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Telangana State Post Graduate Engineering Common Entrance Test
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Engineering Mathematics
List of top Engineering Mathematics Questions asked in Telangana State Post Graduate Engineering Common Entrance Test
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
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Matrix
The maximum area of a rectangle that can be inscribed in a circle of radius $R$ is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
3D Geometry
The value of the integral \[ \int_C \frac{2e^z}{(z-4)(z-2)} \, dz \] where \( C: |z| = 3 \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Complex numbers
A continuous random variable \(X\) has a probability density function \( f(x) = 3x^2, \ 0 \leq x \leq 1 \). If \( P(X \leq a) = P(X>a) \), then the value of 'a' is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Probability and Statistics
If the random variable \( X \) takes the values 1, 2, 3, and 4 such that \( 2P(X=1) = 3P(X=2) = P(X=3) = 5P(X=4) \), then the mean of \( X \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Probability and Statistics
The divergence of the vector field \( \vec{F} = yz\,\hat{i} - zx\,\hat{k} \) at \( (-2, 0, 1) \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Vectors
The particular integral of \( \frac{d^2y}{dx^2} + y = \cos(2x - 1) \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Differential Equations
The value of \( \int_0^1 \int_y^{\sqrt{y}} yx \, dxdy \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Calculus
The equation \( x^3 - 6x - 4 = 0 \) has one real root between 2 and 3. The 2ndapproximation to the root of the equation by bisection method will be
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Numerical Methods
The Laplace transform \( \mathcal{L}\{t^2 \sin 2t\} \) is
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Laplace transforms
The approximate solution of the initial value problem \( \frac{dy}{dx} = 1 + xy \), \( y(0) = 1 \) by Picard’s method will be
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Differential Equations
Evaluate \( \log_{e^{2000}} e^{2021} \cdot \log_{e^{2021}} e^{2022} \cdot \log_{e^{2022}} e^{2023} \cdot \log_{e^{2023}} e^{2024} \)
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Linear Algebra
If the characteristic polynomial of the matrix \( A_{3\times3} \) is given by \( f(\lambda) = \lambda^3 - 10\lambda^2 + 27\lambda - 18 \), then trace of A and determinant of A respectively are
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Linear Algebra
If the equations $x^2+2x+K=0$ and $x^2+Kx+2=0$ have one root in common, then the product of the other two roots is?
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Linear Algebra
If $b_{yx}$ and $b_{xy}$ are regression coefficients and they are equal, then?
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Probability and Statistics
If $$ A = \begin{pmatrix} 3 & -2 \\ 4 & -2 \end{pmatrix} $$ satisfies the matrix equation $$ A^2 - K A + 2I = 0, $$ then the value of $ K $ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Linear Algebra
Given $$ x = 4y + 5, \quad y = Kx + 4, $$ the lines of regression of $ x $ on $ y $ and $ y $ on $ x $ respectively. What is the value of $ K $, if the value of correlation coefficient $ r = 0.5 $?
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Statistics
If $ X $ is a Poisson variate such that $ P(X=1) = \frac{3}{10} $ and $ P(X=2) = \frac{1}{5} $, then the mean of the distribution is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Probability
Compute the Jacobian $ \frac{\partial(x,y)}{\partial(u,v)} $ of the transformation: $$ x = \frac{u+v}{1 - uv}, \quad y = \tan^{-1} u + \tan^{-1} v $$
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Calculus
The value of $$ \int_0^1 x^4 (1 - x)^2 \, dx $$ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Calculus
The Newton-Raphson iteration $$ x_{n+1} = \frac{1}{3} \left( 2 x_n + \frac{N}{x_n^2} \right) $$ is used to compute
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Numerical Methods
The unit normal vector to the level surface $$ x^2 y + 2 x z = 4 $$ at the point $ (2, -2, 3) $ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Vector Calculus
The particular integral of $$ (x^2 D^2 + 4 x D + 2) y = x^2 $$ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Differential Equations
The general solution of the differential equation $$ (D^2 - 5D + 6) y = e^{3x} $$ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Differential Equations
If $$ A = \frac{1}{2} \begin{pmatrix} -1 & 1 & 1 & 1 \\ 1 & -1 & 1 & 1 \\ 1 & 1 & -1 & 1 \\ 1 & 1 & 1 & -1 \end{pmatrix}, $$ then the inverse of $ AA^T $ is:
TS PGECET - 2024
TS PGECET
Engineering Mathematics
Linear Algebra
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