List of top Mathematics Questions asked in AP EAPCET

If the origin is shifted to a point $ P $ by the translation of axes to remove the $ y $-term from the equation $ x^2 - y^2 + 2y - 1 = 0 $, then the transformed equation of it is:

A line $ L $ intersects the lines $ 3x - 2y - 1 = 0 $ and $ x + 2y + 1 = 0 $ at the points $ A $ and $ B $. If the point $ (1,2) $ bisects the line segment $ AB $ and $ \frac{a}{b} x + \frac{b}{a} y = 1 $ is the equation of the line $ L $, then $ a + 2b + 1 = ? $

The real valued function $ f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) $ defined by $ f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| $ is:

The range of the real valued function $ f(x) =$ $\sin^{-1} \left( \frac{1 + x^2}{2x} \right)$ $+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)$ is:

The number of positive divisors of 1080 is:

Imaginary part of $ \frac{(1 - i)^3}{(2 - i)(3 - 2i)} $ is:

Suppose the axes are to be rotated through an angle $ \theta $ so as to remove the $ xy $ term from the equation $3 x^2 + 2\sqrt{3}xy + y^2 = 0 $. Then in the new coordinate system, the equation $ x^2 + y^2 + 2xy = 2 $ is transformed to:

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

If $ y = \tan(\log x) $, then $ \frac{d^2y}{dx^2} $ is given by:

The square root of $ 7 + 24i $ is:

In the expansion of $\frac{2x+1}{(1+x)(1-2x)}$, the sum of the coefficients of the first 5 odd powers of $x$ is:

If the solution of the system of simultaneous linear equations: $$ x + y - z = 6, $$ $$ 3x + 2y - z = 5, $$ $$ 2x - y - 2z + 3 = 0 $$ is $ x = \alpha, y = \beta, z = \gamma $, then $ \alpha + \beta = ?$

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:

If \[ A = \begin{bmatrix} 1 & 0 & 2\\ 2 & 1 & 3 \\3 & 2 & 4 \end{bmatrix}, \] then evaluate $ A^2 - 5A + 6I $=

Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots \text{ up to 50 terms=} \]

If $ A(1,0,2) $, $ B(2,1,0) $, $ C(2,-5,3) $, and $ D(0,3,2) $ are four points and the point of intersection of the lines $ AB $ and $ CD $ is $ P(a,b,c) $, then $ a + b + c = ? $

If a function $f(x)$ is defined as: $$ f(x) = \begin{cases} \frac{\tan(4x) + \tan 2x}{x} & \text{if } x> 0 \\ \beta & \text{if } x = 0 \\ \frac{\sin 3x - \tan 3x}{x^2} & \text{if } x < 0 \end{cases} $$ and is continuous at $x = 0$, then find $|\alpha| + |\beta|$.

Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin^3 x}{4 - \cos^2 x} dx. \]

If \[ \int \frac{2}{1+\sin x} dx = 2 \log |A(x) - B(x)| + C \] and $ 0 \leq x \leq \frac{\pi}{2} $, then $ B(\pi/4) = $ ?

Evaluate the integral: \[ \int \frac{2x^2 - 3}{(x^2 - 4)(x^2 + 1)} \,dx = A \tan^{-1} x + B \log(x - 2) + C \log(x + 2) \] Given that, \[ 64A + 7B - 5C = ? \]

If $ x, y $ are two positive integers such that $ x + y = 20 $ and the maximum value of $ x^3 y $ is $ k $ at $ x = a, y = \beta $, then $ \frac{k}{\alpha^2 \beta^2} = ? $

The angle between the curves $ y^2 = 2x $ and $ x^2 + y^2 = 8 $ is

In $ \triangle ABC $, if $ a = 13 $, $ b = 14 $, and $ \cos \frac{C}{2} = \frac{3}{\sqrt{13}} $, then $ 2r_1 = $:

If $ 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots $ (n terms) = $ n(n + 1)f(n) - 3n $, then $ f(1) = $:

$\begin{vmatrix} a+b+2c & a & b \\[0.3em] c & b+c+2c & b \\[0.3em] c & a & c+a2b \end{vmatrix}$