List of top Questions asked in AP EAPCET

The value of \( c \) such that the straight line joining the points \[ (0,3) \quad \text{and} \quad (5,-2) \] is tangent to the curve \[ y = \frac{c}{x+1} \] is:
If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad \text{and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:
If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
The equation of the plane which bisects the angle between the planes $$ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 3z - 3 = 0 \quad \text{which contains the origin is:} $$ 
Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \cos^2 x)}{x^2}. \]
If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at \( x = 0 \), then \( f(0) \) is:
If \[ \frac{d}{dx} \left(\frac{1 + x^2 + x^4}{1 + x + x^2}\right) = ax + b, \] then \( (a,b) \) is:
If the percentage error in the radius of a circle is 3, then the percentage error in its area is:
The distance \( s \) traveled by a particle in time \( t \) is given by: $$ s = 4t^2 + 2t + 3. $$ The velocity of the particle when \( t = 3 \) seconds is: 
Evaluate the integral \[ \int \frac{\sin^6 x}{\cos^8 x} \, dx. \]
Evaluate the integral \[ \int \frac{x^5}{x^2 + 1} dx. \]
Evaluate the integral \[ \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{2r} dx. \]
Evaluate the integral \[ \int e^x (x+1)^2 dx. \]
Evaluate the integral \[ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx \]
The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]
A 4 kg stone is attached to a steel wire being whirled at a constant speed of \( 12 \) m/s in a horizontal circle. The wire is 4 m long with a diameter of 2 mm, and Young’s modulus is \( 2 \times 10^{11} \) Nm\(^2\). The strain in the wire is:
A spherical ball of radius \( 1 \times 10^{-4} \) m and density \( 10^4 \) kgm\(^{-3}\) falls freely under gravity before entering water. The distance \( h \) before velocity change in water is:
An ideal gas is found to obey \( PV^{\frac{3}{2}} = \text{constant} \) during an adiabatic process. If such a gas initially at a temperature \( T \) is adiabatically compressed to \( \frac{1}{4} \)th of its volume, then its final temperature is:
The condition \( dw = dq \) holds good in the following process:
The efficiency of a Carnot engine is found to increase from 25\% to 40\% on increasing the temperature (\(T_1\)) of the source alone through 100 K. The temperature (\(T_2\)) of the sink is given by:
The electric field intensity (\(E\)) at a distance of 3 m from a uniform long straight wire of linear charge density 0.2 \(\mu C m^{-1}\) is:
A cell of emf 1.2 V and internal resistance 2 \( \Omega \) is connected in parallel to another cell of emf 1.5 V and internal resistance 1 \( \Omega \). If the like poles of the cells are connected together, the emf of the combination of the two cells is:
A proton and an alpha particle moving with energies in the ratio \( 1:4 \) enter a uniform magnetic field of 37 T at right angles to the direction of the field. The ratio of the magnetic forces acting on the proton and the alpha particle is:
A charged particle moving along a straight-line path enters a uniform magnetic field of \( 4 \) mT at right angles to the direction of the magnetic field. If the specific charge of the charged particle is \( 8 \times 10^7 \) C/kg, the angular velocity of the particle in the magnetic field is:
At a place the horizontal component of earth’s magnetic field is \( 3 \times 10^{-5} \) T and the magnetic declination is \( 30^\circ \). A compass needle of magnetic moment \( 18 \) A\(m^2\) pointing towards geographic north at this place experiences a torque of: