NTA JEE Mains 05th April 2024 Shift 2

The maximum height reached by a projectile is $$64$$ m. If the initial velocity is halved, the new maximum height of the projectile is ______ m.

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $$\frac{x}{5}$$. The value of $$x$$ is ______.

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $$10$$ N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ______ N.

A sonometer wire of resonating length $$90$$ cm has a fundamental frequency of $$400$$ Hz when kept under some tension. The resonating length of the wire with fundamental frequency of $$600$$ Hz under same tension ______ cm.

The electric field at point $$p$$ due to an electric dipole is $$E$$. The electric field at point $$R$$ on equitorial line will be $$\frac{E}{x}$$. The value of $$x$$ 

A wire of resistance $$20\Omega$$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ______ $$\Omega$$.

A solenoid of length $$0.5$$ m has a radius of $$1$$ cm and is made up of '$$m$$' number of turns. It carries a current of $$5$$ A. If the magnitude of the magnetic field inside the solenoid is $$6.28 \times 10^{-3}$$ T then the value of $$m$$ is ______.

The current in an inductor is given by $$I = (3t + 8)$$ where $$t$$ is in second. The magnitude of induced emf produced in the inductor is $$12$$ mV. The self-inductance of the inductor ______ mH.

In a single slit experiment, a parallel beam of green light of wavelength $$550$$ nm passes through a slit of width $$0.20$$ mm. The transmitted light is collected on a screen $$100$$ cm away. The distance of first order minima from the central maximum will be $$x \times 10^{-5}$$ m. The value of $$x$$ is :

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $$915$$ Å. The longest wavelength of spectral lines in the Balmer series will be ______ Å.