NTA JEE Main 1st February 2023 Shift 1

The density of 3M solution of NaCl is 1.0 g mL$$^{-1}$$. Molality of the solution is _____ $$\times 10^{-2}$$ m (Nearest integer).
Given: Molar mass of Na is 23 and Cl is 35.5 g mol$$^{-1}$$ respectively.

Electrons in a cathode ray tube have been emitted with a velocity of 1000 ms$$^{-1}$$. The number of following statements which is/are true about the emitted radiation is
Given: h = 6 $$\times$$ 10$$^{-34}$$Js, m$$_e$$ = 9 $$\times$$ 10$$^{-31}$$ kg
(A) The deBroglie wavelength of the electron emitted is 666.67 nm
(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube.
(C) The cathode rays start from cathode and move towards anode.
(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube..

At 25°C, the enthalpy of the following processes are given:
H$$_2$$(g) + O$$_2$$(g) $$\to$$ 2OH(g) $$\Delta$$H$$^0$$ = 78 kJ mol$$^{-1}$$
H$$_2$$(g) + 1/2O$$_2$$(g) $$\to$$ H$$_2$$O(g) $$\Delta$$H$$^0$$ = -242 kJ mol$$^{-1}$$
H$$_2$$(g) $$\to$$ 2H(g) $$\Delta$$H$$^0$$ = 436 kJ mol$$^{-1}$$
1/2O$$_2$$(g) $$\to$$ O(g) $$\Delta$$H$$^0$$ = 249 kJ mol$$^{-1}$$
H$$_2$$O(g) $$\to$$ Hg + OHg $$\Delta$$H$$^0$$ = X kJmol$$^{-1}$$
What would be the value of X for the following reaction? (Nearest integer)

(i) X(g) $$\rightleftharpoons$$ Y(g) + Z(g) K$$_{p1}$$ = 3
(ii) A(g) $$\rightleftharpoons$$ 2B(g) K$$_{p2}$$ = 1
If the degree of dissociation and initial concentration of both the reactants X(g) and A(g) are equal, then the ratio of the total pressure at equilibrium $$\frac{p_1}{p_2}$$ is equal to x : 1. The value of x is (Nearest integer)

The total number of chiral compound/s from the following is

25 mL of an aqueous solution of KCl was found to require 20 mL of 1M AgNO$$_3$$ solution when titrated using K$$_2$$CrO$$_4$$ as an indicator. What is the depression in freezing point of KCl solution of the given concentration?
(Nearest integer).
(Given: K$$_f$$ = 2.0 K kg mol$$^{-1}$$)
Assume 1) 100% ionization and 2) density of the aqueous solution as 1 g mL$$^{-1}$$

At what pH, given half cell MnO$$_4^-$$(0.1M) | Mn$$^{2+}$$(0.001 M) will have electrode potential of 1.282 V? (Nearest Integer)
Given E$$^0_{MnO_4^-/Mn^{2+}}$$ = 1.54 V, $$\frac{2.303RT}{F}$$ = 0.059 V

A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of both of them to be same? _____ min.

Sum of oxidation states of bromine in bromic acid and perbromic acid is

Number of isomeric compounds with molecular formula C$$_9$$H$$_{10}$$O which
(i) do not dissolve in NaOH
(ii) do not dissolve in HCl.
(iii) do not give orange precipitate with 2, 4-DNP
(iv) on hydrogenation give identical compound with molecular formula C$$_9$$H$$_{12}$$O is