GATE CY 2026 Question Paper (07-Feb-2026) (Shift 2)

A 0.005 M solution of compound X transmits 80% of the incident light of wavelength ($\lambda$) 500 nm. The absorbance of 0.01 M solution of X is ______ (rounded off to three decimal places).
(Given: path length = 1.0 cm)

The microwave spectrum of gaseous HF consists of a series of lines separated by 41.11 cm${}^{-1}$. The bond length (in Å) of HF is ______ (rounded off to two decimal places).
(Given: Atomic mass (in amu): H = 1.008, F = 18.998;
1 amu = $1.661\times 10^{-27}$ kg; $h=6.626\times 10^{-34}$ J s; $c=2.998\times 10^8$ m s${}^{-1}$)

In a ${}^{1}H$ NMR spectrum obtained from a spectrometer operating at a magnetic field of 14.1 T, two resonances are observed at 1.25 ppm and 5.75 ppm. The separation between the two resonances (in Hz) is ______ (rounded off to one decimal place).
(Given: gyromagnetic ratio ($\gamma$) of H = $2.675\times 10^8$ T${}^{-1}$ s${}^{-1}$)

The maximum work (|$W_{max}$ |, in kJ) that can be obtained by complete combustion of 1.0 mol of $C{H}_4$ at constant pressure and 25 ${}^{\circ }$ C is ______ (rounded off to one decimal place).
(Given: $\Delta S=-241.60$ J K${}^{-1}$ mol${}^{-1}$; $\Delta H=-890.01$ kJ mol${}^{-1}$; $R=8.314$ J mol${}^{-1}$ K${}^{-1}$)

If the ionic mobility of $A{g}^{+}$ ion in a very dilute aqueous solution of $AgN{O}_3$ at 298 K is $y\times 10^{-8}$ m${}^2$ V${}^{-1}$ s${}^{-1}$, then the value of $y$ is ______ (rounded off to two decimal places).
(Given: viscosity of water at 298 K = $8.94\times 10^{-4}$ kg m${}^{-1}$ s${}^{-1}$; $k=1.38\times 10^{-23}$ J K${}^{-1}$; $F=96500$ C mol${}^{-1}$; $R=8.314$ J mol${}^{-1}$ K${}^{-1}$; Stokes radius of $A{g}^{+}$ = 0.15 nm)