JEE MAIN 2024 ONLINE 6TH APRIL MORNING SHIFT

Consider the following complexes

(A) \(\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}\), (B) \(\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}\), (C) \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}\), (D) \(\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_4\right]^{2+}\)

The correct order of A, B, C and D in terms of wavenumber of light absorbed is :

$$\int_\limits0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x \text { is equal to }$$

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is \(\frac{10}{x}\). The value of \(x\) is ________.

An ideal gas, \(\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}\), is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is \(298 \mathrm{~K}\) and \(5 \mathrm{~atm}\), respectively then the final temperature is _________ \(\mathrm{K}\) (nearest integer).

[\(\overline{\mathrm{c}}_{\mathrm{v}}\) is the molar heat capacity at constant volume]

If the second, third and fourth terms in the expansion of \((x+y)^n\) are 135, 30 and \(\frac{10}{3}\), respectively, then \(6\left(n^3+x^2+y\right)\) is equal to __________.

To find the spring constant \((k)\) of a spring experimentally, a student commits \(2 \%\) positive error in the measurement of time and \(1 \%\) negative error in measurement of mass. The percentage error in determining value of \(k\) is :