List of top Questions asked in AP EAPCET

If \( A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \) and \( B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix} \), then which one of the following is True?
If \( \frac{x^4 - 6x^3 + 9x^2 + 5x - 20}{x^2 - x - 2} = f(x) + \frac{a}{x + p} + \frac{b}{x + q} \), then \( 2(a + b) = \)
If \( \mathbf{a} = (2x + y)\mathbf{i} + 3\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \mathbf{j} - (x - y)\mathbf{k} \) are two collinear vectors, then \( x^3 + 27y^3 = \)
If \( y = x \log \left( \frac{1}{ax} \right) \), then \( x(1 + x) \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - y = \)
If \( \lim_{x \to \infty} y(x) = \frac{\pi}{2} \), then the solution of \( x^3 \sin y \frac{dy}{dx} = 2 \) is \( \cos y = \)
For a positive real number \( \lambda \), if the vector \( \vec{a} = \lambda \vec{i} - 5\vec{j} + 6\vec{k} \) satisfies the equation \[ \left[ \vec{i} \times (\vec{a} \times \vec{i}) + \vec{j} \times (\vec{a} \times \vec{j}) + \vec{k} \times (\vec{a} \times \vec{k}) \right]^2 = 440, \] then \( \lambda = \)
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
If \( A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \), then \( \text{Tr}[A] - \text{Tr}[B] \) equals:
A truck of mass \( M \) and a car of mass \( \frac{M}{10} \) moving with the same momentum are brought to halt by the application of the same breaking force. The ratio of the distances travelled by the truck and car before they come to stop is:
A 50 g ice cube at -10°C is added to 200 g of water at 30°C. The final temperature of the mixture is: (Specific heat of water = 1 cal g\(^{-1}\)°C\(^{-1}\), latent heat of fusion of ice = 80 cal g\(^{-1}\), specific heat of ice = 0.5 cal g\(^{-1}\)°C\(^{-1}\))
In a hydrogen atom, an electron in an orbit with principal quantum number \( n \) jumps to the first excited state, emitting a photon of wavelength \( \lambda \). Then the value of \( n \) is:
The process which involves the treatment of the ore with a suitable reagent so as to make it soluble but not impurities is called
The time taken by a net force of 10 N to change the velocity by 4 m/s of a body of mass 10 kg is:
According to Newton's law of cooling, the temperature of a body is \( T \) at time \( t \) and the temperature of the surroundings is \( T_s \). The rate of change of temperature is given by \[ \frac{dT}{dt} = k(T_s - T) \] If the initial temperature at time \( t = 0 \) is \( T_0 \), then the temperature \( T \) is:
In \( \triangle ABC \), \( (\cot A + \cot B)(\cot B + \cot C)(\cot C + \cot A) = \)
If \[ \frac{-x^2 + 6x + 1}{(x - 1)^2 (x^2 + 2)} = \frac{A}{x - 1} + \frac{B}{(x - 1)^2} + \frac{Cx - 3}{x^2 + 2}, \] then \(A + B + C =\) ?
The area bounded by the curve \( x = \log(|y|) \), the lines \( x = -1 \) and \( x = 0 \) is:
Satellites which give high value data for remote sensing, meteorology, and environmental studies are
Two electric dipoles, each of dipole moment ‘P’, are placed at points A (\(a,0\)) and B (\(-a,0\)) as shown in the figure. The work done in rotating both the dipoles through 90° in clockwise direction is (E = Electric field)
Two electric dipoles, each of dipole moment ‘P
The major product of the following reaction is
alkyl group
What are 'X' and 'Y' respectively in the following reaction sequence? \[ \ce{C6H5CH3→[X] C6H5CO2H →[Y] C6H5CH2OH} \]
The ordinates of the points on the curve \( y = \tan^{-1}(\sin(\sqrt{x})) \), \( 0 \leq x \leq 8\pi^2 \), at which the tangent is parallel to the X-axis are:
When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:
A work of 166.28 J is done to adiabatically compress one mole of a gas. If the increase in the temperature of the gas is \( 8^\circ C \), the gas is:
Positron is the antiparticle of