List of top Questions asked in AP EAPCET- 2025

A plane EM wave of frequency $25~\text{MHz}$ propagates in vacuum. If electric field is $6.3~\text{V/m}$, then magnitude of magnetic field is
If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is
A particle of mass $8~\mu g$ collides with another stationary particle of mass $4~\mu g$. If the collision is perfectly elastic and one dimensional, the ratio of de Broglie wavelengths after collision is
Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
Which of the following statements are correct? (only correct)
I) The energy of hydrogen atom in its ground state is -13.6 eV.
II) On the basis of Bohr's model, the radius of the 3$^{rd}$ orbit of hydrogen atom is 158.7 pm.
III) The order of radius of the first orbit of H, He$^+$, Li$^{2+}$ and Be$^{3+}$ is H > He$^+$ > Li$^{2+}$ > Be$^{3+}$
\( \int \frac{1 + x + \sqrt{x + x^2}}{\sqrt{x + \sqrt{1 + x}}} dx = \)
Identify the catalytic reaction in which both reactants are in different phases.
Two thin convex lenses are kept in contact coaxially. If the focal length of the combination is $4~\text{cm$ and the sum of the focal lengths of the two lenses is $18~\text{cm}$, then the focal length of the lens of low power is}
If \( \int x^2 \cos^3 x\, dx = \frac{1}{6}f(x) + g(x) \sin 2x + h(x) \cos 2x + c \), then \( f(1) + g(2) + h\left(\frac{1}{2}\right) = \)
If \( \int \frac{dx}{(x-1)^2(x-3)^2 = \sqrt{f(x)} + c \), then \( f(-1) - f(0) = \)}
If \( \int e^{\sin x}(1 + \sec x \tan x)\, dx = e^{\sin x}f(x) + c \), then in \( 0 \leq x \leq 2\pi \), the number of solutions of \( f(x) = 1 \) is
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
If \( ax^2 + bx + e>0 \) for all \( x \in \mathbb{R} \) and the expressions \( cx^2 + ax + b \) and \( ax^2 + bx + c \) have their extreme values at the same point \( x \), then for the expression \( cx^2 + ax + b \), find the correct statement regarding its extreme value.
If $(3 + 4i)^{2025} = 5^{2023}(x + iy)$, then find $\sqrt{x^2 + y^2}$.
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s, then the initial velocity of the ball is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
If a particle of mass 'm' covers half of the horizontal circle with constant speed 'v', then the change in its kinetic energy is
If a car travels 40% of the total distance with a speed $v_1$, then the remaining distance with the car is
Identify the correct option from the following:
If bullets are fired in all possible directions from same point with equal velocity of 10 m s$^{-1}$ and an angle of projection 45$^\circ$, then the area covered by the bullets on the ground nearby (acceleration due to gravity 10 m s$^{-2}$) is
Identify the correct option from the following:
If the equation of the hyperbola having foci at \((8,3)\), \((0,3)\) and eccentricity \( \frac{4}{3} \) is \[ \frac{(x-\alpha)^2}{p} - \frac{(y-\beta)^2}{q} = 1, \] then find \( p + q \). Options:
Let \( H(x) = 3x^4 + 6x^3 - 2x^2 + 1 \) and \( g(x) \) be a linear polynomial. If \[ \frac{H(x)}{(x-1)(x+1)(x-2)} = f(x) + \frac{g(x)}{(x-1)(x+1)(x-2)}, \] then find \( H(-1) + 2H(2) - 3H(1) \).
If \(630^\circ<\theta<810^\circ\) and \(\tan \theta = -\frac{7}{24}\), then find \(\cos \left(\frac{\theta}{4}\right)\).