List of practice Questions

The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, 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

Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $(1 + x - x^2)^6$ is

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 ?

What are $ X $ and $ Y $ in the following reaction? $$ \text{nCl/CH}_2 \xrightarrow{X} Y $$

Nature of two oxides of nitrogen X and Y formed in the reaction of sodium nitrite with hydrochloric acid is

Adsorption of a gas on solids follows the Freundlich adsorption isotherm. The graph drawn between log $\frac{x}{m}$ (on the y-axis) and log $ p $ (on the x-axis) is a straight line with a slope equal to 3 and an intercept equal to 0.30. What is the value of $\frac{x}{m}$ at a pressure of 2 atm?
(Given: log 2 = 0.3)

Match the following