List of top Questions asked in AP EAPCET

The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:

If \( \left(\frac{2}{3},0\right) \) is the centroid of the triangle formed by the lines \( 4x^2 - y^2 = 0 \) and \( lx + my + n = 0 \), then \( l+m+n= \):

Consider the following: Statement-I: In the extraction of Al by Hall-Heroult process, pure \( Al_2O_3 \) mixed with \( Na_3AlF_6 \) lowers its melting point and increases conductivity. Statement-II: Zirconium metal is purified by zone refining method. The correct answer is:

Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]

The number of solutions of the equation $\sec x \cos 5x + 1 = 0$ in the interval $[0, 2\pi]$ is

When 30 mL of 0.2 M \( NH_4OH \) is added to 30 mL of 2 M \( NH_4Cl \) solution. If the pH of the buffer formed is 8.2, what is the \( pK_b \) of \( NH_4OH \)?

At \( T \)(K), hydrogen and oxygen gases are mixed in the ratio of \( 1:2 \) by mass in a closed vessel of volume \( V \) litres. If the total pressure of the gaseous mixture is \( p \) atm, the partial pressure of oxygen (in atm) is:

At \( 298 \) K, \( \Delta U^\circ \) and \( \Delta S^\circ \) for the following reaction are \( -10.5 \) kJ and \( +44.1 \) J\( K^{-1} \); \( 2X(g) + Y(g) \longrightarrow 2Z(g) \). What is \( \Delta G^\circ \) (in kJ) for this reaction? (\( R = 8.314 \) J\( K^{-1} \)mol\(^{-1} \))

Three letters are chosen at random from the letters of the word VARIABLE and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is:

In a shoe rack there are 4 pairs of shoes and 4 shoes are drawn one after the other at random without replacement. Then the probability of getting at least one correct pair of shoes among the four shoes drawn is:

If the sum of two roots of the equation \( x^4 + 2x^3 - 7x^2 - 8x + 12 = 0 \) is zero, then the sum of the squares of the other two roots is

If \(1, \omega, \omega^2\) are the cube roots of unity, then \( \left(1\left(2+\frac{1}{\omega}\right)\left(2+\frac{1}{\omega^2}\right) + 2\left(3+\frac{1}{\omega}\right)\left(3+\frac{1}{\omega^2}\right) + 3\left(4+\frac{1}{\omega}\right)\left(4+\frac{1}{\omega^2}\right) + \dots + 10 \text{ terms}\right) = \)

The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is

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 $\alpha-\beta=$

From a point \( P(-4, 0) \), two tangents are drawn to the circle \( x^2+y^2-4x-6y-12=0 \) touching the circle at \( A \) and \( B \). If the equation of the circle passing through \( P, A, B \) is \( x^2+y^2+2gx+2fy+c=0 \), then \( (g,f) = \):

The logic gate equivalent to the circuit shown in the figure 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 $\alpha^2 + \beta^2 =$

If a wheel with 24 metallic spokes each \( 40 \) cm long is rotated with a speed of \( 180 \) rev/min in a plane normal to the horizontal component of Earth's magnetic field, the emf induced between the axle and the rim of the wheel is \( E \). If the number of spokes is made \( 12 \) and the wheel is rotated with a speed of \( 90 \) rev/min in the same field, the induced emf is:

If \( x = \sqrt{2}e^t(\sin t - \cos t) \) and \( y = \sqrt{2}e^t(\sin t + \cos t) \), then \( \left[ \frac{d^2y}{dx^2} \right]_{t=\frac{\pi}{4}} \) is:

Of the following, the pair of physical quantities not having the same dimensional formula is:

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

A molecule has a T-shape. The total number of electron pairs in the valence shell of its central atom is:

The sum of bond order values of \( C_2 \) and \( O_2^{2-} \) is \( x \), which is equal to the sum of bond order values of \( a, b, \) and \( c \). What are \( a, b, \) and \( c \)?

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