Instructions

For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.

Question 31

The solubility of a salt of weak acid (AB) at $$p^{H}$$ is $$Y \times 10^{-3} mol L^{-1}$$ The value of Y is ____.(Given that the value of solubility product of $$AB (K_{sp}) = 2 \times 10^{-10}$$ and the value of ionization constant of $$HB (K_{a}) = 1 \times 10^{-8}$$

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Question 32

The plot given below shows 𝑃 − 𝑇 curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents.

On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of

these solvents, the elevation of boiling point of solvent X is three times that of solvent Y.

Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is

0.7 in solvent Y, the degree of dimerization in solvent X is ____.

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Instructions

Treatment of benzene with $$\frac{CO}{HCl}$$ in the presence of anhydrous $$\frac{AlCl_{3}}{CuCl}$$ followed by reaction with $$\frac{Ac_{2}O}{NaOAc}$$ gives compound X as the major product. Compound X upon reaction with $$\frac{Br_{2}}{Na_{2}CO_{3}}$$, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with $$\frac{H_{2}}{Pd-C}$$, followed by $$H_{3}PO_{4}$$ treatment gives Z as the major product.

Instructions

An organic acid P (C11H12O2) can easily be oxidized to a dibasic acid which reacts with ethyleneglycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic

ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S

Instructions

For the following questions answer them individually

Question 37

For a non-zero complex number 𝑧, let arg(𝑧) denote the principal argument with $$-\pi<arg(Z)\leq \pi$$ Then, which of the following statement(s) is (are) FALSE?

Question 38

In a triangle 𝑃𝑄𝑅, let $$\angle PQR=30^\circ$$ and the sides 𝑃𝑄 and 𝑄𝑅 have lengths 10\sqrt{3} and 10,respectively. Then, which of the following statement(s) is (are) TRUE?

Question 39

Let $$P_{1}:2x+y-z=3$$ and $$P_{2}:x+2y+z=2$$be two planes. Then, which of the following statement(s) is (are) TRUE?

Question 40

For every twice differentiable function $$f : R \rightarrow [-2, 2]$$ with $$(f(0))^{2}+(f'(0))^{2}=85$$ which of the following statement(s) is (are) TRUE?