List of top Questions asked in AP EAMCET

If $ \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}$ is a purely imaginary number, then $ \theta $ is:

If \[ x = 3 \left[ \sin t - \log \left( \cot \frac{t}{2} \right) \right], \quad y = 6 \left[ \cos t + \log \left( \tan \frac{t}{2} \right) \right] \] then find $ \frac{dy}{dx} $.

The relation between time $ t $ and displacement $ x $ is $ t = \alpha x^2 + \beta x $, where $\alpha$ and $\beta$ are constants. If $ \nu $ is the velocity, the retardation is:

In which of the following metals extraction, impurities are removed as slag?

The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:

Find the differential equation representing the family of circles having their centers on the Y-axis. Given that $ y_1 = \frac{dy}{dx} $ and $ y_2 = \frac{d^2y}{dx^2} $.

Choose the incorrect statements regarding definition of Living:
(A) Cell division replaces lost cells in certain tissues
(B) In living organisms, growth is from outside
(C) Metabolism is the sum total of all chemical reactions occurring in the living organism
(D) In unicellular organisms, reproduction is not synonymous with the growth

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

Choose the incorrect combination among the following:

Evaluate the limit: \[ \lim\limits_{x \to 2} \frac{\sqrt{1 + 4x} - \sqrt{3} + 3x}{x^3 - 8}. \]

If the potential difference across $PQ$ is 4V, the potential difference across $A$ and $B$ in the given figure is:

Toluene on reaction with the reagent X gave Y, which dissolves in NaHCO$ _3 $ and when reacted with Br$ _2 $/Fe gave Z. What are X and Z?

The motion of a particle is given by $X = a \cos t$, $Y = a \sin t$ and $Z = t$. The trajectory traced by the particle as a function of time is:

A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:

If \[ \int \log \left( 6\sin^2x + 17\sin x + 12 \right)^{\cos x} \, dx = f(x) + c \] then, \[ f\left(\frac{\pi}{2}\right) = \]

The angle between the line with the direction ratios $ (2, 5, 1) $ and the plane $ 8x + 2y - z = 4 $ is given by

If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is:

A body is thrown with a velocity $ (5\hat{i} + 6\hat{j}) \, \text{m/s} $. Its maximum height is (given that acceleration due to gravity = $ 10 \, \text{m/s}^2 $):

If $ S_1 $, $ S_2 $, and $ S_3 $ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively, and $ \theta $ is the angle of contact at the solid-liquid interface, then

If the coefficients of the $ r^{th} $, $ (r+1)^{th $, and $ (r+2)^{th} $ terms in the expansion of $ (1 + x)^n $ are in the ratio $ 4:15:42 $, then $ n - r $ is:}

A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?

Let P be any point on the circle x² + y² = 25. Let L be the chord of contact of P with respect to the circle x^2 + y^2 = 9. The locus of the poles of the lines L with respect to the circle x² + y² = 36 is:

The foot of the perpendicular drawn from a point $ A(1,1,1) $ onto a plane $ \pi $ is $ P(-3,3,5) $. If the equation of the plane parallel to the plane $ \pi $ and passing through the midpoint of $ AP $ is \[ ax - y + cz + d = 0, \] then $ a + c - d $ is:

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

At 240.55 K, for one mole of an ideal gas, a graph of $ P $ (on y-axis) and $ V^{-1} $ (on x-axis) gave a straight line passing through the origin. Its slope (m) is 2000 J mol$^{-1}$. What is the kinetic energy (in J mol$^{-1}$) of the ideal gas?