NTA JEE Main 20th July 2021 Shift 1 - Physics

If $$\vec{A}$$ and $$\vec{B}$$ are two vectors satisfying the relation $$\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$$. Then the value of $$|\vec{A} - \vec{B}|$$ will be:

A butterfly is flying with a velocity $$4\sqrt{2}$$ m s$$^{-1}$$ in north-east direction. Wind is slowly blowing at 1 m s$$^{-1}$$ from north to south. The resultant displacement of the butterfly in 3 seconds is:

The normal reaction $$N$$ for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possible speed without skidding is ___ $$\times 10^3$$ kg m s$$^{-2}$$.

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m s$$^{-2}$$. The normal reaction $$R'$$ by the floor if mass of the iron cylinders are equal and of 20 kg each is (in N),
[Take $$g = 10$$ m s$$^{-2}$$ and $$\mu_s = 0.2$$]

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m s$$^{-2}$$ and 4 m s$$^{-2}$$, respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

The value of tension in a long thin metal wire has been changed from $$T_1$$ to $$T_2$$. The lengths of the metal wire at two different values of tension $$T_1$$ and $$T_2$$ are $$\ell_1$$ and $$\ell_2$$, respectively. The actual length of the metal wire is:

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0 $$^\circ$$C to 50 $$^\circ$$C when no work is done is ($$R$$ is the universal gas constant)

The entropy of any system is given by,
$$S = \alpha^2 \beta \ln\left[\frac{\mu kR}{J\beta^2} + 3\right]$$
where $$\alpha$$ and $$\beta$$ are the constants. $$\mu$$, $$J$$, $$k$$ and $$R$$ are number of moles, mechanical equivalent of heat, Boltzmann's constant and gas constant, respectively.
[Take $$S = \frac{dQ}{T}$$]
Choose the incorrect option from the following:

Consider a mixture of gas molecules of types A, B and C having masses $$m_A < m_B < m_C$$. The ratio of their root mean square speeds at normal temperature and pressure is:

A certain charge $$Q$$ is divided into two parts $$q$$ and $$(Q - q)$$. How should the charges $$Q$$ and $$q$$ be divided so that $$q$$ and $$(Q - q)$$ placed at a certain distance apart experience maximum electrostatic repulsion?

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m$$^2$$. At every point the direction of current density is at an angle of 60$$^\circ$$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (resistivity of magnesium $$\rho = 44 \times 10^{-8}$$ $$\Omega$$m)

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $$r_d$$ and $$r_\alpha$$ be their respective radii of circular path. The value of $$\frac{r_d}{r_\alpha}$$ is equal to:

The arm PQ of a rectangular conductor is moving from $$x = 0$$ to $$x = 2b$$ outwards and then inwards from $$x = 2b$$ to $$x = 0$$ as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from $$x = 0$$ to $$x = b$$. Identify the graph showing the variation of different quantities with distance:

AC voltage $$V(t) = 20 \sin \omega t$$ of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m$$^2$$. The amplitude of the oscillating displacement current for the applied AC voltage is [Take $$\varepsilon_0 = 8.85 \times 10^{-12}$$ F m$$^{-1}$$]

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is:

The radiation corresponding to $$3 \to 2$$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $$5 \times 10^{-4}$$ T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is:
(Mass of electron $$= 9.1 \times 10^{-31}$$ kg)

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years, respectively. What will be the time after the which one third of the material remains? (Take ln 3 = 1.1)

A nucleus of mass $$M$$ emits $$\gamma$$-ray photon of frequency $$\nu$$. The loss of internal energy by the nucleus is: [Take $$c$$ as the speed of electromagnetic wave]

For the circuit shown below, calculate the value of $$I_z$$:

In a spring gun having spring constant 100 N m$$^{-1}$$ a small ball $$B$$ of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance $$d$$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of $$d$$ is ___ m.
$$(g = 10$$ m s$$^{-2})$$

A body having specific charge 8 $$\mu$$C g$$^{-1}$$ is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V m$$^{-1}$$ is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ___ s.

A rod of mass $$M$$ and length $$L$$ is lying on a horizontal frictionless surface. A particle of mass $$m$$ travelling along the surface hits at one end of the rod with a velocity $$u$$ in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $$\left(\frac{m}{M}\right)$$ is $$\frac{1}{x}$$. The value of $$x$$ will be ___.

A circular disc reaches from top to bottom of an inclined plane of length $$L$$. When it slips down the plane, it takes time $$t_1$$. When it rolls down the plane, it takes time $$t_2$$. The value of $$\frac{t_2}{t_1}$$ is $$\sqrt{\frac{3}{x}}$$. The value of $$x$$ will be ___.

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___ $$\pi$$ J.

The amplitude of wave disturbance propagating in the positive $$x$$-direction is given by $$y = \frac{1}{(1+x)^2}$$ at time $$t = 0$$ and $$y = \frac{1}{1+(x-2)^2}$$ at $$t = 1$$ s, where $$x$$ and $$y$$ are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___ m s$$^{-1}$$.

The frequency of a car horn encountered a change from 400 Hz to 500 Hz. When the car approaches a vertical wall. If the speed of sound is 330 m s$$^{-1}$$. Then the speed of car is ___ km h$$^{-1}$$.

In an $$LCR$$ series circuit, an inductor 30 mH and a resistor 1 $$\Omega$$ are connected to an AC source of angular frequency 300 rad s$$^{-1}$$. The value of capacitance for which the current leads the voltage by 45$$^\circ$$ is $$\frac{1}{x} \times 10^{-3}$$ F. Then the value of $$x$$ is ___.

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification 6, gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to ___ cm.

A carrier wave $$V_C(t) = 160 \sin(2\pi \times 10^6 t)$$ volts is made to vary between $$V_{max} = 200$$ V and $$V_{min} = 120$$ V by a message signal $$V_m(t) = A_m \sin(2\pi \times 10^3 t)$$ volts. The peak voltage $$A_m$$ of the modulating signal is ___.