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 _______}

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

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 _______}

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 _______}

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 $P(A \cup B) = \_\_\_\_\_\_\_$

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