NTA JEE Main 25th June 2022 Shift 1

A uniform chain of $$6$$ m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is $$0.5$$, the maximum length of the chain hanging from the table is ______ m.

A force on an object of mass $$100$$ g is $$(10\hat{i} + 5\hat{j})$$ N. The position of that object at $$t = 2$$ s is $$a\hat{i} + b\hat{j}$$ m after starting from rest. The value of $$\frac{a}{b}$$ will be ______.

A $$0.5$$ kg block moving at a speed of $$12$$ ms$$^{-1}$$ compresses a spring through a distance $$30$$ cm when its speed is halved. The spring constant of the spring will be ______ Nm$$^{-1}$$

The velocity of upper layer of water in a river is $$36$$ km h$$^{-1}$$. Shearing stress between horizontal layers of water is $$10^{-3}$$ N m$$^{-2}$$. Depth of the river is ______ m. (Co-efficient of viscosity of water is $$10^{-2}$$ Pa s)

A steam engine intakes $$50$$ g of steam at $$100°$$C per minute and cools it down to $$20°$$C. If latent heat of vaporization of steam is $$540$$ cal g$$^{-1}$$, then the heat rejected by the steam engine per minute is ______ $$\times 10^3$$ cal
(Given : specific heat capacity of water : $$1$$ cal g$$^{-1}$$ °C$$^{-1}$$)

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $$20$$ cm. The length of the open organ pipe is ______ cm

The equivalent capacitance between points $$A$$ and $$B$$ in below shown figure will be ______ $$\mu$$F.

A resistor develops $$300$$ J of thermal energy in $$15$$ s, when a current of $$2$$ A is passed through it. If the current increases to $$3$$ A, the energy developed in $$10$$ s is ______ J.

The total current supplied to the circuit as shown in the figure by the $$5$$ V battery is ______ A.

The current in a coil of self inductance $$L = 2.0$$ H is increasing according to the law $$i = 2\sin t^2$$. Find the amount of energy spent (in J) during the period when the current changes from $$0$$ to $$2$$ A.