List of top Questions asked in AP EAPCET- 2024

Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

Identify the method of preparation of a colloidal sol from the following:

Evaluate the limit: \[ \lim_{x \to 1} \frac{x + x^2 + x^3 + \dots + x^n - n}{x - 1}. \]

A body is executing simple harmonic motion. At a displacement $ x $, its potential energy is $ E_1 $, and at a displacement $ y $, its potential energy is $ E_2 $. The potential energy $ E $ at a displacement $ (x + y) $ is:

A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4; then the total modulation index is:

Observe the following reaction: $ 2A_2(g) + B_2(g) \xrightarrow{T(K)} 2A_2B(g) + 600 \text{ kJ} $. The standard enthalpy of formation $ (\Delta_f H^\circ) $ of $ A_2B(g) $ is:

Which of the following is an example for fibre?

Match the following (f is the number of degrees of freedom):

Monoatomic Diatomic (rigid) Diatomic Polyatomic (non-rigid)

The density of nitric acid solution is 1.5 g mL$^{-1}$. Its weight percentage is 68. What is the approximate concentration (in mol L$^{-1}$) of nitric acid? (N = 14 u; O = 16 u; H = 1 u)

If $ 5 \sinh x - \cosh x = 5 $, then one of the values of $ \tanh x $ is:

The current passing through a coil of 120 turns and inductance $ 40 $ mH is $ 30 $ mA. The magnetic flux linked with the coil is:

Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]

When the load applied to a wire is increased from 5 kg wt to 8 kg wt, the elongation of the wire increases from 1 mm to 1.8 mm. The work done during the elongation of the wire is (Acceleration due to gravity = 10 m/s$^2$):

When a wave enters into a rarer medium from a denser medium, the property of the wave which remains constant is:

The correct order of bond angles of the molecules $ SiCl_4 $, $ SO_3 $, $ NH_3 $, $ HgCl_2 $ is:

If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then $ f'(2) $ is:

The capacitance of an isolated sphere of radius $ r_1 $ is increased by 5 times when enclosed by an earthed concentric sphere of radius $ r_2 $. The ratio $ \frac{r_1}{r_2} $ is:

Let $ f(x) = 3 + 2x $ and $ g_n(x) = (f \circ f \circ \dots \text{n times}) (x) $. If for all $ n \in \mathbb{N} $, the lines $ y = g_n(x) $ pass through a fixed point $ (a, \beta) $, then $ \alpha + \beta = ? $

If the line segment joining the points $ (1,0) $ and $ (0,1) $ subtends an angle of $ 45^\circ $ at a variable point $ P $, then the equation of the locus of $ P $ is:

If $ a $ is a common root of $ x^2 - 5x + \lambda = 0 $ and $ x^2 - 8x - 2\lambda = 0 $ ($ \lambda \neq 0 $) and $ \beta, \gamma $ are the other roots of them, then $ a + \beta + \gamma + \lambda = $:

The two reactions involved in the conversion of benzene diazonium chloride to biphenyl are respectively

Let $ F $ and $ F' $ be the foci of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ (where $ b<2 $), and let $ B $ be one end of the minor axis. If the area of the triangle $ FBF' $ is $ \sqrt{3} $ sq. units, then the eccentricity of the ellipse is:

Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]

Identify the incorrect set from the following: