arithmetic mean of \( ^nC_0, ^nC_1, \ldots, ^nC_n \) is

Variance of first 20 natural numbers

The differential equation whose general solution is \( y = e^x(A\cos x + B\sin x) \) is

The real part of \( (i - \sqrt{3})^{13} \) is