List of top Questions asked in AP EAPCET

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

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:

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}) $

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 $

The number of positive integers less than 10000 which contain the digit 5 at least once is

Which one of the following gases is the major contributor to global warming?

Identify the incorrect statement regarding the interstitial compounds.

If $$ \int \frac{a \cos x + 3 \sin x}{5 \cos x + 2 \sin x} dx = \frac{26}{29} x - \frac{k}{29} \log |5 \cos x + 2 \sin x| + c, $$ then find $ |a + k| $.

If the normal drawn at the point $$ P \left(\frac{\pi}{4}\right) $$ on the ellipse $$ x^2 + 4y^2 - 4 = 0 $$ meets the ellipse again at $ Q(\alpha, \beta) $, then find $ \alpha $.

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:

The domain of the real valued function $ f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x) $ is

The sum of the bond orders of O$_2^+$, O$_2^-$, O$_2$, O$_2^{2-$, and the sum of the unpaired electrons in them respectively are

Consider the following statements:
Statement-I: Shaving soaps contain glycerol to prevent rapid drying.
Statement-II: Laundry soaps contain sodium carbonate as filler.
Which of the following is correct?

Consider the following:
Statement-I: Both internal energy (U) and work (w) are state functions.
Statement-II: During the free expansion of an ideal gas into vacuum, the work done is zero.
The correct answer is

The signs of $\Delta H^\circ$ and $\Delta S^\circ$ for a reaction to be spontaneous at all temperatures respectively are

5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $

A metal crystallizes in simple cubic lattice. The radius of the metal atom is $x\, pm$. What is the volume of the unit cell in $pm^3$?

If $$ \int \frac{dx}{1 - \sin^4 x} = A \tan x + B \tan^{-1}(\sqrt{2} \tan x) + C, $$ then find $ A^2 - B^2 $.

Evaluate: $$ \lim_{x \to \infty} \left( \sqrt[3]{x^3 + 4x^2} - \sqrt{x^2 - 3x} \right) $$

Which of the following reactions give $\mathrm{H_2}$ as one of the products? (Reactions are not balanced.)

• $\mathrm{NaBH_4 + I_2}$
• $\mathrm{B_2H_6 + N(CH_3)_3}$
• $\mathrm{Al + NaOH + H_2O}$
• $\mathrm{BF_3 + NaH}$

The number of significant figures in 0.03240 is

A real valued function $ f: A \to B $ defined by $ f(x) = \frac{4 - x^2}{4 + x^2} \ \forall x \in A $ is a bijection. If $ -4 \in A $, then $ A \cap B = $

Two values of $ (-8 - 8\sqrt{3}i)^{1/4} $ are

If $ r_1 $ and $ r_2 $ are radii of two circles touching all the four circles $$ (x \pm r)^2 + (y \pm r)^2 = r^2, $$ then find the value of $$ \frac{r_1 + r_2}{r}. $$