List of top Questions asked in AP EAPCET- 2025

A metallic disc of radius 0.3 m is rotating with a constant angular speed of \( 60 \, \text{rad s}^{-1} \) in a plane perpendicular to a uniform magnetic field of \( 5 \times 10^{-2} \, \text{T} \). The emf induced between a point on the rim and the centre of the disc is
A resistor of \(450 \, \Omega\) and an inductor are connected in series to an ac source of frequency \( \frac{75}{\pi} \, \text{Hz} \). If the power factor of the circuit is 0.6, then the inductance connected in the circuit is
When a stretched wire of fundamental frequency f is divided into three segments, the fundamental frequencies of these three segments are \(f_1\), \(f_2\) and \(f_3\) respectively. Then the relation among \(f, f_1, f_2, f_3\) and f is (Assume tension is constant) % "and f is" seems redundant
In Young's double slit experiment, the wavelength of monochromatic light is increased by 20% and the distance between the two slits is decreased by 25%. If the initial fringe width is 0.3 mm, then the final fringe width is
An aeroplane of mass \( 4.5 \times 10^4 \) kg and total wing area of \( 600 \, \text{m}^2 \) is travelling at a constant height. The pressure difference between the upper and lower surfaces of its wings is (Acceleration due to gravity \( = 10 \, \text{m s}^{-2} \))
A crane of efficiency 80% is used to lift 8000 kg of coal from a mine of depth 108 m. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in kW) is (Acceleration due to gravity \( = 10 \, \text{m s}^{-2} \))
A body of mass 1 kg is suspended from a spring of force constant \( 600 \, \text{N m}^{-1} \). Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of \( 3 \, \text{m s}^{-1} \) and embedded in it. The amplitude of motion is
Two satellites A and B are revolving around the earth in orbits of heights \(1.25R_E\) and \(19.25R_E\) from the surface of earth respectively, where \(R_E\) is the radius of the earth. The ratio of the orbital speeds of the satellites A and B is
The general solution of the differential equation \( \frac{dy}{dx} + \frac{\sec x}{\cos x + \sin x}y = \frac{\cos x}{1+\tan x} \) is
The number of significant figures in the simplification of \( \frac{0.501}{0.05}(0.312-0.03) \) is
If the displacement 'x' of a body in motion in terms of time 't' is given by \(x = A\sin(\omega t + \theta)\), then the minimum time at which the displacement becomes maximum is
If the magnitude of a vector \( \vec{p} \) is 25 units and its y-component is 7 units, then its x-component is
\( \int \sqrt{x^2+x+1} \ dx \)
If \( k \in N \) then \( \lim_{n\to\infty} \left[ \frac{1}{n+1} + \frac{1}{n+2} + \frac{1}{n+3} + \dots + \frac{1}{kn} \right] = \) (Note: The last term should be \( \frac{1}{n+ (k-1)n} = \frac{1}{kn} \) or sum up to \(n+(k-1)n\). The given form \(1/kn\) as the endpoint of the sum means sum from \(r=1\) to \((k-1)n\). The sum is usually \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \). If the last term is \( \frac{1}{kn} \), it means \( n+r = kn \implies r = (k-1)n \). So it's \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \).) Let's assume the sum goes up to \( \frac{1}{n+(k-1)n} = \frac{1}{kn} \). So the sum is \( \sum_{r=1}^{(k-1)n} \frac{1}{n+r} \). No, this seems to be \( \frac{1}{n+1} + \dots + \frac{1}{n+(kn-n)} \). The sum should be written as \( \sum_{i=1}^{(k-1)n} \frac{1}{n+i} \). The dots imply the denominator goes up. The last term is \( \frac{1}{kn} \). This means the sum is actually \( \frac{1}{n+1} + \frac{1}{n+2} + \dots + \frac{1}{n+(k-1)n} \). The number of terms is \( (k-1)n \).
\( \int_{-1}^{4} \sqrt{\frac{4-x}{x+1}} \ dx = \)
\( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4\sin^2 x} dx = \)
\( \int_{5\pi}^{25\pi} |\sin 2x + \cos 2x| \ dx = \)
The differential equation of the family of circles passing through the origin and having centre on X-axis is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{x+y}{x-y} \) is
Which one of the following functions is monotonically increasing in its domain?
If \( \beta \) is an angle between the normals drawn to the curve \( x^2+3y^2=9 \) at the points \( (3\cos\theta, \sqrt{3}\sin\theta) \) and \( (-3\sin\theta, \sqrt{3}\cos\theta) \), \( \theta \in \left(0, \frac{\pi}{2}\right) \), then
\( \int \left( \sum_{r=0}^{\infty} \frac{x^r 2^r}{r!} \right) dx = \)
If \( \int \frac{\cos^3 x}{\sin^2 x + \sin^4 x} dx = c - \operatorname{cosec} x - f(x) \), then \( f\left(\frac{\pi}{2}\right) = \)
If Q \( (\alpha, \beta, \gamma) \) is the harmonic conjugate of the point P(0,-7,1) with respect to the line segment joining the points (2,-5,3) and (-1,-8,0), then \( \alpha - \beta + \gamma = \)
If the line of intersection of the planes \(2x+3y+z=1\) and \(x+3y+2z=2\) makes an angle \( \alpha \) with the positive x-axis, then \( \cos \alpha = \)