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Physics

What will be the nature of flow of water from a circular tap, when its flow rate increased from \( 0.18 \, \text{L/min} \) to \( 0.48 \, \text{L/min} \)? The radius of the tap and viscosity of water are \( 0.5 \, \text{cm} \) and \( 10^{-3} \, \text{Pa s} \), respectively.
(Density of water : \( 10^{3} \, \text{kg/m}^{3} \))

2.

For the given circuit, comment on the type of transformer used.

3.

The refractive index of a converging lens is \( 1.4 \). What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are \( R_{1} \) and \( R_{2} \) respectively.

4.

The following logic gate is equivalent to:

5.

A large block of wood of mass \( M = 5.99 \, \text{kg} \) is hanging from two long massless cords. A bullet of mass \( m = 10 \, \text{g} \) is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance \( h = 9.8 \, \text{cm} \) before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take \( g = 9.8 \, \text{m s}^{-2} \)).

6.

In order to determine the Young’s Modulus of a wire of radius \( 0.2 \, \text{cm} \) (measured using a scale of least count = \( 0.001 \, \text{cm} \)) and length \( 1 \, \text{m} \) (measured using a scale of least count = \( 1 \, \text{mm} \)), a weight of mass \( 1 \, \text{kg} \) (measured using a scale of least count = \( 1 \, \text{g} \)) was hanged to get the elongation of \( 0.5 \, \text{cm} \) (measured using a scale of least count \( 0.001 \, \text{cm} \)). What will be the fractional error in the value of Young’s Modulus determined by this experiment ?

7.

Two identical antennas mounted on identical towers are separated from each other by a distance of \( 45 \, \text{km} \). What should nearly be the minimum height of receiving antenna to receive the signals in line of sight?
(Assume radius of earth is \( 6400 \, \text{km} \))

8.

The half-life of \( \mathrm{Au}^{198} \) is \( 2.7 \) days. The activity of \( 1.50 \, \text{mg} \) of \( \mathrm{Au}^{198} \) if its atomic weight is \( 198 \, \text{g mol}^{-1} \), is, \( (N_A = 6 \times 10^{23} / \text{mol}) \).

9.

Red light differs from blue light as they have:

10.

Calculate the time interval between \( 33\% \) decay and \( 67\% \) decay if half-life of a substance is \( 20 \) minutes.

11.

Find out the surface charge density at the intersection of point \( x = 3 \, \text{m} \) plane and x-axis, in the region of uniform line charge of \( 8 \, \text{nC/m} \) lying along the z-axis in free space.

12.

A mosquito is moving with a velocity \( \vec{v} = 0.5 \, t^{2} \, \hat{i} + 3 t \, \hat{j} + 9 \hat{k} \, \text{m/s} \) and accelerating in uniform conditions. What will be the direction of mosquito after \( 2 \, \text{s} \)?

13.

Calculate the value of mean free path \(( \lambda )\) for oxygen molecules at temperature \( 27^\circ \text{C} \) and pressure \( 1.01 \times 10^{5} \, \text{Pa} \). Assume the molecular diameter \( 0.3 \, \text{nm} \) and the gas is ideal.
\( (k = 1.38 \times 10^{-23} \, \text{J K}^{-1} )\)

14.

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \( 100 \, \text{V} \). What should nearly be the ratio of their wavelengths? \( m_{p} = 1.00727 \, u,\; m_{e} = 0.00055 \, u \)

15.

A charge \( Q \) is moving \( \vec{dl} \) distance in the magnetic field \( \vec{B} \). Find the value of work done by \( \vec{B} \).

16.

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \( = 500 \, \text{g} \), Decay constant \( = 20 \, \text{g/s} \) then how much time is required for the amplitude of the system to drop to half of its initial value? \( (\ln 2 = 0.693) \)

17.

The magnetic field in a region is given by \( \vec{B} = B_{0} \left( \dfrac{x}{a} \right) \hat{k} \). A square loop of side \( d \) is placed with its edges along the \( x \) and \( y \) axes. The loop is moved with a constant velocity \( \vec{v} = v_{0} \hat{i} \). The emf induced in the loop is:

18.

Statement I: A cyclist is moving on an unbanked road with a speed of \( 7 \, \text{km h}^{-1} \) and takes a sharp circular turn along a path of radius of \( 2 \, \text{m} \) without reducing the speed. The static friction coefficient is \( 0.2 \). The cyclist will not slip and pass the curve. \( (g = 9.8 \, \text{m s}^{-2}) \)
Statement II: If the road is banked at angle of \( 45^\circ \), cyclist can cross the curve of \( 2 \, \text{m} \) radius with the speed of \( 18.5 \, \text{km h}^{-1} \) without slipping.
In the light of the above statements, choose the correct answer from the options given below.

19.

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will:

20.

A resistor develops \( 500 \, \text{J} \) of thermal energy in \( 20 \, \text{s} \) when a current of \( 1.5 \, \text{A} \) is passed through it. If the current is increased from \( 1.5 \, \text{A} \) to \( 3 \, \text{A} \), what will be the energy developed in \( 20 \, \text{s} \).

21.

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be \( \dfrac{x}{5} \dfrac{GM^{2}}{R} \) where \( x \) is ______
(Round off to the Nearest Integer)
\( M \) is the mass of earth, \( R \) is the radius of earth, \( G \) is the gravitational constant

22.

A deviation of \( 2^\circ \) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as \( 0.02 \) and \( 0.03 \) respectively and refractive index for yellow light for these glasses are \( 1.5 \) and \( 1.6 \) respectively. The refracting angles for crown glass prism will be ______ \( ^\circ \) (in degree). (Round off to the Nearest Integer)

23.

A closed organ pipe of length \( L \) and an open organ pipe contain gases of densities \( \rho_{1} \) and \( \rho_{2} \) respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is \( \dfrac{x}{3} L \sqrt{\dfrac{\rho_{1}}{\rho_{2}}} \) where \( x \) is ______. (Round off to the Nearest Integer)

24.

A body of mass \( 2 \, \text{kg} \) moves under a force of \( (2\hat{i} + 3\hat{j} + 5\hat{k} )\, \text{N} \). It starts from rest and was at the origin initially. After \( 4 \, \text{s} \), its new coordinates are \( (8, b, 20) \). The value of \( b \) is ______. (Round off to the Nearest Integer)

25.

A solid disc of radius '\( a \)' and mass '\( m \)' rolls down without slipping on an inclined plane making an angle \( \theta \) with the horizontal. The acceleration of the disc will be \( \dfrac{2}{b} g \sin \theta \) where \( b \) is __________ . (Round off to the Nearest Integer)
(\( g \) = acceleration due to gravity \( \theta =\) angle as shown in figure)

26.

A force \( \vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k} \) is applied on a intersection point of \( x = 2 \) plane and x-axis. The magnitude of torque of this force about a point \( (2, 3, 4) \) is __________. (Round off to the Nearest Integer)

27.

The energy dissipated by a resistor is \( 10 \ \text{mJ} \) in \( 1 \ \text{s} \) when an electric current of \( 2 \ \text{mA} \) flows through it. The resistance is __________ \( \Omega \). (Round off to the Nearest Integer)

28.

For an ideal heat engine, the temperature of the source is \( 127^\circ \text{C} \). In order to have \( 60\% \) efficiency the temperature of the sink should be __________ \( ^\circ \text{C} \). (Round off to the Nearest Integer)

29.

In a parallel plate capacitor set up, the plate area of capacitor is \( 2 \ \text{m}^{2} \) and the plates are separated by \( 1 \ \text{m} \). If the space between the plates are filled with a dielectric material of thickness \( 0.5 \ \text{m} \) and area \( 2 \ \text{m}^{2} \) (see figure) the capacitance of the set-up will be ________ \( \varepsilon_{0} \). (Dielectric constant of the material \( = 3.2 \)) (Round off to the Nearest Integer)

30.

A swimmer can swim with velocity of \( 12 \ \text{km/h} \) in still water. Water flowing in a river has velocity \( 6 \ \text{km/h} \). The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is __________.\(^\circ\) (Round off to the Nearest Integer) (Find the angle in degrees)

JEE Main 2021 16th March Evening Shift

Physics Chemistry Mathematics

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Statement I: A cyclist is moving on an unbanked road with a speed of \( 7 \, \text{km h}^{-1} \) and takes a sharp circular turn along a path of radius of \( 2 \, \text{m} \) without reducing the speed. The static friction coefficient is \( 0.2 \). The cyclist will not slip and pass the curve. \( (g = 9.8 \, \text{m s}^{-2}) \)
Statement II: If the road is banked at angle of \( 45^\circ \), cyclist can cross the curve of \( 2 \, \text{m} \) radius with the speed of \( 18.5 \, \text{km h}^{-1} \) without slipping.
In the light of the above statements, choose the correct answer from the options given below.

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ