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

Given the probability density function $ f(X=x)= \begin{cases} 0, & x<2 \\ \frac{3+2x}{18}, & 2\leq x\leq4 \\ 0, & x>4 \end{cases} $ then the probability that X lies between 2 and 3 is

If the chance that a bus arrives safely at a bus stand is $ \frac{9}{10} $, then the probability that out of 5 buses at least 4 will arrive safely is

If $a = 2024$, $b = 2023$, and $c = 2022$, then the determinant \[ \begin{vmatrix} \log_a a & \log_a b & \log_a c \\ \log_b a & \log_b b & \log_b c \\ \log_c a & \log_c b & \log_c c \end{vmatrix} \] is:

The value of $\int_0^\infty e^{-x^2} \, dx$ is:

The necessary condition for the equation $ M(x,y)dx + N(x,y)dy = 0 $ to be exact is

If Rolle’s theorem is applied for $ f(x) = x^3 - x $ in $ [-1,1] $, then the values of ‘c’ of this theorem are:

Let $A$ be a $3 \times 3$ matrix. If $\lambda_1, \lambda_2, \lambda_3$ are the eigenvalues of $A$, then the eigenvalues of the matrix $(I + aA)^{-1}(I + bA)$, where $a, b$ are scalars such that $a \lambda_i \neq -1$ and $b \lambda_i \neq -1$ for $i = 1, 2, 3$, are:

The system of equations $ \begin{bmatrix} -2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix} $ has

If $ \begin{bmatrix} \frac{1}{\sqrt{3}} & \frac{1+i}{\sqrt{3}} \\ \frac{1-i}{\sqrt{3}} & \frac{K}{\sqrt{3}} \end{bmatrix} $ is a unitary matrix, then the sum of all possible values of K is

$ \int_{0}^{2} \int_{0}^{\sqrt{y}} e^{y/x} dx dy = $

Two numbers are drawn simultaneously from the set of integers from 1 to 12. If it is known that the sum of drawn two numbers is odd, then the probability that only one of the two numbers is a prime number, is

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

In a communication network, 98% of messages are transmitted correctly with no error. If the random variable X denotes the number of messages transmitted with error, then the probability that at most two messages are transmitted with error out of 1000 messages sent, is

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 $\ln$)

Let $ \vec{F} $ be a vector point function defined inside and on the surface (S) of the sphere $ x^2+y^2+z^2=1 $. Then $ \oint_S (\text{Curl} \vec{F}) \cdot \hat{n} ds = $

The complete solution of $ (mz-ny)\frac{\partial z}{\partial x} + (nx-lz)\frac{\partial z}{\partial y} = ly-mx $ is

Which of the following pair of functions are linearly dependent

The probability density function is given by $ f(x) = \begin{cases} C(x-1), & \text{for } 1<x<4 \\ 0, & \text{otherwise} \end{cases} $. Find $P(2<X<3)$.

Consider the linear system of non homogeneous equation in three variables AX = B. $\rho(A)$ and $\rho([A:B])$ are roots of the equation $x^2+bx+c=0$. AX = B has infinite number of solutions, then the option containing two possible pairs of values of (b,c) is (Note: $\rho$ denotes rank.)

Which of the following is a convergent series?

Consider the following problem of vibration of a string. A tightly stretched string with fixed end points $x=0$ and $x=L$ is initially in a position given by $y(x,0) = f(x)$. It is released from this rest position and allowed to vibrate. The mathematical representation of this problem which depicts the displacement of the string $y(x,t)$ at different times for different values of $x, 0 \le x \le L$ is

A and B are two nonsingular matrices. If the characteristic equation of A is $ a_0\lambda^3 + a_1\lambda^2 + a_2\lambda + a_3 = 0 $ and characteristic equation of $ B^{-1}AB $ is $ b_0\lambda^3 + b_1\lambda^2 + b_2\lambda + b_3 = 0 $, then