List of top Questions asked in AP EAMCET

200 g of water is heated from 40°C to 60°C. The change in its internal energy [No expansion is taken place] specific heat of water is 4200 J kg⁻¹ K⁻¹

If \[ \int \frac{\sqrt[4]{x}}{\sqrt{x} + \sqrt[4]{x}} \, dx = \frac{2}{3} \left[ A \sqrt[4]{x^3} + B \sqrt[4]{x^2} + C \sqrt[4]{x} + D \log \left( 1 + \sqrt[4]{x} \right) \right] + K \] then $ \frac{2}{3} (A + B + C + D) = $}

A body is projected horizontally from the top of a tall tower. At a time of 3.5 s from the projection, the horizontal and vertical displacements of the body are equal. The velocity of projection of the body is (acceleration due to gravity = 10 ms$^2$)

Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]

Which physical quantity is measured in barn?

What is D in the given sequence of reaction?

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then $ (\alpha, \beta) $ is:

If $ A = (1,2,3), B = (3,4,7) $ and $ C = (-3,-2,-5) $ are three points then the ratio in which the point C divides AB externally is

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

The length of x-intercept made by the pair of lines $ 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 $ is:

At temperature $ T $ (K), the equilibrium constant $ K_c $ for the reaction: \[ A_2(g) \rightleftharpoons B_2(g) \] is 99.0. Two moles of $ A_2(g) $ were heated in a 1L closed flask to reach equilibrium. What are the equilibrium concentrations (in $ mol \ L^{-1} $) of $ A_2(g) $ and $ B_2(g) $?

If \[ \frac{x^2+3}{x^4+2x^2+9} = \frac{Ax+B}{x^2+ax+b} + \frac{Cx+D}{x^2+cx+d} \] then $ aA + bB + cC + dD = $

Let $ A $ be a $ 4 \times 4 $ matrix and $ P $ be its adjoint matrix. If $ |P| = \left| \frac{A}{2} \right| $, then $ |A^{-1}| = ? $

The equation $ 2x^2 - 3xy - 2y^2 = 0 $ represents two lines $ L_1 $ and $ L_2 $. The equation $ 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 $ represents another two lines $ L_3 $ and $ L_4 $. Let $ A $ be the point of intersection of lines $ L_1 $ and $ L_3 $, and $ B $ be the point of intersection of lines $ L_2 $ and $ L_4 $. The area of the triangle formed by the lines $ AB $, $ L_3 $, and $ L_4 $ is: .

If the roots of the equation $ x^3 - 13x^2 + Kx - 27 = 0 $ are in geometric progression, then $ K = $:

Evaluate the limit: \[ \lim_{x \to 0} \frac{e^{x} - a - \log(1+x)}{\sin x} = 0, { then find } a. \]

Given below are two statements: I. Cytosine and guanine are formed in equal quantities in DNA hydrolysis.
II. Adenine and uracil are formed in equal quantities in RNA hydrolysis. The correct answer is:

Equation of the normal to the curve $ y = x^2 + x $ at the point $ (1,2) $ is:

Let $[r]$ denote the largest integer not exceeding $r$, and the roots of the equation $ 3z^2 + 6z + 5 + \alpha(x^2 + 2x + 2) = 0 $ are complex numbers whenever $ \alpha > L $ and $ \alpha < M $. If $ (L - M) $ is minimum, then the greatest value of $[r]$ such that $ Ly^2 + My + r < 0 $ for all $ y \in \mathbb{R} $ is:

If the line $ 5x - 2y - 6 = 0 $ is a tangent to the hyperbola $ 5x^2 - ky^2 = 12 $, then the equation of the normal to this hyperbola at $ (\sqrt{6}, p) $ 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 $):

The number of unit cells present in 5.85 g of a cube-shaped crystal of sodium chloride is $ x \times 10^y $. $ x $ and $ y $ respectively are (Na = 23 u, Cl = 35.5 u) \[ (N_A = 6 \times 10^{23} { mol}^{-1}) \]

A straight wire of resistance $R$ is bent in the shape of a square. A cell of emf 12 V is connected between two adjacent corners of the square. The potential difference across any diagonal of the square is:

If \[ \cos x \frac{dy}{dx} - y \sin x = 6x, \quad (0<x<\frac{\pi}{2}) \quad {and} \quad y(\frac{\pi}{3}) = 0, \quad {then} \quad y(\frac{\pi}{6}) = \]

If $ n_e $ and $ n_h $ are concentrations of electrons and holes in a semiconductor, then the intrinsic carrier concentration ($ n_i $) in thermal equilibrium is