List of top Questions asked in KEAM- 2018

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

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 determinant of matrix is zero, then system is

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

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

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

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

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

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

\( \int_{0}^{\pi/2} \frac{2\sin x}{2\sin x + 2\cos x} dx \)

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

\( \int_{\pi/4}^{3\pi/4} \frac{x}{1+\sin x} \, dx \) is equal to

\( \lim_{x\to\infty} \left(\sqrt{x^2+1} - \sqrt{x^2-1}\right) \)

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

Point equidistant from \( (2,0,3), (0,3,2), (0,0,1) \)

If the points \( (2a,a), (a,2a), (a,a) \) form a triangle of area 18, find centroid

If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to

If \( \theta \) is the angle between the pair of straight lines \( x^2 - 5xy + 4y^2 + 3x - 4 = 0 \), then \( \tan^2\theta \) is equal to

The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3,-2). The third vertex lies on \( y = x + 3 \). The coordinates of the third vertex can be

If \( 3\hat{i} + 2\hat{j} - 5\hat{k} = x(2\hat{i} - \hat{j} + \hat{k}) + y(\hat{i} + 3\hat{j} - 2\hat{k}) + z(-2\hat{i} + \hat{j} - 3\hat{k}) \), then

Let \( f:\mathbb{R} \to \mathbb{R} \) be a differentiable function. If \( f \) is even, then \( f'(0) \) is equal to

The area of the triangle in the complex plane formed by \( z, iz \) and \( z + iz \) is

The coordinate of the point dividing internally the line joining the points \( (4,-2) \) and \( (8,6) \) in the ratio \( 7:5 \) is

If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then