List of top Mathematics Questions asked in AP EAMCET

If \( x \notin \left[ 2n\pi - \frac{\pi}{4}, 2n\pi + \frac{3\pi}{4} \right] \) and \( n \in \mathbb{Z} \), then \[ \int \sqrt{1 - \sin 2x} \, dx = \]
The number of all the values of \( x \) for which the function \[ f(x) = \sin x + \frac{1 - \tan^2 x}{1 + \tan^2 x} \] attains its maximum value on \( [0, 2\pi] \).
If Rolle’s theorem is applicable for the function \( f(x) \) defined by \( f(x) = x^3 + Px - 12 \) on \( [0,1] \), then the value of \( C \) of the Rolle's theorem is:
If \( f(x) = x^x \), then the interval in which \( f(x) \) decreases is:
The point which lies on the tangent drawn to the curve \( x^4 e^y + 2 \sqrt{y} + 1 = 3 \) at the point \( (1,0) \) is:
Which one of the following is false?
If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
The rate of change of \( x^{\sin x} \) with respect to \( (\sin x)^x \) is:
If \[ \lim\limits_{x \to \infty} \frac{\left(\sqrt{2x+1} + \sqrt{2x-1}\right) + \left(\sqrt{2x+1} - \sqrt{2x-1}\right) P x^4 - 16} {(x+\sqrt{x^2 - 2}) + (x - \sqrt{x^2 - 2})} = 1, \] then P = ?
The general solution of the differential equation: \[ (1 + \tan y) (dx - dy) + 2x \, dy = 0. \]
The general solution of the differential equation: \[ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. \]
Evaluate the integral: \[ I = \int \frac{\sin 7x}{\sin 2x \sin 5x} \,dx. \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]
Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]
The area (in square units) bounded by the curves \( x = y^2 \) and \( x = 3 - 2y^2 \) is:
Evaluate the integral: \[ I = \int \frac{1}{x^2\sqrt{1 + x^2}} \,dx. \]
Evaluate the integral: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \,dx. \]
Evaluate the integral: \[ I = \int \frac{2}{1 + x + x^2} \,dx. \]
Displacement \( s \) of a particle at time \( t \) is expressed as \( s = 2t^3 - 9t \). Find the acceleration at the time when the velocity vanishes.
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
Evaluate the integral: \[ \int \frac{x^3 \tan^{-1}(x^4)}{1 + x^8} \,dx. \]
Equation of the normal to the curve \( y = x^2 + x \) at the point \( (1,2) \) is:
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
The orthocentre of triangle formed by points: \( (2,1,5) \), \( (3,2,3) \) and \( (4,0,4) \) is: