List of top Mathematics Questions asked in TS PGECET

If $A = \begin{bmatrix} 2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2 \end{bmatrix}$ and $P = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 2 \\ 0 & 1 & 5 \end{bmatrix}$, then $\left|P^{-1}AP - 2I\right| =$}

A function satisfying the conditions of Lagrange's mean value theorem on the interval $[1, 5]$ is:

The system of equations $2x + y = 2z$, $y + z = 0$, $3y + \alpha z = x$ has:

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

If a random variable \( X \), defined such that \( E(X-1)^2 = 10 \) and \( E(X-2)^2 = 6 \) then mean \( (\mu) \) and variance \( (\sigma^2) \) are

Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)

If the particular integral of \( y'' - 4y' = x^2 e^{2x} \) is in the form \( y_p = e^{2x} y(x) \), then \( y(x) \) is

\( \mathcal{L}\{ \sin(t-3)u(t-3) \ = \)}

If \( f \) and \( g \) are the solutions of Laplace equation then \( \nabla \cdot \{(f \nabla g) - (g \nabla f)\ = \)}

Let the matrix \( A = \begin{bmatrix} 1 & 4 \\ 2 & -1 \end{bmatrix} \).
Statement-I: \( A^2 = 9I \)
Statement-II: The eigen values of \( A \) are \( -3 \) and \( 3 \)
The correct answer is

If \( \lambda_1, \lambda_2 \) and \( \lambda_3 \) are the eigen values of a square matrix \( A \), then the eigen values of \( A^{-1} + 2I + A \) are

If $f(x)$ is the probability density function of an exponential distribution and $\frac{1}{\lambda}$ is its mean, then $\int_0^\infty x^2 f(x) \, dx =$}

The solution of $\frac{dy}{dx} - y - 2x + x^2 = 0$, $y(0) = 1$ at $x = 0.2$ using Euler's method is:

By assuming that the solution to the equation $x^4 - x - 10 = 0$ lies between $x = 1.8$ and $x = 2$, then the next approximate solution by Regula-falsi method is (Take $f(1.8) = -1.3024$):

Two dice are thrown simultaneously. Let $X$ be the random variable representing the absolute difference of the numbers appeared on the dice. The mean of $X$ is:

A function satisfying the conditions of Lagrange's mean value theorem on the interval $[1, 5]$ is:

The value of $\oint_C x \, dy - y \, dx$, where $C$ is the boundary of the rectangular region formed by $x = 5$, $x = 12$, $y = 0$, and $y = 8$ is:

Laplace transform of $\int_0^t u^2 \sin(t - u) \, du$ is:

If the integrating factor of $\frac{dy}{dx} + \left[(x^2 - 2x)\cos x + 2(x - 1)\sin x\right]y = x^2$ is $e^{f(x)}$, then $f(3) =$}

The system of equations $2x + y = 2z$, $y + z = 0$, $3y + \alpha z = x$ has:

If $A = \begin{bmatrix} 2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2 \end{bmatrix}$ and $P = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 2 \\ 0 & 1 & 5 \end{bmatrix}$, then $\left|P^{-1}AP - 2I\right| =$}

If a random variable \( X \), defined such that \( E(X-1)^2 = 10 \) and \( E(X-2)^2 = 6 \) then mean \( (\mu) \) and variance \( (\sigma^2) \) are

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)

The Laurent's series for the function \( f(z) = 1 + \frac{3{z+2} - \frac{8}{z+3} \) in the region \( |z| < 2 \) is}