List of top Questions asked in AP EAPCET

A unit vector that is perpendicular to the vector \( 2\vec{i} - \vec{j} + 2\vec{k} \) and coplanar with the vectors \( \vec{i} + \vec{j} - \vec{k} \) and \( 2\vec{i} - 2\vec{j} - \vec{k} \) is

The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:

Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]

If the vectors \( 2\vec{i} - \vec{j} + 3\vec{k}, \vec{i} + 4\vec{j} + \vec{k}, 4\vec{i} + p\vec{j} + \vec{k} \) are coplanar, then \( p = \)

In Young's double slit experiment, the distance between the slits is \( 0.2 \) cm, the distance between the screen and the slits is \( 1 \) m. If the wavelength of light used in the experiment is \( 5000 \) Å, then the distance between two consecutive dark fringes on the screen is:

The logic gate equivalent to the circuit shown in the figure is:

If a wheel with 24 metallic spokes each \( 40 \) cm long is rotated with a speed of \( 180 \) rev/min in a plane normal to the horizontal component of Earth's magnetic field, the emf induced between the axle and the rim of the wheel is \( E \). If the number of spokes is made \( 12 \) and the wheel is rotated with a speed of \( 90 \) rev/min in the same field, the induced emf is:

If \( x = \sqrt{2}e^t(\sin t - \cos t) \) and \( y = \sqrt{2}e^t(\sin t + \cos t) \), then \( \left[ \frac{d^2y}{dx^2} \right]_{t=\frac{\pi}{4}} \) is:

If the given graph shows the logarithmic values of pressure (P) and volume (V) of an ideal gas, then the ratio of the specific heat capacities of the gas is:

A molecule has a T-shape. The total number of electron pairs in the valence shell of its central atom is:

The sum of bond order values of \( C_2 \) and \( O_2^{2-} \) is \( x \), which is equal to the sum of bond order values of \( a, b, \) and \( c \). What are \( a, b, \) and \( c \)?

The correct order of density of Be, Mg, Ca, Sr is:

If \( \theta \) is the acute angle between the tangents drawn from the point \( (1,1) \) to the hyperbola \( 4x^2-5y^2-20=0 \), then \( \tan\theta \) is:

The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is

A long straight wire of circular cross-section of radius \( a \) is carrying a steady current. The current is distributed uniformly across the cross-section of the wire. The ratio of the magnetic fields at points \( 0.5a \) and \( 1.5a \) from the centre of the wire is:

At \( 27^\circ C \) kinetic energy of 4 g of \( H_2 \) is \( x \) J. What is the kinetic energy (in J) of 6.4 g of oxygen at \( 127^\circ C \)?

The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:

In the given reaction sequence, conversion of Acetophenone (\( C_6H_5COCH_3 \)) to Ethylbenzene (\( C_6H_5CH_2CH_3 \)) is an example of: \[ \text{CH}_3\text{COC/} \] \[ \text{Anhy. AlCl}_3 \xrightarrow{\text{X}} \xrightarrow{\text{(1) N}_2\text{H}_4} Y \] \[ \Delta \xrightarrow{\text{(2) KOH / glycol}} \]

If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)

If the tension in the horizontal wire shown in the figure is 30 N, then the weight \( W \) and tension in the wire \( OA \) are respectively:

Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:

The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm. At \( T \)(K), the gas pressure is \( 2 \) atm. What is the value of \( \frac{x}{m} \)? (\( n = 2 \) and \( k \) = constant)

At \( T \)(K), the vapour pressure of pure benzene and toluene are \( 75 \) and \( 22 \) mm Hg respectively. 23.4 g of benzene and 64.4 g of toluene are mixed to form an ideal solution. If the vapours are in equilibrium with the liquid mixture, the mole fraction of toluene in vapour phase is:

The ratio of the magnitudes of the electric field and \( 10^8 \) times the magnetic field of a plane electromagnetic wave is:

From a point \( P(-4, 0) \), two tangents are drawn to the circle \( x^2+y^2-4x-6y-12=0 \) touching the circle at \( A \) and \( B \). If the equation of the circle passing through \( P, A, B \) is \( x^2+y^2+2gx+2fy+c=0 \), then \( (g,f) = \):