List of top Questions asked in AP EAPCET

In triangle \(ABC\), if \(\cos A \cos B + \sin A \sin B \sin C = 1\), then \(\sin A + \sin B + \sin C =\)
If A and B are positive acute angles satisfying $3\cos^2 A + 2\cos^2 B = 4$ and $\frac{3\sin A}{\sin B} = \frac{2\cos B}{\cos A}$, then A+2B=
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:
If the maximum and minimum amplitudes of a modulated wave are \( 25 \) V and \( 5 \) V respectively, then the modulation index is:
The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:
Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]
If the tangents drawn from a point \( P \) to the ellipse \( 4x^2+9y^2-16x+54y+61=0 \) are perpendicular, then the locus of \( P \) is:
If the volume of a sphere is increasing at the rate of 12 \( \text{cm}^3/\text{sec} \), then the rate (in \( \text{cm}^2/\text{sec} \)) at which its surface area is increasing when the diameter of the sphere is 12 cm is:
For which reaction \( \Delta H \neq \Delta U \)?
At \(25 ^\circ\text{C}\), \(K_a\) of formic acid is \(1.8 \times 10^{-4}\). What is the \(K_b\) of \( \text{HCOO}^- \)?
If \( \alpha, \beta \) are the acute angles such that \( \frac{\sin \alpha}{\sin \beta} = \frac{6}{5} \) and \( \frac{\cos \alpha}{\cos \beta} = \frac{9}{5\sqrt{5}} \) then \( \sin \alpha = \)
Two charged conducting spheres of radii 5 cm and 10 cm have equal surface charge densities. If the electric field on the surface of the smaller sphere is E, then the electric field on the surface of the larger sphere is
Consider the following reaction A(g) + 3B(g) \( \longrightarrow \) 2C(g); \( \Delta H^\ominus = -24 \) kJ. At \(25 \, ^\circ\text{C}\) if \( \Delta G^\ominus \) of the reaction is -9 kJ, the standard entropy change (in JK\(^{-1}\)) of the same reaction at same temperature is
If the circles \( x^2+y^2-2\lambda x - 2y - 7 = 0 \) and \( 3(x^2+y^2) - 8x + 29y = 0 \) are orthogonal, then \( \lambda = \)
If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively \( 5 \, \text{m s}^{-1} \) and \( 10 \, \text{m s}^{-2} \), then the time period of oscillation of the particle is
As shown in the figure, if the values of the electric potential at three points A, B and C in a uniform electric field (\( \vec{E} \)) are \(V_A\), \(V_B\), and \(V_C\) respectively, then
electric potential at three points A, B and C
Consider the following A) 0.0025 B) 500.0 C) 2.0034 Number of significant figures in A, B and C respectively, are
If Q \( (\alpha, \beta, \gamma) \) is the harmonic conjugate of the point P(0,-7,1) with respect to the line segment joining the points (2,-5,3) and (-1,-8,0), then \( \alpha - \beta + \gamma = \)
If \( \int \frac{\cos^3 x}{\sin^2 x + \sin^4 x} dx = c - \operatorname{cosec} x - f(x) \), then \( f\left(\frac{\pi}{2}\right) = \)
If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is
A body of mass 1 kg is suspended from a spring of force constant \( 600 \, \text{N m}^{-1} \). Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of \( 3 \, \text{m s}^{-1} \) and embedded in it. The amplitude of motion is
What are X and Y respectively in the following reaction sequence? (\(anhy = \text{anhydrous}\)) \[ \text{C}_6\text{H}_5\text{N}_2^+\text{X}^- \xrightarrow{\text{C}_2\text{H}_5\text{OH}} \text{X} \xrightarrow{\text{CO, HCl, anhy. AlCl}_3} \text{Y} \] % The question implies the first X is an anion, the second X is an organic product. Let's call the organic product P1 to avoid confusion. % So, C6H5N2+Anion- → P1 → Y
If the displacement 'x' of a body in motion in terms of time 't' is given by \(x = A\sin(\omega t + \theta)\), then the minimum time at which the displacement becomes maximum is
If the point of contact of the circles \( x^2+y^2-6x-4y+9=0 \) and \( x^2+y^2+2x+2y-7=0 \) is \( (\alpha, \beta) \), then \( 7\beta = \)
If the probability distribution of a discrete random variable X is given by \( P(X=k) = \frac{2^{-k}(3k+1)}{2^c} \), k = 0, 1, 2, ..., \( \infty \) then P(X \( \le \) c) = (The expression seems to be \( \frac{2^{-k}(3k+1)}{K} \) where K is a constant, or \(2^c\) is part of the constant. Assuming \(2^c\) is the normalization constant \(K\).)