List of top Questions asked in AP EAPCET

Let \( \vec{a} = 2\vec{i} + \vec{j} - 2\vec{k} \) and \( \vec{b} = \vec{i} + \vec{j} \) be two vectors. If \( \vec{c} \) is a vector such that \( \vec{a} \cdot \vec{c} = |\vec{c}| \), \( |\vec{c} - \vec{a}| = 2\sqrt{2} \) and the angle between \( \vec{a} \times \vec{b} \) and \( \vec{c} \) is \( 30^\circ \), then \( |(\vec{a} \times \vec{b}) \times \vec{c}| = \)

If \( \frac{1}{2} \sin^{-1} \left( \frac{3\sin 2\theta}{5+4\cos 2\theta} \right) = \tan^{-1} x \) then \( x = \)

If the equation \(2\cot^{-1}(x^2 + 2x + k) = -3\tan^{-1}(x^2 + 2x + k)\) has two distinct real solutions, then all the values of \(k\) lie in the interval

If $\sin x - \sin y = \frac{27}{65}$ and $\cos x - \cos y = -\frac{21}{65}$, then $\sin(x+y)= $

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=

If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos^2 \frac{x}{4} + \sin \frac{x}{4}$, $x \in \mathbb{R}$, then $\alpha-\beta=$

If $x>\sqrt{3}$ and $\frac{x^2+1}{(x^2+2)(x^2+3)}$ is expanded in terms of powers of $x$, then the coefficient of $x^{-8}$ is

If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $(1 + \alpha x + \beta x^2)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2 + \beta^2 =$

Evaluate the infinite series: \[ \left|\begin{array}{ccc} 2 & 1 & \frac{1}{3} \\ 3 & 1 & 1 \\ \end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{3} & \frac{1}{2} \\ 3 & 1 & 1 \\ \end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{4} & \frac{1}{9} \\ 3 & 1 & 1 \\ \end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{4} & \frac{1}{27} \\ 3 & 1 & 1 \\ \end{array}\right| + \cdots = ? \]

The range of the real valued function \( f(x) = \cos^{-1} \left( \dfrac{3}{\sqrt{9x^2 - 12x + 22}} \right) \) is

If a function \( f(x) \) is given as: \[ f(x) = \begin{cases} \frac{\sqrt{1+ax^2+bx^3}-\sqrt{1-ax^2-bx^3}}{x^2}, & x<0 \\ 5, & x = 0 \\ \frac{\tan3x-\sin3x}{bx^3}, & x>0 \end{cases} \] and is continuous at \( x = 0 \), then the geometric mean of \( a \) and \( b \) is:

Match the following polymers with their applications:

List-I (Polymer)	List-II (Used in making)
Polymer 1	Application 1
Polymer 2	Application 2
Polymer 3	Application 3
Polymer 4	Application 4

The structure of the product 'Z' in the reaction sequence is: \[ \text{CHO} \] \[ \mid \] \[

The amphoteric oxide of Vanadium (V) reacts with alkali and forms an oxoion \( X \) and with acid forms an oxoion \( Y \). The oxidation states of \( V \) in \( X \) and \( Y \) are respectively:

The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm. At \( T \)(K), the gas pressure is \( 2 \) atm. What is the value of \( \frac{x}{m} \)? (\( n = 2 \) and \( k \) = constant)

Which one of the following acts as an autocatalyst during titration of \( KMnO_4 \) and oxalic acid in presence of dilute \( H_2SO_4 \)?

The correct order of density of Be, Mg, Ca, Sr is:

Identify the reaction in which diborane is produced on an industrial scale:

Which one of the following reactions is not feasible?

Consider the following gaseous equilibrium reactions (I), (II) and (III) with equilibrium constants \( K_1 \), \( K_2 \), and \( K_3 \) respectively:
I) \( \frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3 \)
II) \( 2NO \rightleftharpoons N_2 + O_2 \)
III) \( H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2O \)
The correct expression for the equilibrium constant for the gaseous equilibrium reaction: \[ 2NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2NO + 3H_2O \]

The de Broglie wavelengths of two fast-moving particles \( X \), \( Y \) are \( 1 \) nm, \( 3 \) nm respectively. Mass of \( X \) is nine times the mass of \( Y \). The ratio of kinetic energies of \( X \), \( Y \) is: