List of top Mathematics Questions asked in AP PGECET

To find the root of the equation $f(x) \equiv e^{-x} - x = 0$, the Newton-Raphson method is used. If the initial guess for the root is 1, then the estimate of the root after first iteration is _______}

A unit vector which is perpendicular to the surface of the paraboloid of revolution $z = x^2 + y^2$ at the point (1,2,5) is

If $y(x) = C_1 \cos 2x + C_2 \sin 2x + A(x) \log (\sec 2x + \tan 2x)$ is the general solution of the differential equation $\frac{d^2y}{dx^2} + 4y = \tan 2x$, then $A(x) = \_\_\_\_\_\_\_$}

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A}) = 0.3$, $P(B) = 0.4$ and $P(A \cap \bar{B}) = 0.5$, then $P(A \cup B) = \_\_\_\_\_\_\_$

A function $y(x)$ such that $y(0) = 1$ and $y(1) = 4e$ is a solution of the differential equation $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$. Then, $y(2)$ is equal to _______}

The residue of $f(z) = e^{-1/z}$ at $z = 0$ is}

The variance of the Binomial distribution with probability mass function $p(x) = {}^{15}C_x \left(\frac{2}{3}\right)^x \left(\frac{1}{3}\right)^{15-x}$, $x = 0,1,\dots,15$, is _______}

The number of values of $k$ for which the following system of linear equations: \[ \begin{pmatrix} 4 & k & 2\\ k & 4 & 1\\ 2 & 2 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} \] possess a non-zero solution, is _______

Let $A$ be a $2 \times 2$ matrix such that $\text{trace}(A) = \det(A) = a (a \neq 0)$. Then the trace of $A^{-1}$ is}

The value of $\int_0^{\infty} \int_0^{\infty} e^{-(x^2+y^2)} dx dy$ is}

A number is selected randomly from each of the following two sets:
{1, 2, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8, 9}
What is the probability that the sum of the numbers is 9?

The ratio of the ages of A and B is 5:3. After 6 years, their ages will be in the ratio 6:4. What is the current age of A?

Consider the system of equations:
\[ x + 2y - z = 3 \\ 2x + 4y - 2z = 7 \\ 3x + 6y - 3z = 9 \]
Which of the following statements is true about the system?

Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?

Determine the value of $\lambda$ and $\mu$ for which the system of equations
$x + 2y + z = 6$,
$x + 4y + 3z = 10$,
$2x + 4y + \lambda z = \mu$
has a unique solution.

Let \( z \) be a complex variable and \( C : |z| = 3 \) be a circle in the complex plane. Then,

\[ \oint_C \frac{z^2}{(z - 1)^2(z + 2)} \, dz = \]

If the matrix \[ A = \begin{pmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{pmatrix} \] has three distinct eigenvalues, and one of its eigenvectors is \[ \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}, \] then which of the following can be another eigenvector of \( A \)?

Which of the options correctly represents the Laplace inverse of \( \dfrac{2}{s^3} \)?

The probability of a component being defective is 0.01. There are 100 such components in a machine. Then the probability of two or more defective components in the machine is ...........

If the Laplace transform of a function \( f(t) \) is given by \[ \frac{2s + 1}{(s + 1)(s + 2)} \] then \( f(0) \) is equal to ______

Consider the ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0 \] with \( y(x) \) as a general solution. Given the values of \( y(1) = 1 \), \( y(2) = 5 \), the value of \( y(3) \) is equal to ______

The solution of the differential equation
\[ (D^3 - 5D^2 + 7D - 3)y = e^{-2x} \] is:

The given differential equation
$(x y^2 + n x^2 y) dx + (x^3 + x^2 y) dy = 0$ is exact when $n =$

Let $X$ be an exponential random variable with mean parameter one. Then the conditional probability $P(X>10 | X>5)$ is equal to