List of top Mathematics Questions asked in AP EAPCET

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:

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 $|\alpha| + |\beta|$.

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \] is:

Find the area of the region (in square units) enclosed by the curves: \[ y^2 = 8(x+2), \quad y^2 = 4(1-x) \] and the Y-axis.

Evaluate the integral: $$ I = \int_{\frac{1}{\sqrt[5]{32}}}^{\frac{1}{\sqrt[5]{31}}} \frac{1}{\sqrt[5]{x^{30} + x^{25}}} \, dx. $$

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

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

If \[ \int \frac{3}{2\cos 3x \sqrt{2} \sin 2x} dx = \frac{3}{2} (\tan x)^{\beta} + \frac{3}{10} (\tan x)^4 + C \] then $ A = $ ?

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: \[ I = \int \frac{\cos x + x \sin x}{x (x + \cos x)} dx =\]

Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]

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} = ? $

If the function f(x) = $\sqrt{x^2 - 4}$ satisfies the Lagrange’s Mean Value Theorem on $[2, 4]$, then the value of $ C $ is}

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

If $ T = 2\pi \sqrt{\frac{L}{g}} $, $ g $ is a constant and the relative error in $ T $ is $ k $ times to the percentage error in $ L $, then $ \frac{1}{k} = $ ?

If $ y = x - x^2 $, then the rate of change of $ y^2 $ with respect to $ x^2 $ at $ x = 2 $ is:

For $ x<0 $, $ \frac{d}{dx} [|x|^x] $ is given by:

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

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) = $:

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

Assertion (A): If $ B $ is a $ 3 \times 3 $ matrix and $ |B| = 6 $, then $ | \text{Adj}(B) | = 36 $. Reason (R): If $ B $ is a square matrix of order $ n $, then $ |\text{Adj}(B)| = |B|^n $.