List of top Questions asked in AP EAPCET

If $ P(\bar{A}) = 0.3,\ P(B) = 0.4,\ P(A \cap \bar{B}) = 0.5 $, then find $ P(B / (A \cup \bar{B})) $

At $T(K)$, the vapor pressure of water is $x$ kPa. What is the vapor pressure (in kPa) of 1 molal solution containing non-volatile solute?

A polymer sample contains 10 molecules each with molecular mass 5,000 and 5 molecules each with molecular mass 50,000. The number average molecular mass of the polymer sample is

If $ x - y - 3 = 0 $ is a normal drawn through the point $ (5, 2) $ to the parabola $ y^2 = 4x $, then the slope of the other normal that can be drawn through the same point to the parabola is?

If the line joining points $ \vec{r}_1 = \hat{i} + 2\hat{j} $ and $ \vec{r}_2 = \hat{j} - 2\hat{k} $ intersects the plane through the points $ \vec{A} = 2\hat{i} - \hat{j},\ \vec{B} = -2\hat{j} + 3\hat{k},\ \vec{C} = \hat{k} - 2\hat{i} $ at $ T $, then find $ \vec{r}_T \cdot (\hat{i} + \hat{j} + \hat{k}) $

If the equation of the plane passing through point $ (3, 2, 5) $ and perpendicular to the planes $$ 2x - 3y + 5z = 7, \quad 5x + 2y - 3z = 11 $$ is $$ x + by + cz + d = 0, $$ then find $ 2b + 3c + d $.

The direction cosines of the line making angles $$ \frac{\pi}{4}, \frac{\pi}{3} $$ and $ \theta $ (where $ 0<\theta<\frac{\pi}{2} $) with X, Y, and Z axes respectively are:

In a solenoid, if the current of 15 A passes through the solenoid of length 25 cm, radius 2 cm, and number of turns 500, then the magnetic moment of the solenoid is

A coil of inductive reactance $\frac{1}{\sqrt{3}} \Omega$ and a resistance 1 $\Omega$ are connected in series to a 200 V, 50 Hz ac source. The time lag between voltage and current is

If $ \tan\left( \frac{\pi}{4} + \alpha \right) = \tan^3\left( \frac{\pi}{4} + \beta \right) $, then compute: $$ \tan(\alpha + \beta) \cot(\alpha - \beta) = ? $$

In triangle $ ABC $, if $ a = 5,\ b = 4,\ \cos(A - B) = \frac{31}{32} $, then $ c = ? $

The vector equation of a plane passing through the line of intersection of the planes $$ \vec{r} \cdot (\hat{i} - 2\hat{k}) = 3,\quad \vec{r} \cdot (\hat{j} + \hat{k}) = 5 $$ and also passing through the point $ \vec{r} = \hat{i} + 2\hat{j} + 3\hat{k} $ is:

Three vectors each of magnitude $3\sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$, then the magnitude of the resultant vector of the three vectors is

If $ A + B + C + D = 2\pi $, then $$ \sin A + \sin B + \sin C + \sin D = ? $$

At absolute zero temperature, an intrinsic semiconductor behaves as

If $ \vec{a} = \hat{i} + \hat{j}, \vec{b} = 2\hat{j} - \hat{k} $ are two vectors such that $ \vec{r} \times \vec{a} = \vec{b} \times \vec{a}, \vec{r} \times \vec{b} = \vec{a} \times \vec{b} $, then the unit vector in the direction of $ \vec{r} $ is:

Let vectors: $ \vec{A} = \hat{i} - 2\hat{j} + \hat{k},\ \vec{B} = \hat{i} + \hat{j} - 2\hat{k},\ \vec{C} = 2\hat{i} - \hat{j},\ \vec{D} = \hat{i} + \hat{j} + \hat{k} $ If $ P $ divides $ AB $ in ratio 2:1 internally, and $ Q $ divides $ CD $ in ratio 1:2 externally, find the ratio in which the point $ 5\hat{i} - 6\hat{j} - 5\hat{k} $ divides line $ PQ $

Elements X and Y form two non-volatile compounds (XY and XY$_2$). When 10 g of XY is dissolved in 50 g of ethanol, the depression in freezing point ($\Delta T_f$) was 5.333 K. When 10 g of XY$_2$ is dissolved in 50 g of ethanol, the $\Delta T_f$ was 2.2857 K. What are the atomic weights of X and Y respectively?
($K_f = 2 \, \text{kg mol}^{-1}$)

The points $ A(-1, 2, 3), B(2, -3, 1), C(3, 1, -2) $ are:

If the system of equations $ 2x + 3y - 3z = 3,\ x + 2y + \alpha z = 1,\ 2x - y + z = \beta $ has infinitely many solutions, then $ \frac{\alpha}{\beta} = \frac{\beta}{\alpha} $

If a dielectric slab of dielectric constant 3 is introduced between the plates of a capacitor having electric field $1.5\, N/C$, then the electric displacement is