List of top Questions asked in GATE CY

The major products P and Q formed in the following reactions respectively, are:

The major product formed in the following reaction:

is:

The rate constants for the decomposition of a molecule in the presence of oxygen are \(0.237 \times 10^{-4}\) L mol\(^{-1}\) s\(^{-1}\) at 0 °C and \(2.64 \times 10^{-4}\) L mol\(^{-1}\) s\(^{-1}\) at 25 °C. The activation energy for this reaction (rounded off to one decimal place) is \(\underline{\hspace{2cm}}\) kJ mol\(^{-1}\).
Given: \( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \).

2 L of a gas at 1 atm pressure is reversibly heated to reach a final volume of 3.5 L. The absolute value of the work done on the gas (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\) Joules.

The quantity of the cobalt ore [Co\(_3\)(AsO\(_4\))\(_2\)\( \cdot \) H\(_2\)O] required to obtain 1 kg of cobalt (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\) kg.
Given: Atomic Wt. of Co = 59, As = 75, O = 16, H = 1.

The vapor pressure of toluene (Mol. Wt. = 92) is 0.13 atm at 25 °C. If 6 g of a hydrocarbon is dissolved in 92 g of toluene, the vapor pressure drops to 0.12 atm. The molar mass of the hydrocarbon (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\).

The reaction
\[ \text{CO} (g) + \text{Cl}_2 (g) \rightleftharpoons \text{COCl}_2 (g) \] at 500 °C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl_2, is allowed to reach equilibrium. The partial pressure of COCl_2 (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500 °C (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).

The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol\(^{-1}\) cm\(^{-1}\) at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 mmol L\(^{-1}\) solution (rounded off to one decimal place) is \(\underline{\hspace{2cm}}\) %.

The fundamental vibrational frequency of \( ^1H^{127}I \) is 2309 cm\(^{-1}\). The force constant for this molecule (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\) N m\(^{-1}\).
Given: \( N = 6.022 \times 10^{23}, c = 3.0 \times 10^8 \, \text{m s}^{-1} \).

A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of \( \text{Cl}_2 \) having its fundamental vibration at 560 cm\(^{-1}\). The Stokes line corresponding to this vibration will be observed at \(\underline{\hspace{2cm}}\) cm\(^{-1}\).

The number of photons emitted per nanosecond by a deuterium lamp (400 nm) having a power of 1 microwatt (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\).
Given: \( h = 6.626 \times 10^{-34} \, \text{kg m}^2 \text{s}^{-1}, c = 3.0 \times 10^8 \, \text{m s}^{-1} \).

Given the initial weight of 1 mg of radioactive \( ^{60} \)Co (half-life = 5.27 years), the amount disintegrated in 1 year (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\) mg.

The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 m/s (rounded off to one decimal place) is \(\underline{\hspace{2cm}}\) picometers.
Given: \( N = 6.022 \times 10^{23}, h = 6.626 \times 10^{-34} \, \text{kg m}^2 \text{s}^{-1} \).

The correct statement(s) about the concentration of Na\(^+\) and K\(^+\) ions in animal cells is/are:

The correct statement(s) about actinides is/are: