NTA JEE Main 29th July 2022 Shift 2

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $$x\sqrt{F}$$ rad s$$^{-1}$$. If F be the force exerted by the liquid at the other end then the value of x will be _____

A metal wire of length 0.5 m and cross-sectional area $$10^{-4}$$ m$$^2$$ has breaking stress $$5 \times 10^8$$ N m$$^{-2}$$. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ m s$$^{-1}$$

The velocity of a small ball of mass 0.3 g and density 8 g cc$$^{-1}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g cc$$^{-1}$$, then the value of viscous force acting on the ball will be $$x \times 10^{-4}$$ N, the value of x is _____ [use $$g = 10$$ m s$$^{-2}$$]

Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is $$a \times 10^{-2}$$ W m$$^{-2}$$. The value of 'a' will be

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $$5\sqrt{x}$$ s. The value of x will be _____

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 m s$$^{-1}$$. The area of cross-section of the wire is 2.0 mm$$^2$$ and its Young's modulus is $$1.2 \times 10^{11}$$ N m$$^{-2}$$. The extension of the wire over its natural length due to its tension will be $$x \times 10^{-5}$$ m. The value of x is _____

A capacitor of capacitance 500 $$\mu$$F is charged completely using a DC supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _____ A.

Two radioactive materials A and B have decay constants $$25\lambda$$ and $$16\lambda$$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be 'e' after a time $$\frac{1}{a\lambda}$$. The value of a is _____

A 8V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be _____ $$\Omega$$.

A modulating signal $$2\sin(6.28 \times 10^6 t)$$ is added to the carrier signal $$4\sin(12.56 \times 10^9 t)$$ for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be _____ MHz.