List of top Mathematics Questions asked in KEAM

Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is

The equations of the asymptotes of the hyperbola \( xy + 3x - 2y - 10 = 0 \) are

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

If \( f(x) = x^6 + 6^x \), then \( f'(x) \) is equal to

\( \lim_{x \to 0} \frac{\sqrt{1+2x} - 1}{x} \) is

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

The minimum value of \( f(x) = \max\{x, 1+x, 2-x\} \) is

\( \lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9}{4x^3 + 9x - 2} \) is equal to

If the sides of a triangle are 4, 5 and 6 cms. Then the area of triangle is ______ sq.cms.

If \( \sin \alpha \) and \( \cos \alpha \) are the roots of the equation \( ax^2 + bx + c = 0 \), then

If the sum of the coefficients in the expansion of \( (a^2x^2 - 2ax + 1)^{51} \) is zero, then \( a \) is equal to

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

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

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

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

Area bounded by \( y=\sin^2 x \), \( x=\frac{\pi}{2} \), \( x=\pi \)

\( \lim_{x\to0} \frac{1+x-e^x}{x^2} \)

\( \lim_{x\to0} \frac{\int_0^{x^2} \sin(\sqrt{t}) \, dt}{x^2} \)

If \( \int f(x)\cos x \, dx = \frac{1}{2}\{f(x)\}^2 + c \), then \( f\left(\frac{\pi}{2}\right) \) is

If \( f \) is differentiable and \( \lim_{h\to0} \frac{f(1+h)-f(1)}{h}=5 \), find \( f'(1) \)