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

Let $ f : \mathbb{R} \to \mathbb{R} $ be defined by $ f(x) = \dfrac{|x| + |x|}{1 + x^2} $, then the set of points where $ f(x) $ is not differentiable is

Which of the following can’t be an eigenvalue of any Unitary matrix?

A is a $ m \times n $ matrix where $ m>7 $ and $ n>8 $. If all the minors of the 7th order of A vanish and there is a 6th order non-zero minor existing for A, then rank of A is

The coefficient of correlation between x and y is 0.85. If $u = \frac{x+1.5}{12}$ and $v = \frac{y-2.4}{30}$ Then the correlation coefficient between u and v is

If $L^{-1}\left\{\frac{e^{-\pi s}}{s^2+4s+5}\right\} = \begin{cases} 0, & t \le \pi \\ e^{a(t-\pi)}(f(t)), & t>\pi \end{cases}$, then $f(\pi/2)=$

Consider the statements:
I. If a series of positive terms is not convergent, then it is either divergent or oscillatory.
II. In an alternating series, if $lim⁡n→∞∣un∣≠0\lim_{n \to \infty} |u_n| \neq 0$, then it is convergent.
III. In a series of positive terms, if $lim⁡n→∞un=0\lim_{n \to \infty} u_n = 0$, then it may be convergent or divergent.
IV. If $∑∣un∣\sum |u_n|$ is divergent and $∑un\sum u_n$ is convergent, then $∑un\sum u_n$ is conditionally convergent.

Which of the above statement(s) is(are) correct?

The residue of the function $f(z) = \frac{ze^z}{(z-1)^3}$, at its pole is

The general solution of $\frac{\partial u}{\partial x} = 4\frac{\partial u}{\partial y}$, given $u(0,y) = 8e^{-3y}$ is

The general solution of $(D^2 - 2D + 1)y = x^2e^x$ is

The eigenvalues of a $3 \times 3$ matrix A are 1, 3, 7 then the eigenvalues of $\text{adj}(A)$ are

To solve the equation $ x \log x = 1 $, using Newton-Raphson method, the iterative formula and the first approximate $ x_1 $, when $ x_0 = 1 $ is (Assuming $\log$ is natural logarithm $\ln$)

The residue of $ f(z) = \frac{z^2}{(z-1)^3(z-2)(z-3)} $ at the pole $z=1$ is

Mean of a binomial distribution 12 and variance is 8. The probability of having at least one success is?

In large sample, the critical value for the single tailed test at 5% level of significance is?

For a bivariate data $(x_i, y_i)$ ($i=1,2,3,\dots,10$), $\sum x_i y_i = 6200$, $\sum x_i = 400$, $\sum y_i = 1220$, $\sum x_i^2 = 1800$, then equation of line of best fit is?

Let $X$ be a discrete random variable with probability mass function $P(X=x_i)$ where $x \in \{x_1, x_2, \dots, x_n\}$. If $\sum_{i=1}^{n} (x_i-2)^2 P(X=x_i) = 28$ and $\sum_{i=1}^{n} (x_i+2)^2 P(X=x_i) = 12$. Then variance of $X$ is?

If the probability density function of a continuous random variable X is $f(X=x) = Ke^{-3x}$, $0<x<\infty$, then a solution of $\frac{P^2+1}{P} = \frac{K}{\sqrt{2}}$ is?