List of top Questions asked in AP EAPCET- 2023

If \( f(n) = n!(31-n)! \), where \( n \in \{ 0, 1, 2, \dots, 31 \} \), then the minimum value of \( f(n) \) is:
If \( C_j \) stands for \( \binom{n}{j} \), then: \[ \frac{C_1}{C_0} + 2 \times \frac{C_2}{C_1} + 3 \times \frac{C_3}{C_2} + ... + n \times \frac{C_n}{C_{n-1}} \]
If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on:
A block of steel of mass 2 kg slides down a rough inclined plane of inclination of \( \sin^{-1} \left( \frac{3}{5} \right) \) at a constant speed. The temperature of the block as it slides through 80 cm, assuming that the mechanical energy lost is used to increase the temperature of the block is nearly:
Blue colour of the sky is due to
An ideal gas (X) present in a vessel of volume \( V \) exerted a pressure of 16.4 atm at 200 K. What is its concentration in mol \( L^{-1} \)? % Given Data Given \( R = 0.082 \, \text{L atm mol}^{-1} \text{K}^{-1} \)
The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1, 2, and 6, then the other two observations are:
An inductor and a resistor are connected in series to an AC source. If the power factor of the circuit is 0.5, the ratio of the resistance of the resistor and the reactance of the inductor is:
Which of the following has more pK\(_a\) value?
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
Sphalerite is the ore of metal \( M_1 \) and malachite is the ore of metal \( M_2 \). Atomic numbers of \( M_1 \) and \( M_2 \) are respectively
The correct order of reactivity of the following towards nucleophilic addition reactions is: \[ \text{I. CH}_3\text{COCH}_3,\quad \text{II. CH}_3\text{CH}_2\text{CHO},\quad \text{III. ClCH}_2\text{CHO} \]
The number of elements in the set $ S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \le 0 \text{ and } x^2 - 3x>0 \} $ is
In $ \triangle ABC $, if $ r $ is the inradius and $ r_1, r_2, r_3 $ are the ex-radii, then \[ \frac{1}{4} \left[ b^2 \sin 2C + c^2 \sin 2B \right] = \]
Among the following, Ampere’s circuital law is represented by:
If \( A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \) and \( B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix} \), then which one of the following is True?
If \( \frac{x^4 - 6x^3 + 9x^2 + 5x - 20}{x^2 - x - 2} = f(x) + \frac{a}{x + p} + \frac{b}{x + q} \), then \( 2(a + b) = \)
If \( \mathbf{a} = (2x + y)\mathbf{i} + 3\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \mathbf{j} - (x - y)\mathbf{k} \) are two collinear vectors, then \( x^3 + 27y^3 = \)
If \( y = x \log \left( \frac{1}{ax} \right) \), then \( x(1 + x) \frac{d^2 y}{dx^2} + x \frac{dy}{dx} - y = \)
If \( \lim_{x \to \infty} y(x) = \frac{\pi}{2} \), then the solution of \( x^3 \sin y \frac{dy}{dx} = 2 \) is \( \cos y = \)
For a positive real number \( \lambda \), if the vector \( \vec{a} = \lambda \vec{i} - 5\vec{j} + 6\vec{k} \) satisfies the equation \[ \left[ \vec{i} \times (\vec{a} \times \vec{i}) + \vec{j} \times (\vec{a} \times \vec{j}) + \vec{k} \times (\vec{a} \times \vec{k}) \right]^2 = 440, \] then \( \lambda = \)
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
If \( A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix} \) and \( 2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \), then \( \text{Tr}[A] - \text{Tr}[B] \) equals:
A truck of mass \( M \) and a car of mass \( \frac{M}{10} \) moving with the same momentum are brought to halt by the application of the same breaking force. The ratio of the distances travelled by the truck and car before they come to stop is:
A 50 g ice cube at -10°C is added to 200 g of water at 30°C. The final temperature of the mixture is: (Specific heat of water = 1 cal g\(^{-1}\)°C\(^{-1}\), latent heat of fusion of ice = 80 cal g\(^{-1}\), specific heat of ice = 0.5 cal g\(^{-1}\)°C\(^{-1}\))