List of top Questions asked in AP EAPCET- 2025

Evaluate: $$ \int_0^1 x \sin^{-1} x \, dx $$
A wire of length 20 cm is placed horizontally on the surface of water and is gently pulled up with a force of $1.456 \times 10^{-2}\, N$ to keep the wire in equilibrium. The surface tension of water is
The maximum magnetic field produced by a current of 12 A passing through a copper wire of diameter 1.2 mm is
Identify the incorrect statement regarding the interstitial compounds.
The coefficient of \(x^3\) in the expansion of \(\frac{x^4 + 1}{(x^2 + 1)(x - 1)}\) when it is expressed in terms of positive integral powers of \(x\), is
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 \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is
If the internal energy of 3 moles of a gas at a temperature of 27 °C is 2250R, then the number of degrees of freedom of the gas is (R - Universal gas constant)
Nature of two oxides of nitrogen X and Y formed in the reaction of sodium nitrite with hydrochloric acid is
What are \( X \) and \( Y \) in the following reaction? $$ \text{nCl/CH}_2 \xrightarrow{X} Y $$

Consider the following 
Statement-I: In the nitration of aniline, more amount of m-nitroaniline is formed than expected.
Statement-II: In the presence of a strongly acidic medium, aniline is protonated to form anilinium ion, which is meta directing.
 

Let $\mathbf{a} = 4\mathbf{i} + 3\mathbf{j}$ and $\mathbf{b}$ be two perpendicular vectors in the XOY-plane. A vector $\mathbf{c}$ in the same plane and having projections 1 and 2 respectively on $\mathbf{a}$ and $\mathbf{b}$ is
If \( \vec{a} = 2\vec{i} - \vec{j} + 6\vec{k} \); \( \vec{b} = \vec{i} - \vec{j} + \vec{k} \) and \( \vec{c} = 3\vec{j} - \vec{k} \), then \( \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \)
A line \(L_1\) passing through the point of intersection of the lines \(x-2y+3=0\) and \(2x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3x-y+2=0\) and \(x-3y-2=0\), then the distance between the lines \(L_1\) and \(L_2\) is
\( \int_{-1}^{4} \sqrt{\frac{4-x}{x+1}} \ dx = \)
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
For transmitting a signal of frequency 1000 kHz, the minimum length of the antenna is
Compound 'X' is prepared commercially by the electrolysis of brine solution. Which of the following is not the use of 'X'?
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
A wire of resistance \( R \) is bent in the form of a circular loop. Two points on the circle separated by a quarter circumference are connected to a battery of emf \( E \) and negligible internal resistance. The heat generated in the wire per second is:
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
If the wavelengths of maximum intensity of radiation emitted by two black bodies A and B are \( 0.5 \, \mu\text{m} \) and \( 0.1 \, \text{mm} \) respectively, then ratio of the temperatures of the bodies A and B is
If \( A = \begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix} \) and the rank of \( A \) is 2, then the value of \( x \) is equal to:
If 3 squares are chosen at random from the 64 squares of a chessboard, then the probability that all of them lie along the same diagonal line is:
The equation of the base of an equilateral triangle is \( x + y = 2 \) and its opposite vertex is \( (2,1) \). If \( m_1, m_2 \) are the slopes of the other two sides and the length of its side is \( a \), then \( |m_1 - m_2| + a\sqrt{2} = \):