List of top Questions asked in AP EAMCET

The horizontal range of a projectile projected at an angle of \( 45^\circ \) with the horizontal is 50 m. The height of the projectile when its horizontal displacement is 20 m is:
The centripetal acceleration of a particle in uniform circular motion is \( 18 \, {ms}^{-2} \). If the radius of the circular path is \( 50 \) cm, the change in velocity of the particle in a time of \( \frac{T}{18} \) is:
An object is projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of 8 s and the object reaches the foot after 16 s. The height of the tower is (Given \( g = 10 \, m/s^2 \))
The time period of revolution of a satellite (\( T \)) around the earth depends on the radius of the circular orbit (\( R \)), mass of the earth (\( M \)) and universal gravitational constant (\( G \)). The expression for \( T \), using dimensional analysis, is (where \( K \) is a constant of proportionality):
The solution of the differential equation \[ (x + 2y^3) \frac{dy}{dx} = y \] is:
If \[ y = a e^{bx} + c e^{dx} + x e^{bx} \] is the general solution of a differential equation, where \( a \) and \( c \) are arbitrary constants and \( b \) is a fixed constant, then the order of the differential equation is:
The differential equation formed by eliminating \( a \) and \( b \) from the equation \[ y = ae^{2x} + bxe^{2x} \] is:
The area of the region under the curve \( y = |\sin x - \cos x| \) in the interval \( 0 \leq x \leq \frac{\pi}{2} \), above the x-axis, is (in square units):
If \[ \int_{1}^{n} f(x) \,dx = 120, \] then \( n \) is:
If \[ f(x) = \begin{cases} \frac{6x^2 + 1}{4x^3 + 2x + 3}, & 0 < x < 1 \\ x^2 + 1, & 1 \leq x < 2 \end{cases} \] then \[ \int_{0}^{2} f(x) \,dx = ? \]
Evaluate the limit: \[ \lim_{n \to \infty} \frac{17^7 + 27^7 + \dots + n^{77}}{n^{78}}. \]
If \( n \geq 2 \) is a natural number and \( 0<\theta<\frac{\pi}{2} \), then \[ \int \frac{(\cos^n \theta - \cos \theta)^{1/n}}{\cos^{n+1} \theta} \sin \theta \, d\theta = \]
If \[ 729 \int_1^3 \frac{1}{x^3 (x^2 + 9)^2} \, dx = a + \log b, \] then \( a - b = \) ?
If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of \( \frac{\pi}{4} - \beta \) is:
Evaluate the integral: \[ \int e^x \left( \frac{x + 2}{(x+4)} \right)^2 dx. \]
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 = ?
An organic compound (X) has an empirical formula C\(_4\)H\(_8\)O. This gives a pale yellow precipitate with iodine in NaOH solution. What is X?