List of top Questions asked in AP EAPCET

The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ (with $a \ne 0$) from the set $\{0,1,2,4\}$ is
A metal crystallizes in simple cubic lattice. The volume of one unit cell is \( 6.4 \times 10^{-7} \, \text{pm}^3 \). What is the radius of the metal atom in pm?
The number of ways of dividing 15 persons into 3 groups containing 3, 5 and 7 persons so that two particular persons are not included into the 5 persons group is
A family consists of 8 persons. If 4 persons are chosen at random and they are found to be 2 men and 2 women, then the probability that there are equal numbers of men and women in that family is:
If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67, then the gas is
Let $[x]$ represent the greatest integer less than or equal to $x$, $\{x\} = x - [x]$. Given \[ \sqrt{2} = 1.414
\text{and}
\sqrt{3} = 1.732. \] If \[ f(x) = x + \frac{x}{1 + x^2} \] is a real valued function, then find \[ f(\sqrt{2}) + f(-\sqrt{3}). \]
The layer of the atmosphere that reflects low frequency (LF) electromagnetic waves during daytime only is
The general solution of the differential equation \((1 + \sin^2 x) \, \frac{dy}{dx} + \sin 2x = 0\) is?
In a series LCR circuit, the voltages across the capacitor, resistor, and inductor are in the ratio 2:3:6. If the voltage of the source in the circuit is 240 V, then the voltage across the inductor is
If a body of mass \(2 \, \text{kg}\) moving with initial velocity of \(4 \, \text{m/s}\) is subjected to a force of \(3 \, \text{N}\) for a time of 2 seconds normal to the direction of its initial velocity, then the resultant velocity of the body is:
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
The coefficient of $x^{10}$ in the expansion of $\left(x + \frac{2}{x} - 5 \right)^{12}$ is
A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is:
In space, the electric potential varies as $V = 20|r|$ volt, where $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ is the position vector. Then electric field in (N/C) at the point (4 m, 3 m, -5 m) is
If \(f(x) = x^{\sec^{-1} x}\), then find \(f'(2)\).
In a triangle \(ABC\), if \(r_1 : r_2 = 3 : 4\) and \(r_1 : r_3 = 2 : 3\), then find the ratio \(a : b : c\).
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
What is the approximate molality of 10% (w/w) aqueous glucose solution? (Molar mass of glucose = 180 g mol\(^{-1}\))
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
The ratio of the time periods of the revolution of the electrons in the second and third excited states of hydrogen atom is
A narrow slit of width 2 mm is illuminated with monochromatic light of wavelength 500 nm. If the distance between the slit and the screen is 1 m, then first minima are separated by a distance of
The van't Hoff factor for 0.5 m aqueous CH₃COOH solution is 1.075. What is the experimentally observed \(\Delta T_f\) (in K) for this solution? \( K_f = 1.86 \, \text{K kg mol}^{-1} \)
If the velocity at the maximum height of a projectile projected at an angle of \(45^\circ\) is \(20 \, \text{m/s}\), then the maximum height reached by the projectile is:
Which one of the statements regarding X is not correct?
3-Hydroxybutanoic acid → 3-Hydroxypentanoic acid → X X is:
The internal energy of 4 moles of a monoatomic gas at a temperature of 77°C is