List of top Questions asked in AP EAPCET

E, m, L, G represent energy, mass, angular momentum and gravitational constant respectively. The dimensions of \[ \frac{EL^2}{mG^2} \] will be that of 

The general solution of the differential equation \[ (y^2 + x + 1) dy = (y + 1) dx \] is: 

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

The sum of the order and degree of the differential equation: \[ \frac{d^y}{dx^t} = c + \left( \frac{d^y}{dx^t} \right)^{\frac{3}{2}} \] 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 the function f(x) = \(\sqrt{x^2 - 4}\)  satisfies the Lagrange’s Mean Value Theorem on \([2, 4]\), then the value of \( C \) is} 

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 

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: 

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

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 limit: \[ \lim_{x \to 1} \frac{\sqrt{x} - 1}{(\cos^{-1} x)^2} =\] 

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sqrt{1 + \sqrt{1 + x^4}} - \sqrt{2 + x^5 + x^6}}{x^4} =\]

The distance from a point \( (1,1,1) \) to a variable plane \(\pi\) is 12 units and the points of intersections of the plane with X, Y, Z-axes are \( A, B, C \) respectively. If the point of intersection of the planes through the points \( A, B, C \) and parallel to the coordinate planes is \( P \), then the equation of the locus of \( P \) is: 

The direction cosines of two lines are connected by the relations \( 1 + m - n = 0 \) and \( lm - 2mn + nl = 0 \). If \( \theta \) is the acute angle between those lines, then \( \cos \theta = \) ?