List of top Questions asked in AP EAMCET

Match the following:

The area of the triangle formed by the lines represented by $ 3x + y + 15 = 0 $ and $ 3x^2 + 12xy - 13y^2 = 0 $ is:

The depth $ d $ at which the value of acceleration due to gravity becomes $ \frac{1}{n} $ times the value at the surface (radius of Earth $ R $) is:

If the normal chord drawn at $ (2a,2a\sqrt{2}) $ on the parabola $ y^2 = 4ax $ subtends an angle $ \theta $ at its vertex, then $ \theta $ is:

The length of the tangent drawn at the point $ P \left( \frac{\pi}{4} \right) $ on the curve $ x^{2/3} + y^{2/3} = 2^{2/3} $ is:

Two mercury drops, each with same radius $ r $, merged to form a bigger drop. If $ T $ is the surface tension of mercury, then the surface energy of the bigger drop is given by

An alkyl halide C$_4$H$_8$Br(X) undergoes hydrolysis preferably in polar protic solvents. X can be prepared from which of the following reactants?

If $ \alpha $ and $ \beta $ are two distinct negative roots of the equation $ x^5 - 5x^3 + 5x^2 - 1 = 0 $, then the equation of least degree with integer coefficients having $ \sqrt{-\alpha} $ and $ \sqrt{-\beta} $ as its roots is:

Match the following:

What is the percentage of carbon in the compound X, formed in the given sequence of reactions?

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

Identify Z in the following reaction sequence.

tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =

The centripetal acceleration of a particle in uniform circular motion is $ 18 \, {ms}^{-2} $. If the radius of the circular path is $ 50 $ cm, the change in velocity of the particle in a time of $ \frac{T}{18} $ is:

The rate of emission of radiation of a black body at 27°C is $E_1$. If the temperature increased to 327°C the emission is $E_2$, then $E_2$ is:

The area (in square units) bounded by the curves $ x = y^2 $ and $ x = 3 - 2y^2 $ is:

If $I_{n}=\int_{0}^{\pi/4}\tan^{n}x~dx,$ then $I_{13}+I_{11}=$

Evaluate the integral: $$ \int \frac{x^3 \tan^{-1}(x^4)}{1 + x^8} \,dx. $$

Match List I with List II and select the correct answer.

If the eleventh term in the binomial expansion of $ (x + a)^n $ is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is:

Polymers that can be softened on heating and hardened on cooling are called

What are $ X $ and $ Y $ respectively in the following reaction sequence? \begin{center} \includegraphics[]{139.png} \end{center}

Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces). The acceleration of the centre of mass of the two blocks is (Given $ g = 10 \, \text{m/s}^2 $):

If $ A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} $ is a singular matrix, then the quadratic equation having the roots $ k $ and $ \frac{1}{k} $ is:

The speed of a projectile at its maximum height is $ \frac{\sqrt{3}}{2} $ times its initial speed. If the range of the projectile is $ n $ times the maximum height attained by it, then $ n $ is equal to: