NTA JEE Main 28th June 2022 Shift 1

A hanging mass $$M$$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $$2Mg$$ force. In this situation, tension in the string is $$\frac{x}{5}Mg$$ for $$x =$$ ______. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

A pendulum is suspended by a string of length $$250$$ cm. The mass of the bob of the pendulum is $$200$$ g. The bob is pulled aside until the string is at $$60°$$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ______ m s$$^{-1}$$. (if $$g = 10$$ m s$$^{-2}$$)

A man of $$60$$ kg is running on the road and suddenly jumps into a stationary trolly car of mass $$120$$ kg. Then the trolly car starts moving with velocity $$2$$ m s$$^{-1}$$. The velocity of the running man was ______ m s$$^{-1}$$, when he jumps into the car.

The position vector of $$1$$ kg object is $$\vec{r} = (3\hat{i} - \hat{j})$$ m and its velocity $$\vec{v} = (3\hat{j} + \hat{k})$$ m s$$^{-1}$$. The magnitude of its angular momentum is $$\sqrt{x}$$ N m s, where $$x$$ is ______

The total internal energy of two mole monoatomic ideal gas at temperature $$T = 300$$ K will be ______ J. (Given $$R = 8.31$$ J mol$$^{-1}$$ K$$^{-1}$$)

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $$R$$ using a given resistor of $$15$$ $$\Omega$$. The galvanometer $$(G)$$ shows null deflection when tapping key is at $$43$$ cm mark from end $$A$$. If the end correction for end $$A$$ is $$2$$ cm, then the determined value of $$R$$ will be ______ $$\Omega$$.

Current measured by the ammeter $$(A)$$ in the reported circuit when no current flows through $$10\Omega$$ resistance, will be ______ A.

A singly ionized magnesium atom $$(A = 24)$$ ion is accelerated to kinetic energy $$5$$ keV, and is projected perpendicularly into a magnetic field $$B$$ of the magnitude $$0.5$$ T. The radius of path formed will be ______ cm.

An AC source is connected to an inductance of $$100$$ mH, a capacitance of $$100$$ $$\mu$$F and a resistance of $$120$$ $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity $$2$$ J °C$$^{-1}$$ will get heated by $$16°$$C is ______ s.

A telegraph line of length $$100$$ km has a capacity of $$0.01$$ $$\mu$$F km$$^{-1}$$ and it carries an alternating current at $$0.5$$ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ______ mH. (If $$\pi = \sqrt{10}$$)