List of top Questions asked in AP EAMCET

The equation of one side of an equilateral triangle is \( x + y = 2 \), and one vertex is \( (2,-1) \). The length of the side is:
From a point \( (1,0) \) on the circle \( x^2 + y^2 - 2x + 2y + 1 = 0 \), if chords are drawn to this circle, then locus of the poles of these chords with respect to the circle \( x^2 + y^2 = 4 \) is:
If A and B are the centres of similitude with respect to the circles \( x^2 + y^2 - 14x + 6y + 33 = 0 \) and \( x^2 + y^2 + 30x - 2y + 1 = 0 \), then midpoint of \( AB \) is:
If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
If the perpendicular distance from \( (1,2,4) \) to the plane \( 2x + 2y - z + k = 0 \) is 3, then \( k \) is:
If \( f(x) = \left(\frac{1+x}{1-x}\right)^{\frac{1}{x}} \) is continuous at \( x = 0 \), then \( f(0) \) is:
The function \( f(x) = |x - 24| \) is:
The value \( c \) of Lagrange’s Mean Value Theorem for \( f(x) = e^x + 24 \) in \( [0,1] \) is:
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.
If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]
Evaluate the integral: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \,dx. \]
Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]
The general solution of the differential equation: \[ (1 + \tan y) (dx - dy) + 2x \, dy = 0. \]
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{4 \cos^2 x + 3 \sin^2 x} dx \):
The sum of the order and degree of the differential equation: \[ x \left( \frac{d^2 y}{dx^2} \right)^{1/2} = \left( 1 + \frac{dy}{dx} \right)^{4/3} \] is:
A body thrown vertically upwards reaches a maximum height \( H \). The ratio of the velocities of the body at heights \( \frac{3H}{4} \) and \( \frac{8H}{9} \) from the ground is:
The equation of projectile motion is given by \( y = 3x - 0.8x^2 \). The time of flight of the projectile is (Acceleration due to gravity \( g = 10 \) m/s²):
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity \( g = 10 \) ms\(^{-2}\)):
A satellite moving around the Earth in a circular orbit has kinetic energy \( E \). Then, the minimum amount of energy to be added so that it escapes from the Earth is:
A metal ball of mass 100 g at \( 20^\circ C \) is dropped in 200 ml of water at \( 80^\circ C \). If the resultant temperature is \( 70^\circ C \), then the ratio of specific heat of the metal to that of water is:
An ideal gas is taken around ABCA as shown in the P-V diagram. The work done during a cycle is:
An ideal gas is taken
The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is:
The vibrations of four air columns are shown below. The ratio of frequencies is:
The vibrations of four air columns
A neutral ammonia (NH\(_3\)) molecule in its vapour state has an electric dipole moment of magnitude \( 5 \times 10^{-30} \) C·m. How far apart are the molecule's centers of positive and negative charge?