NTA JEE Main 27th July 2022 Shift 2

Two inclined planes are placed as shown in figure.
A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $$t(\sqrt{2} + 1)$$ s. The value of t is _____ (use $$g = 10 \ m s^{-2}$$)

A solid cylinder of length is suspended symmetrically through two massless strings, as shown in the figure.
The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $$4 \ m s^{-1}$$, is _____ cm. (take $$g = 10 \ m s^{-2}$$)

In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross-section area $$(2 \ mm^2)$$ were taken and the curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph was obtained. If the Young's modulus of the given steel wire is $$x \times 10^{11} \ N m^{-2}$$, then the value of $$x$$ is _____

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of another single soap bubble of radius $$r$$ cm. The value of $$r$$ is _____

A wire of length 30 cm, stretched between rigid supports, has its $$n^{th}$$ and $$(n+1)^{th}$$ harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, its linear mass density is _____ kg m$$^{-1}$$.

As shown in the figure, in steady state, the charge stored in the capacitor is _____ $$\times 10^{-6}$$ C.

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _____ $$\epsilon_0$$ J. (Where $$\epsilon_0$$ is the permittivity of free space)

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be _____ cm.

A conducting circular loop is placed in X-Y plane in presence of magnetic field $$\vec{B} = (3t^3\hat{j} + 3t^2\hat{k})$$ in SI unit. If the radius of the loop is 1 m, the induced emf in the loop, at time, $$t = 2$$ s is $$n\pi$$ V. The value of $$n$$ is _____

A thin prism of angle $$6^\circ$$ and refractive index for yellow light $$(n_Y) = 1.5$$ is combined with another prism of angle $$5^\circ$$ and $$n_Y = 1.55$$. The combination produces no dispersion. The net average deviation $$\delta$$ produced by the combination is $$\left(\frac{1}{x}\right)^\circ$$. The value of $$x$$ is _____