JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given \(\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\))

For \(\mathrm{a}, \mathrm{b}>0\), let \(f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x< 0 \\ 3, & x=0 \\ \frac{\sqrt{\mathrm{a} x+\mathrm{b}^2 x^2}-\sqrt{\mathrm{a} x}}{\mathrm{~b} \sqrt{\mathrm{a}} x \sqrt{x}}, & x> 0\end{cases}\) be a continuous function at \(x=0\). Then \(\frac{\mathrm{b}}{\mathrm{a}}\) is equal to :

Wavenumber for a radiation having 5800 \(\mathop A\limits^o\) wavelength is \(x \times 10 \mathrm{~cm}^{-1}\) The value of \(x\) is ________. (Integer answer)

If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(x=\) ________.

The number of distinct real roots of the equation \(|x+1||x+3|-4|x+2|+5=0\), is _______

A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is ________ (Integer answer) (Given : Molar mass in \(\mathrm{g} \mathrm{~mol}^{-1}\) Ethyl alcohol : 46 water : 18)