List of top Questions asked in AP EAPCET

If the vectors $2\mathbf{i} + 4\mathbf{j} - 3\mathbf{k}$, $-\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$, and $p\mathbf{i} - 2\mathbf{j} + \mathbf{k}$ are coplanar, then the unit vector in the direction of the vector $9p\mathbf{i} - 4\mathbf{j} + 4\mathbf{k}$ is
Assertion (A): For the lines $\mathbf{r} = \mathbf{a} + t \mathbf{b}$ and $\mathbf{r} = \mathbf{p} + s \mathbf{q}$, if $(\mathbf{a} - \mathbf{p}) \cdot (\mathbf{b} \times \mathbf{q}) \neq 0$, then the two lines are coplanar. Reason (R): $|(\mathbf{a} - \mathbf{p}) \cdot (\mathbf{b} \times \mathbf{q})|$ is $|\mathbf{b} \times \mathbf{q}|$ times the shortest distance between the lines $\mathbf{r} = \mathbf{a} + t \mathbf{b}$ and $\mathbf{r} = \mathbf{p} + s \mathbf{q}$.
If the position vectors of the vertices A, B, C of a triangle are $3\mathbf{i} + 4\mathbf{j} - \mathbf{k}$, $\mathbf{i} + 3\mathbf{j} + \mathbf{k}$, and $5(\mathbf{i} + \mathbf{j} + \mathbf{k})$ respectively, then the magnitude of the altitude drawn from A onto the side BC is
The sum of the solutions of $\cos x \sqrt{16 \sin^2 x} = 1$ in $(0, 2\pi)$ is
$\cos(13^\circ)\sin(17^\circ)\sin(21^\circ)\cos(47^\circ) =$
$\sin\left(\frac{\pi}{5}\right) + \sin\left(\frac{2\pi}{5}\right) + \sin\left(\frac{3\pi}{5}\right) + \sin\left(\frac{4\pi}{5}\right) =$
If $\frac{3x^2 - 7x + 1}{(x - 2)^3} = \frac{A}{x - 2} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3}$, then $A(B + C + D + E) =$
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $(1 + x - x^2)^6$ is
All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is
The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + ... \infty$, then
The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$

Consider the following 
Statement-I: In the nitration of aniline, more amount of m-nitroaniline is formed than expected.
Statement-II: In the presence of a strongly acidic medium, aniline is protonated to form anilinium ion, which is meta directing.
 

What is \( A \) in the following reaction? 

\[ \mathrm{CH}_3-\mathrm{CH}= \mathrm{CH}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CN} \xrightarrow{(1)\, \text{A} (\mathrm{i-Bu})_2} \xrightarrow{(2)\, \mathrm{H}_2\mathrm{O}} \rightarrow A \]

Consider the following sequence of reactions. 
\[ \mathrm{C}_6\mathrm{H}_5\mathrm{COONa} \xrightarrow{\text{NaOH/CaO}, \Delta} \text{X} \xrightarrow{\text{CO} + \text{HCl}, \text{Anhyd. AlCl}_3} \text{Y} \xrightarrow{\text{NaOH}} \text{A} + \text{B} \] 
If A is the reduction product of Y, what is B?

An alkyl bromide \( X (\mathrm{C}_5\mathrm{H}_{11}\mathrm{Br}) \) undergoes hydrolysis in a two-step mechanism. 
\( X \) is converted to a Grignard reagent and then reacted with \( \mathrm{CO}_2 \) in dry ether followed by acidification to give \( Y \).
What is \( Y \)?

The most reactive compound towards nucleophilic substitution with an aqueous NaOH is:
Which of the following is not an example of a synthetic detergent?
The deficiency of vitamin (X) causes convulsions. Source of X is Y. What are X and Y ?

Consider the following 
Statement-I: Cane sugar is a disaccharide of \(\alpha\)-D-glucose and \(\beta\)-D-fructose
Statement-II: Milk sugar is a disaccharide of \(\alpha\)-D-glucose and \(\beta\)-D-galactose

 

What are \( X \) and \( Y \) in the following reaction? $$ \text{nCl/CH}_2 \xrightarrow{X} Y $$
Identify the complex ion with spin only magnetic moment of 4.90 BM.