JEE MAIN 2024 ONLINE 5TH APRIL MORNING SHIFT

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of \(1 / \theta\) vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is _________ \(\times 10^{-1} \mathrm{~A} /\) division. [The source has emf \(2 \mathrm{~V}\)]

An artificial cell is made by encapsulating \(0.2 \mathrm{~M}\) glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell is placed within a \(0.05 \mathrm{~M}\) solution of \(\mathrm{NaCl}\) at \(300 \mathrm{~K}\) is ________ \(\times 10^{-1}\) bar. (nearest integer).

[Given : \(\mathrm{R}=0.083 \mathrm{~L} \mathrm{~bar} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) ]

Assume complete dissociation of \(\mathrm{NaCl}\)

If the constant term in the expansion of \(\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9\) is \(\mathrm{p}\), then \(108 \mathrm{p}\) is equal to ________.

The density and breaking stress of a wire are \(6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3\) and \(1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2\) respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \(\frac{1}{3}^{\text {rd }}\) of the value on the surface of earth. The maximum length of the wire with breaking is _______ \(\mathrm{m}\) (take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\)).

The value of Rydberg constant \((R_H)\) is \(2.18 \times 10^{-18} \mathrm{~J}\). The velocity of electron having mass \(9.1 \times 10^{-31} \mathrm{~kg}\) in Bohr's first orbit of hydrogen atom = ________ \(\times 10^5 \mathrm{~ms}^{-1}\) (nearest integer).

The number of distinct real roots of the equation \(|x||x+2|-5|x+1|-1=0\) is __________.