List of top Questions asked in AP EAMCET

If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done is:
The de Broglie wavelength of a particle of mass 1 mg moving with a velocity of \( 10 \) ms\(^{-1}\) is (h = \( 6.63 \times 10^{-34} \) Js)
The rate of change of \( x^{\sin x} \) with respect to \( (\sin x)^x \) is:
If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]
If the slope of one of the pair of lines represented by \( 2x^2 + 3xy + Ky^2 = 0 \) is 2, then the angle between the pair of lines is:

If the circle S = 0 cuts the circles x2 + y2 - 2x + 6y = 0, x2 + y2 - 4x - 2y + 6 = 0, and x2 + y2 - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

The speed of the electron in a hydrogen atom in the \( n = 3 \) level is:

A force of \( (4\hat{i} + 2\hat{j} + \hat{k}) \) N is acting on a particle of mass \( 2 \) kg displaces the particle from a position of \( (2\hat{i} + 2\hat{j} + \hat{k}) \) m to a position of \( (4\hat{i} + 3\hat{j} + 2\hat{k}) \) m. The work done by the force on the particle in joules is:
In a triangle, if the angles are in the ratio \( 3:2:1 \), then the ratio of its sides is:
Path of projectile is given by the equation \( Y = Px - Qx^2 \), match the following accordingly (acceleration due to gravity = \( g \))
Path of projectile is given by the equation Y = Px−Qx2
If the period of the function \( f(x) = \frac{\tan 5x \cos 3x}{\sin 6x} \) is \( \alpha \), then find \( f \left( \frac{\alpha}{8} \right) \):
Match the following (\( f \) is the number of degrees of freedom): \includegraphics[]{100.png}
The molar specific heat capacity of a diatomic gas at constant pressure is \( C \). The molar specific heat capacity of a monatomic gas at constant volume is

What are X and Y respectively in the following reactions? 

In which of the following thermodynamic processes, the total amount of heat supplied to the system is only used to rise the temperature?
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]

Match the following

A 10 L vessel contains 1 mole of an ideal gas with pressure of P(atm) and temperature of T(K). The vessel is divided into two equal parts. The pressure (in atm) and temperature (in K) in each part is respectively.

Evaluate the integral \( \int \frac{dx}{\sqrt{\sin^3 x \cdot \cos (x - \alpha)}} \):

The elastic energy stored per unit volume in terms of longitudinal strain \( e \) and Young’s modulus \( Y \) is:
The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:
The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:
If the area of the triangle formed by the straight lines \(-15x^2 + 4xy + 4y^2 = 0\) and \(x = a\) is \(200 \, {sq. units}\), then \(|a| =\)