List of top Engineering Mathematics Questions asked in TS PGECET

While evaluating \(\int_{a}^{b} f(x) \, dx\) using Trapezoidal rule and Simpson's one-third rule, \([a,b]\) is divided into n number of subintervals so that both the methods can be applied for the same division, then a possible value of n is

Newton-Raphson method is used to find the root of \(x^2 - 3 = 0\). If the initial solution is taken as \(x = -2\), then the iterations tend to

From a set \(\{1,2,3,4,5,6,7\}\) two numbers are selected at random. The random variable \(X\) is defined as the absolute difference of the numbers selected. The mean of \(X\) is

The maximum value of \(x^2 y z^3\), subject to \(x + y + z = 42\) exist at \((x, y, z) = (\alpha, \beta, \gamma)\), then \(\alpha\beta\gamma =\)

Given below are pair of functions \(f(x)\) and \(g(x)\). Which pair is not linearly independent?

The solution of \(\frac{\partial^2 u}{\partial t^2} = 4\frac{\partial^2 u}{\partial x^2}\), \(t > 0\), \(-\infty < x < \infty\) satisfying the conditions \(u(x,0) = x\) and \(\frac{\partial u}{\partial t}(x,0) = 0\) is

Which of the following cannot be an eigen value for an unitary matrix?

If \(A\) is symmetric, \(P\) and \(B\) are skew symmetric matrices, then which of the following is correct?

If X is a Poisson random variable with variance \(P(X = 2) = 9 P(X = 4)\) then the mean and variance respectively are

If X and Y are independent random variables with variances \(\sigma_x^2 = 5\) and \(\sigma_y^2 = 3\) then the variance of the random variable \(Z = 3X + 2Y - 5\) is

The value of the integral \(\displaystyle\oint_{C}\frac{z e^{-z}}{(z-1)(z-2)}\,dz\) where \(C:|z|=\dfrac{3}{2}\) is

For which values of \(k\) does the function \(f(z)=\left(x^3-3xy^2\right)+i\left(kx^2y-y^3\right)\) become analytic?

If \(u=\sin^{-1}\left(\dfrac{x^{1/3}+y^{1/3}}{x^{1/2}-y^{1/2}}\right)^{1/2}\), then \(x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y}=\)

For the function \(f(x)=\log x\), the number \(c\) strictly between \(e^2\) and \(e^3\) that satisfies \(f'(c)=\dfrac{f(e^3)-f(e^2)}{e^3-e^2}\) is

Let \(a,b\) and \(c\) be real numbers. Suppose there exist real numbers \(x,y,z\) which are not all zero such that the system of equations \(x = cy + bz\), \(y = cx + az\) and \(z = bx + ay\) has a non-zero solution then \(\left(a+b+c\right)^2 =\)

Let \(A=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}\). If \(u_1\) and \(u_2\) are column matrices such that \(Au_1 = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}\) and \(Au_2 = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}\), then \(u_1 - u_2\) is

The Eigenvalues of \(3\times 3\) real matrix A are 1, 2, 3 then \(A^{-1} =\)

The directional derivative of \(f(x,y,z)=4e^{2x-y+z}\) at the point \((1,1,-1)\) in the direction of the vector \(\vec{a}=-4\hat{i}+4\hat{j}+7\hat{k}\) is