List of top Engineering Mathematics Questions asked in AP PGECET

The coefficient of correlation is independent of
If \( x^2 - x - 4 = 0 \) by bisection method, first two approximations \( x_1 \) and \( x_2 \) are 1 and 2, then \( x_3 \) is
Probability Density function $f(x)$ of a continuous random variable is given by $f(x) = ce^{-|x|}, -\infty<x<\infty$. If the total probability $\int_{-\infty}^{\infty} f(x) dx = 1$ then $c =$
A problem of statistics is given to three students A, B and C whose chances of solving are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved?
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with the probability 0.2 then $P(A) + P(B) = $?
Augmented matrix of equations $x - y + z = 9; 2x - 3y + 4z = 25; 2x + 6y + 4z = 10$ is reduced to Echelon form as $\begin{bmatrix} 1 & -1 & 1 & 9 \\ 0 & -2 & 3 & 16 \\ 0 & 0 & 7 & 28 \end{bmatrix}$. Then the solution set $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is
$\lim_{x \to \infty} x \tan \left( \frac{1}{x} \right) = $ _____
$\int_{-\pi/6}^{\pi/6} \frac{(\sin x)^5 (\cos x)^3}{x^4} dx =$
Evaluate $\oint_C (y^2 dx - x^3 dy)$, where $C$ is the positively oriented circle of radius 2 centered at origin.
$f(x) = 2x^2 - 2x + 6$ will have a minimum value at $x=$ _____
If $f(x)$ is differentiable function in x then it is
As per Green's theorem $\oint_C Mdx + Ndy = \iint_R (_____)dxdy$
The rank of the matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 4 & 2 \\ 2 & 6 & 5 \end{bmatrix}$ is
For the matrix $\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ which of the following is not an Eigen Vector

If \(\mathbf{f} = f_1(y, z) \hat{i + f_2(z, x) \hat{j} + f_3(x, y) \hat{k}}\), then \( \mathbf{f} \) is

What is the correct formula for Runge-Kutta 3rd order method?
One of the two events must occur. The chance of one is \( \frac{2}{3} \) of the other, then odds in favor of the other are
If \( \mathbf{F} = ax \hat{i} + by \hat{j} + cz \hat{k} \), where \( a, b, c \) are constants, then
If \( f(x) = (x^2 - 16)^2 \), where \( x \) is real, \( f(x) \) has
Solution of the differential equation \( xy \frac{dy}{dx} = 1 + x + y + xy \) is
If \( \mathbf{a} \) is a constant vector, then \( \text{div}[\mathbf{a} \times (\mathbf{r} \times \mathbf{a})] \) is
If \( A \) is an orthogonal matrix, then \( A^{-1} \) is
The work done in displacing a particle from \( r = 0 \) to \( r = 1 \) in a curve \( x = t^2 + 1 \) and \( z = t^2 + 1 \) in a force field \( \mathbf{F} = (2xy, 3x, -5z) \) is
Solution of the system of equations \( 3x + y + 2z = 3 \), \( 2x - 3y - z = -3 \), \( x + 2y + z = 4 \)
Starting from \( x_0 = 1 \), one step Newton-Raphson method in solving the equation \( x^3 + 3x - 7 = 0 \) gives the next value as