List of top Questions asked in AP EAPCET

If the area of the triangle formed by the lines \( y = x + c \) and \( 2x^2 + 5xy + 3y^2 = 0 \) is \( \frac{1}{20} \) sq. units, then \( c = \)

The charge flowing through a resistance \( R \) varies with time as \( q = at - bt^2 \), where \( a, b \) are positive constants. The total heat produced in \( R \) is:

Let \( \pi_1 \) be the plane determined by the vectors \( \overline{\mathbf{i}} + 2\overline{\mathbf{j}} - 2\overline{\mathbf{k}} \) and \( \overline{\mathbf{i}} + 3\overline{\mathbf{j}} - 2\overline{\mathbf{k}} \). Let \( \pi_2 \) be the plane determined by the vectors \( \overline{\mathbf{j}} + 2\overline{\mathbf{k}} \) and \( 3\overline{\mathbf{k}} - 2\overline{\mathbf{i}} \). If \( \theta \) is the angle between \( \pi_1 \) and \( \pi_2 \), then \( \cos \theta = \)

If \( f(x) = \int_0^x \frac{5t^8 + 7t^6}{(t^2 + 2t + 1)^2} dt \) and \( f(0) = 0 \), then the value of \( f(1) \) is:

The time required (in hours) to reduce 3 mol of \( Fe^{3+} \) ions to \( Fe^{2+} \) ions with 2.0 amperes of current is (1 F = 96500 C mol\(^{-1} \))

Two capacitors of capacity 4 μF and 6 μF are connected in series to a 500 V battery. The potential difference across the 4 μF capacitor is:

If \( \alpha \) and \( \beta \) are respectively the order and degree of the differential equation \[ y = e^{\frac{d^2y}{dx^2}}, \] then the value of \( \alpha + \alpha^\beta + \alpha^{2\beta} + \dots + \alpha^{2023\beta} \) is:

In the circuit with 6 V battery and resistors of 2Ω each, current is 2 A. Find potential at B with respect to A.

A solid cylinder of length \( L \) and diameter \( d \), made of a material with specific heat \( s \), is rotating about its axis with \( n \) rotations per second. When stopped, 50% of its energy is used in rising its temperature. The change in its temperature is:

Small amplitude progressive wave in a stretched string has a speed of \( 100 \, \text{cm/s} \) and frequency \( 100 \, \text{Hz} \). The phase difference between two points 2.75 cm apart on the string, in radians, is:

The product of the four values of \( \left( 1 + i\sqrt{3} \right)^{3/4} \) is:

If \( y = \log x \), then the value of \( x^2 \frac{d^2y}{dx^2} + 3x \frac{dy}{dx} + y \) at the point \( \left( \sqrt{e}, \sqrt{e} \right) \) is:

Match the following

Which of the following electron arrangement does not obey Hund’s rule?

A particle of charge \( q \) is shot with speed \( V \) towards another fixed particle of charge \( Q \). It reaches the closest distance \( r \) and then returns. If \( q \) were shot with speed \( 2V \), then the closest distance of approach of \( Q \) is:

The gauge pressure at a depth of 50 m in a sea is

In SN2 reaction, the carbon in the transition state is:

A steel ball of radius 0.05 cm and density \( 7.8 \, \text{g/cm}^3 \) is dropped into water. What is its terminal velocity?
(Density of water \( = 1 \, \text{g/cm}^3 \), Viscosity of water \( = 0.001 \, \text{Pas} \))

If the chord of contact of the point \( P(h, k) \) with respect to the circle \( x^2 + y^2 - 4x - 4y + 8 = 0 \) meets the circle in two distinct points and it also makes an angle \( 45^\circ \) with the positive X-axis in the positive direction, then \( (h, k) \) cannot be: