List of top Mathematics Questions asked in AP EAPCET

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The value of \(c\) of Lagrange's Mean Value Theorem for \[ f(x)=\sqrt{25-x^2} \] on \([1,5]\) is:

If the system of linear equations $x + y + z = 1$, $x + 2y + 4z = \eta$, $x + 4y + 10z = \eta^2$ has a solution, then the value of $\eta$ is:

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $A^{-1} =$

The function \[ f(x)=2x+\cot^{-1}x+\log\!\left(\sqrt{1+x^2}-x\right) \] is

The sum \(S_n\) of the first \(n\) terms of the series \[ 1^2+2\times 2^2+3^2+2\times 4^2+5^2+2\times 6^2+\cdots \] is given by

If the system of linear equations $x + y + z = 1$, $x + 2y + 4z = \eta$, $x + 4y + 10z = \eta^2$ has a solution, then the value of $\eta$ is:

If \( \theta_1 \) and \( \theta_2 \) are the values of \( \theta \in (0,\pi) \) for which the system of linear equations \[ x+3y+7z=0, \] \[ -x+4y+7z=0, \] \[ (\sin 3\theta)x+(\cos 2\theta)y+2z=0 \] has a non-trivial solution, then \( |\theta_1-\theta_2| \) is equal to

If \(f:(-\infty,0)\to \mathbb{R}\) is defined by \[ f(x)=\frac{[x]}{|x|} \] then \(f(x):x\in(-\infty,0)\) is:

Evaluate: \[ \lim_{x\to \frac{\pi}{3}} \frac{\tan^3x-3\tan x} {\cos\left(x+\frac{\pi}{6}\right)} \]

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is 255, then $d =$

The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

If \[ \log_a 2+\log_a 5=1, \] then the value of \(a\) is:

If the normal drawn to the curve \(y^4=16x^3\) at the point of intersection of this curve and the line \(y=2\) meets the \(X\)- and \(Y\)-axes at \(A\) and \(B\) respectively, then \(OA+3OB=\)

If $f(x) = \sqrt{3}\sin x - \cos x - 2ax + b$ decreases for all $x \in \mathbb{R}$, then:

If \[ \int \frac{2\cos x+3\sin x} {3\cos x+4\sin x}\,dx = Ax+B\log|3\cos x+4\sin x|+C, \] then \[ A\cdot B= \]

The slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is:

If $^{n}C_{12} = ^{n}C_{8}$, then $^{n}C_{17} =$

If the equation of a line passing through \[ \left(\frac13,-\frac12\right) \] and making an angle of \(60^\circ\) with the line \[ 2x-3y+4=0 \] is \[ (2+3\sqrt3)x+by=c, \] then \(c=\)

If \(A\), \(B\), \(C\) are independent events of a random experiment such that \[ P(A)=\frac34,\qquad P(B)=\frac56,\qquad P(C)=\frac23, \] then the probability that exactly one of the events occurs is

The order and degree of the differential equation \[ \left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2} = \frac{d^2y}{dx^2} \] are respectively

If $\int x^5 e^{-4x^3} dx = \frac{1}{48}e^{-4x^3} f(x) + c$, then $f(x) =$

If $\alpha, \beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^n + \beta^n$ is:

If the angles of a triangle are in the ratio 4: 1: 1, then the ratio between its largest side and its perimeter is

The origin is shifted to the point \((1,1)\) by translation of axes and then the axes are rotated through an angle \[ \frac{\pi}{3} \] about \((1,1)\) in the positive direction. After these two transformations, if the point \[ P(3,2) \] becomes \(P(\alpha,\beta)\), then \[ 4\alpha+2\beta= \]