NTA JEE Main 26th August 2021 Shift 2 - Physics

If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:

The angle between vector $$\left(\vec{A}\right)$$ and $$\left(\vec{A} - \vec{B}\right)$$ is:

Match List - I with List - II:
        List - I                                    List - II
a. Magnetic induction        i.   $$ML^2T^{-2}A^{-1}$$
b. Magnetic flux                  ii.  $$M^0L^{-1}A$$
c. Magnetic permeability   iii. $$MT^{-2}A^{-1}$$
d. Magnetization                 iv.  $$MLT^{-2}A^{-2}$$
Choose the most appropriate answer from the options given below:

A particle of mass $$m$$ is suspended from a ceiling through a string of length $$L$$. The particle moves in a horizontal circle of radius $$r$$ such that $$r = \frac{L}{\sqrt{2}}$$. The speed of particle will be:

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:

The solid cylinder of length 80 cm and mass $$M$$ has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $$CD$$ parallel to $$AB$$ as shown in figure is 2.7 kg m$$^2$$.

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $$\frac{24}{\pi} \times 10^2$$ N m$$^{-2}$$. What is the minimum radius of the wire?

(take g = 10 m s$$^{-2}$$)

The temperature of equal masses of three different liquids $$x$$, $$y$$ and $$z$$ are 10°C, 20°C and 30°C respectively. The temperature of mixture when $$x$$ is mixed with $$y$$ is 16°C and that when $$y$$ is mixed with $$z$$ is 26°C. The temperature of mixture when $$x$$ and $$z$$ are mixed will be:

A refrigerator consumes an average 35 W power to operate between temperature -10°C to 25°C. If there is no loss of energy then how much average heat per second does it transfer?

A cylindrical container of volume $$4.0 \times 10^{-3}$$ m$$^3$$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is:
[Take gas constant as 8.3 J mol$$^{-1}$$ K$$^{-1}$$]

The two thin coaxial rings, each of radius $$a$$ and having charges $$+Q$$ and $$-Q$$ respectively are separated by a distance of $$s$$. The potential difference between the centres of the two rings is:

A parallel-plate capacitor with plate area $$A$$ has separation $$d$$ between the plates. Two dielectric slabs of dielectric constant $$K_1$$ and $$K_2$$ of same area $$\frac{A}{2}$$ and thickness $$\frac{d}{2}$$ are inserted in the space between the plates. The capacitance of the capacitor will be given by:

An electric bulb of 500 W at 100 V is used in a circuit having a 200 V supply. Calculate the resistance $$R$$ to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

If you are provided a set of resistances, 2 $$\Omega$$, 4 $$\Omega$$, 6 $$\Omega$$ and 8 $$\Omega$$. Connect these resistances to obtain an equivalent resistance of $$\frac{46}{3}$$ $$\Omega$$.

In the given circuit the AC source has $$\omega = 100$$ rad s$$^{-1}$$. Considering the inductor and capacitor to be ideal, what will be the current $$I$$ flowing through the circuit?

A light beam is described by $$E = 800 \sin\omega\left(t - \frac{x}{c}\right)$$. An electron is allowed to move normal to the propagation of light beam with a speed of $$3 \times 10^7$$ m s$$^{-1}$$. What is the maximum magnetic force exerted on the electron?

The de-Broglie wavelength of a particle having kinetic energy $$E$$ is $$\lambda$$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

At time $$t = 0$$, a material is composed of two radioactive atoms $$A$$ and $$B$$, where $$N_A(0) = 2N_B(0)$$. The decay constant of both kind of radioactive atoms is $$\lambda$$. However, $$A$$ disintegrates to $$B$$ and $$B$$ disintegrates to $$C$$. Which of the following figures represents the evolution of $$\frac{N_B(t)}{N_B(0)}$$ with respect to time $$t$$?

Four NOR gates are connected as shown in figure. The truth table for the given figure is:

A transmitting antenna at top of a tower has a height of 50 m, and the height of receiving antenna is 80 m. What is the range of communication for the line of sight (LOS) mode?
[use radius of the earth = 6400 km]

The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass $$m$$ to undertake oscillations of time period $$T$$ is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which $$E$$ is known is _________ %

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _________ N (take $$g = 10$$ m s$$^{-2}$$)

Two simple harmonic motions are represented by the equations $$x_1 = 5\sin\left(2\pi t + \frac{\pi}{4}\right)$$ and $$x_2 = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t)$$. The amplitude of the second motion is _________ times the amplitude in the first motion.

Two waves are simultaneously passing through a string and their equations are:
$$y_1 = A_1 \sin k(x - vt)$$, $$y_2 = A_2 \sin k(x - vt + x_0)$$. Given amplitudes $$A_1 = 12$$ mm and $$A_2 = 5$$ mm, $$x_0 = 3.5$$ cm and wave number $$k = 6.28$$ cm$$^{-1}$$. The amplitude of resulting wave will be _________ mm.

If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth the speed of light is:
[$$m_p = 1.67 \times 10^{-27}$$ kg, $$e = 1.6 \times 10^{-19}$$ C, Speed of light = $$3 \times 10^8$$ m s$$^{-1}$$]

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $$\sqrt{x} \times 10^{-5}$$ Nm. The value of $$x$$ is _________

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$$^{-1}$$ in a uniform horizontal magnetic field of $$3.0 \times 10^{-2}$$ T. The maximum emf induced in the coil will be _________ $$\times 10^{-2}$$ volt (rounded off to the nearest integer).

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on another side of the lens at 8 cm as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be _________ cm

A source of light is placed in front of a screen. The intensity of light on the screen is $$I$$. Two Polaroids $$P_1$$ and $$P_2$$ are so placed in between the source of light and screen that the intensity of light on the screen is $$\frac{I}{2}$$. Then the $$P_2$$, should be rotated by an angle of _________ (degrees) so that the intensity of light on the screen becomes $$\frac{3I}{8}$$.

For the given circuit, the power across zener diode is _________ mW.