List of top Engineering Mathematics Questions asked in Telangana State Post Graduate Engineering Common Entrance Test

If the linear transformation $ X = BY $ transforms $ X^\top AX $ to $ Y^\top PY $, then $ P = $:

Let $ A = \begin{bmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1 \end{bmatrix} $, $ P = \begin{bmatrix} -1 & 1 & 1 \\ 0 & -1 & 2 \\ 1 & 1 & 1 \end{bmatrix} $. Then $ \det(P^{-1} A P - 2I) $ is equal to:

Let $f(x) = \begin{cases} h(x), & 0<x<C \\-h(-x), & -C<x<0 \end{cases}$ and $f(x+2C)=f(x) \; \forall x \in \mathbb{R}$. If the Fourier series of $f(x) = \sum_{n=0}^\infty \left(a_n \cos\frac{n\pi x}{C} + b_n \sin\frac{n\pi x}{C}\right)$ then $\sum_{n=0}^\infty a_n b_n =$

If the characteristic equation of a $3 \times 3$ square matrix A is $ax^3+bx^2+cx+d=0$, $(a \neq 0)$ then the Trace of A + det A =

If $\lambda_1$ and $\lambda_2$ are two distinct eigen values of a symmetric matrix, $X_1$ and $X_2$ are the eigen vectors corresponding to $\lambda_1, \lambda_2$ respectively, then

The real part of an analytic function $ f(z) = u + iv $, where $ v(x, y) = \left( \frac{e^{-y} - e^y}{2} \right) \sin x $, is:

When the IVP $ \frac{dy}{dx} = y + x,\; y(0) = 1 $ is solved by Rung–Kutta fourth order method to find $ y(0.2) $, the approximate value of $ y(0.2) $ by taking step size $ h = 0.2 $ is:

If the probability density function of a continuous random variable $ X $ is $ f(x) $, $ -\infty<x<\infty $, and if the median of $ X $ is $ M $, then:

A card is drawn from a pack of cards successively 5 times by replacing the card drawn in the pack of cards. What is the mean of the number of red cards drawn?

If $ E $ is the region bounded by a closed curve $ C $ in the $ xy $-plane, then $ \iint_E dx\,dy = $

The maximum value of $ f(x, y) = x^2 y^3 (1 - x - y) $ is:

The substitution which reduces the differential equation $ t^2 \frac{d^2y}{dt^2} + 5t \frac{dy}{dt} + 7y = 0 $ to $ \frac{d^2y}{dx^2} + 4 \frac{dy}{dx} + 7y = 0 $ is:

If $ \mathcal{L}(f(t)) = F(s) $, then $ \mathcal{L}((\cosh 2t)f(t)) $ is:

If $f(x)$ is defined on $[a,b]$ and $[a,b]$ is divided into $2n$ equal parts by the points $x_0=a<x_1<x_2<...<x_{2n}=b$. Then by Simpson's $\frac{1}{3}$ rule $\int_a^b f(x)dx =$

Let $\phi(x,y,z) = (x^2+y^2+z^2)^{n/2}$ and $f(x,y,z)=(xyz)^{-n/2}$. Then div Curl grad$\phi$ + (Curl grad $f$) $\cdot$ grad$\phi =$

Particular Integral of $(D^2-4D+4)y = e^x \sin 2x$, $D=\frac{d}{dx}$ is

The probability density function of a continuous random variable X is

The table below gives the values of $ f(x) $ at five equidistant points of $ x $:

x	0	0.5	1.0	1.5	2.0
f(x)	0	0.25	1.0	2.25	4.0

Then the approximate value of $ \int_0^2 f(x) \, dx $ by Trapezoidal Rule is:

If $u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)$, then the value of $ x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} $ is:

Which of the following cannot be the probability mass function of any discrete random variable $X$?

If $2Y - X - 50 = 0$, $3Y - 2X - 10 = 0$ are the two regression equations, then the mean values of the variables $X$ and $Y$ respectively are:

If $ x > 0 $, the series $ x + 2x^2 + 3x^3 + \ldots $ is:

If $ \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} $ is the position vector of a point, then $ \text{curl}(\vec{r}) $ is:

The particular integral of $ (D^2 + 4)y = \cos 3x + \sin 2x $ is:

Laplace transform of $ \frac{e^{-at} - e^{-bt}}{t} $ is: