List of top Questions asked in AP EAPCET

Two forces of magnitude 4 N act on an object of mass 1 kg: \( \vec{F}_1 \) at 30° to x-axis and \( \vec{F}_2 \) along y-axis. Find the magnitude of acceleration.
A ball follows the vertical displacement \( y = (Pt^2 - Qt^3) \), where \( y \) is in meters. Find the maximum height the ball can reach.
A cricket ball of mass 50 g and velocity 50 cm/s is stopped in 0.5 s. What is the force applied?
Two masses \( M_1 \) and \( M_2 \) are arranged as shown. If \( a \) is the acceleration of the system, and \( M_1 \) is doubled, \( M_2 \) halved, then new acceleration is:
Two masses M1 and M2 are arranged as shown
A ball of mass 300 g is dropped from a height of 10 m and penetrates 1.5 m into sand. Find the average resistance by the sand. Take \( g = 10\ \text{m/s}^2 \).
Evaluate: \( \int \frac{1 + \tan x \tan(x + \alpha)}{\tan x \tan(x + \alpha)} dx \):
If \( I_a = \int_0^{\pi/4} \tan^n x \, dx \), then \[ \frac{1}{I_2 + I_4} + \frac{1}{I_3 + I_5} + \frac{1}{I_4 + I_6} = \]
Evaluate: \[ \int_{0}^{\pi/4} e^{\tan^2 \theta} \sin^2 \theta \tan \theta \, d\theta = \]
Evaluate: \[ \int_{\pi/4}^{5\pi/4} \left(\cos t |\sin t| + \sin t |\cos t|\right) dt = \]
If \( f(x) = \max(\sin x, \cos x) \) and \( g(x) = \min(\sin x, \cos x) \), then \[ \int_0^{\pi/2} f(x) dx + \int_0^{\pi/2} g(x) dx = \]
If \( l \) and \( m \) are the order and degree of the differential equation of all the straight lines at constant distance \( P \) units from the origin, then \[ lm^2 + l^2 m = \]
If \( 2x - y + c \log(|x - 2y - 4|) = k \) is the general solution of \[ \frac{dy}{dx} = \frac{2x - 4y - 5}{x - 2y + 2} \] then \( c = \):
By eliminating the arbitrary constants from \[ y = (a + b)\sin(x + c) - de^{x + te^t} \] the differential equation obtained is of order:
If the straight line \( x\cos\alpha + y\sin\alpha = p \) touches the curve \( \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \) at the point (a, b), and \( \frac{1}{a^2} + \frac{1}{b^2} = \frac{k}{p^2} \), then \( k = \):
Condition that two curves \( y^2 = 4ax \) and \( xy = c^2 \) cut orthogonally is:
A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is:
Two particles P and Q located at the points \( P(t, t^3 - 16t - 3) \), \( Q(t+1, t^3 - 6t - 6) \) are moving in a plane. The minimum distance between the points in their motion is:
If \( f(x) = \int_{x^2}^{\cos^2 x} (2x \tan^2 x - 2x - 6 \tan x) dx \), and \( f(0) = \pi \), then \( f(x) = \):
If \( \int e^{\sqrt{x}} / \sqrt{x} (x + \sqrt{x}) dx = e^{\sqrt{x}}[Ax + B\sqrt{x} + C] + K \), then \( A + B + C = \):
If \( \int \frac{1 + \sqrt{\tan x}}{\sin 2x} dx = A \log \tan x + B \tan x + C \), then \( 4A - 2B = \):
If $[\cdot]$ denotes greatest integer function, then $\lim_{x \to 3} \dfrac{[-x]}{x} =$
If $l, m$ $(l<m)$ are roots of $ax^2 + bx + c = 0$, then $\lim_{x \to a} \left| \dfrac{ax^2 + bx + c}{ax^2 + bx + c} \right|$ =
If $x \neq 0$ and $f(x)$ satisfies $8f(x) + 6f\left(\dfrac{1}{x}\right) = x + 5$, then $\dfrac{d}{dx} \left(x^2 f(x)\right)$ at $x = 1$ is
Calculate $\dfrac{d}{dx} \left(\lim_{y \to 2} \dfrac{1}{y-2} \left(\dfrac{1}{x} - \dfrac{1}{x+y-2}\right)\right)$
The number of those tangents to the curve $y^2 - 2x^3 - 4y + 8 = 0$ which pass through the point $(1, 2)$ is