NTA JEE Mains 8th April 2024 Shift 1

Three vectors $$\vec{OP}$$, $$\vec{OQ}$$ and $$\vec{OR}$$ each of magnitude $$A$$ are acting as shown in figure. The resultant of the three vectors is $$A\sqrt{x}$$. The value of $$x$$ is ________.

A uniform thin metal plate of mass $$10 \text{ kg}$$ with dimensions is shown. The ratio of $$x$$ and $$y$$ coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.

A liquid column of height $$0.04 \text{ cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \text{ kg m}^{-3}$$ and surface tension of soap solution is $$0.28 \text{ Nm}^{-1}$$, then diameter of the soap bubble is ______ cm. (if $$g = 10 \text{ m s}^{-2}$$)

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is ________.

An electric field, $$\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \text{ m}^2$$ area having unit vector $$\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is ______ Vm.

Resistance of a wire at $$0°C$$, $$100°C$$ and $$t°C$$ is found to be $$10\Omega$$, $$10.2\Omega$$ and $$10.95\Omega$$ respectively. The temperature $$t$$ in Kelvin scale is ________.

An electron with kinetic energy $$5 \text{ eV}$$ enters a region of uniform magnetic field of $$3 \; \mu T$$ perpendicular to its direction. An electric field $$E$$ is applied perpendicular to the direction of velocity and magnetic field. The value of $$E$$, so that electron moves along the same path, is ______ $$\text{NC}^{-1}$$. (Given, mass of electron $$= 9 \times 10^{-31} \text{ kg}$$, electric charge $$= 1.6 \times 10^{-19} \text{ C}$$)

A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \text{ m}^2$$ and resistance $$100\Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$B = 0.5 \text{ T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \text{ s}$$ is ______ $$\times 10^{-6} \text{ J}$$.

A parallel beam of monochromatic light of wavelength $$600 \text{ nm}$$ passes through single slit of $$0.4 \text{ mm}$$ width. Angular divergence corresponding to second order minima would be ______ $$\times 10^{-3} \text{ rad}$$.

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \text{ m}$$. If target nucleus has atomic number 80, then maximum velocity of $$\alpha$$-particle is ______ $$\times 10^5 \text{ m/s}$$ approximately. $$\left(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ SI unit, mass of } \alpha \text{ particle} = 6.72 \times 10^{-27} \text{ kg}\right)$$