NTA JEE Main 30th January 2023 Shift 1

The energy of one mole of photons of radiation of frequency $$2 \times 10^{12}$$ Hz in J mol$$^{-1}$$ is ______ . (Nearest integer)
(Given: h $$= 6.626 \times 10^{-34}$$ Js, N$$_A = 6.022 \times 10^{23}$$ mol$$^{-1}$$)

When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ______ J. (Nearest integer)

600 mL of 0.01 M HCl is mixed with 400 mL of 0.01 M H$$_2$$SO$$_4$$. The pH of the mixture is ______ $$\times 10^{-2}$$. (Nearest integer)
[Given log2 = 0.30, log3 = 0.48, log5 = 0.69, log7 = 0.84, log11 = 1.04]

A 300 mL bottle of soft drink has 0.2M CO$$_2$$ dissolved in it. Assuming CO$$_2$$ behaves as an ideal gas, the volume of the dissolved CO$$_2$$ at STP is ______ mL. (Nearest integer)
Given: At STP, molar volume of an ideal gas is 22.7 L mol$$^{-1}$$

A solution containing 2 g of a non-volatile solute in 20 g of water boils at 373.52 K. The molecular mass of the solute is ______ g mol$$^{-1}$$. (Nearest integer)
Given, water boils at 373 K, K$$_b$$ for water $$= 0.52$$ K kg mol$$^{-1}$$

Some amount of dichloromethane CH$$_2$$Cl$$_2$$ is added to 671.141 mL of chloroform CHCl$$_3$$ to prepare $$2.6 \times 10^{-3}$$ M solution of CH$$_2$$Cl$$_2$$ DCM. The concentration of DCM is ______ ppm (by mass).
Given: Atomic mass: C = 12; H: 1; Cl = 35.5 density of CHCl$$_3$$ = 1.49 g cm$$^{-3}$$

Consider the cell
Pt, H$$_2$$(g, 1 atm) | H$$^+$$ aq, 1M | Fe$$^{3+}$$ aq, Fe$$^{2+}$$ aq | Pt s
When the potential of the cell is 0.712 V at 298 K, the ratio Fe$$^{2+}$$/Fe$$^{3+}$$ is ______ (Nearest integer)
Given: Fe$$^{3+}$$ + e$$^-$$ = Fe$$^{2+}$$, E° Fe$$^{3+}$$, Fe$$^{2+}$$ Pt = 0.771, $$\frac{2.303RT}{F} = 0.06$$ V

If compound A reacts with B following first order kinetics with rate constant $$2.011 \times 10^{-3}$$ s$$^{-1}$$. The time taken by A (in seconds) to reduce from $$7$$ g to $$2$$ g will be ______. (Nearest Integer)
log5 = 0.698, log7 = 0.845, log2 = 0.301

The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is ______.

A trisubstituted compound 'A', C$$_{10}$$H$$_{12}$$O$$_2$$ gives neutral FeCl$$_3$$ test positive. Treatment of compound 'A' with NaOH and CH$$_3$$Br gives C$$_{11}$$H$$_{14}$$O$$_2$$, with hydroiodic acid gives methyl iodide and with hot conc. NaOH gives a compound B, C$$_{10}$$H$$_{12}$$O$$_2$$. Compound 'A' also decolourises alkaline KMnO$$_4$$. The number of $$\pi$$ bond/s present in the compound 'A' is ______.