List of top Questions asked in AP EAPCET

Let \( A(1,2) \) be the centre and 3 be the radius of a circle \( S \). Let \( B(-1, -1) \) be the centre and \( r \) be the radius of another circle \( S_1 \). If \( \frac{\pi}{3} \) is the angle between the circles \( S \) and \( S_1 \), then the number of possible values of \( r \) is:
Evaluate the integral: \[ \int_0^{\frac{\pi}{4}} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \]
The de Broglie wavelength of an electron travelling with 20% of velocity of light is
The equation of the pair of asymptotes of the hyperbola $x^2 - 2y^2 - 8x + 8y + 4 = 0$ is
Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function such that $|f(x)-f(y)| \le 2|x-y|^{3/2} \ \forall x,y \in \mathbb{R}$. If $f(0)=1$, then $\int_0^1 f^2(x)dx=$
Find A and B
oxide of nitrogen
A body of mass 2 kg is on an inclined plane of inclination 30° and coefficient of friction is $ \frac{1}{\sqrt{3}} $. The minimum force required to move the body up the inclined plane is: \[ \text{(Acceleration due to gravity = 10 ms}^{-2}\text{)} \] Options:
With respect to air, the critical angle in a medium for red light of wave length $ \lambda_1 $ is $ \theta $. Other facts remaining same, the critical angle for yellow light of wave length $ \lambda_2 $ will be Options:

Two charges +q and -q, each 1 $\mu$C are arranged as shown in the figure. If x = 2 cm and y = 3 cm then potential difference ($V_A - V_B$) is

Match the following.

If Young’s modulus of elasticity is $Y = \dfrac{2mg l^2}{5b t e}$, where ‘g’ is the acceleration due to gravity, ‘m’ is the mass, ‘l’ is the length, ‘b’ is the breadth, ‘t’ is the thickness and ‘e’ is the elongation, then the value of $k$ is

Two particles of masses 2 kg and 4 kg are separated by a distance of 3 m. The moment of inertia of the system of the two particles about an axis passing through the centre of mass of the system and perpendicular to the line joining the two particles is
In aqueous solutions, the strongest reducing agents in Group 1 and Group 2 elements of the periodic table respectively are
Nucleotides in RNA are joined by which of the following phosphodiester linkages?
The line \( x + y = k \) meets the curve \( x^2 + y^2 - 2x - 4y + 2 = 0 \) at two points \( A \) and \( B \). If \( O \) is the origin and \( \angle AOB = 90^\circ \), then the value of \( k \) (\( k>1 \)) is
Let the circle \( S \) be concentric with the circle \( x^2 + y^2 - 2x + ky + 4 = 0 \). If one of the diameters of \( S \) lies along the line \( 3x - 2y + 4 = 0 \) and the length of the diameter is 6, then the radius of the circle \( S \) is
IUPAC name of the following molecule is
4-Bromo-6-chloro-3,7-diethylnon-7-en-1-yn-5-one
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
If \[ \frac{d}{dx}\left( \frac{x^2}{(x+2)(2x+3)} \right) = \frac{-A}{(x+2)^2} + \frac{B}{(2x+3)^2}, \] then the value of \( A + B = \):
In a Carnot engine, if the temperatures of the source and sink are both decreased by 100 K, the efficiency:
The electrolyte used in mercury cell is
If the roots of the equation \( 3x^2 + 4kx + 3 = 0 \) are non-real, then \( k \) lies in the interval:
If \( f(x) \) is a function such that \( f'(x) = \sqrt{f^2(x) - 1} \) and \( f(0) = 1 \), then \( f(1) = \):
The density of a substance is 4 g/cc. In a system in which the unit of length is 5 cm and the unit of mass is 20 g, the density of the substance is:
The product of an amine 'X' with benzene sulphonyl chloride produces the product which is insoluble in alkali. The product of 'X' with ethanoyl chloride is: