List of top Questions asked in AP EAPCET

At any instant \( t \), the vertical distance \( Y \) and horizontal distance \( X \) of a projectile are given by \[ 2Y = 6t - g t^2 \quad \text{and} \quad X = 4t, \] The initial velocity of the projectile is:

The time of flight of a vertically projected stone is 8 s. The position of the stone after 6 s from the ground is

If a stone is projected at certain angle ‘θ’ with the horizontal such that its horizontal range is equal to its maximum height, then angle of projection ‘θ’ is

The magnifying power of a telescope with tube length 60 cm is 5. Then the focal length of its eye piece is:

A tank is filled with benzene to a height of \(120~\text{mm}\). The apparent depth of a needle lying at the bottom of the tank, as seen through a microscope, is found to be \(80~\text{mm}\). The refractive index of benzene is

A block of mass 5 kg moving on a rough surface with a velocity of 4 ms\(^{-1}\) is stopped by the friction in 2 seconds. Then the coefficient of friction between the contact surfaces is:

A toy car of mass 100 g is moving with velocity of $(\hat{i}+2\hat{j}-3\hat{k})$ m/s, then the kinetic energy of the car is

When a spring of force constant \(200~\text{Nm}^{-1}\) is compressed by a force of \(10~\text{N}\), then the compression in the spring is

The speed of a body of mass 10 kg changes from 20 ms$^{-1}$ to 30 ms$^{-1}$. The increase in the kinetic energy of the body is

The energy consumed by a 1000 W electric bulb when it is used for 1 hour is

Let the equation of the tangent at a point \( P \) on the parabola \( x^2 - 4x - 4y + 16 = 0 \) be \( 2x - y - 5 = 0 \). If the equation of the normal drawn at \( P \) to this parabola is \( ax + y + c = 0 \), then find \( ac \):

If \( \theta \) is the acute angle between the tangents drawn from the point \( (2, 3) \) to the hyperbola \( 5x^2 - 6y^2 - 30 = 0 \), then \( \tan \theta \) is:

The difference between the focal distances of any point on the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text{ is } 6. \text{ If } (\sqrt{13}, k) \text{ is an end point of a latus rectum of this hyperbola, then } k = \]

Let \( f(x) \) be a real valued function. If \( f'(x) \) is a constant for all \( x \in \mathbb{R}, f(0) = 1 \) and \( f'(0) = 2 \), then

If \( f : \mathbb{R} \to \mathbb{R} \) is defined by: \[ f(x) = \begin{cases} \sin x - \sin \left( \frac{x}{2} \right), & x<0 \\ \frac{x}{\sqrt{x^2 + \sqrt{x^2}}}, & x>0 \end{cases} \] If \( f \) is continuous on \( \mathbb{R} \), then \( f(0) = \)

If \( f(x) \) is a differentiable function, \( f'(x) \geq 5 \) for \( x \in [2,6] \), \( f(2) = 4 \) and \( f(3) = 15 \), then a possible value of \( f(6) \) is: