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Physics

If a rubber ball falls from a height \( h \) and rebounds upto the height of \( \frac{h}{2} \). The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are:

32.

The co-ordinates of a particle moving in x-y plane are given by: \( x = 2 + 4t \) , \( y = 3t + 8t^{2} \). The motion of the particle is:

33.

To measure the internal resistance of a battery, potentiometer is used. For \( R = 10 \, \Omega \), the balance point is observed at \( l = 500 \, \text{cm} \) and for \( R = 1 \, \Omega \) the balance point is observed at \( l = 400 \, \text{cm} \). The internal resistance of the battery is approximately:

34.

An infinitely long positively charged straight thread has a linear charge density \( \lambda \, \text{Cm}^{-1} \). An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

35.

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \( 8 \, \Omega \) and \( 10 \, \Omega \) respectively. After inserting in a hot bath of temperature \( 400^\circ \text{C} \), the resistance of platinum wire is:

36.

A body travels \( 102.5 \, \text{m} \) in \( n^{\text{th}} \) second and \( 115.0 \, \text{m} \) in \( (n + 2)^{\text{th}} \) second. The acceleration is:

37.

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time \( t \). Which of the following curve best describes acceleration of the block with time:

38.

An effective power of a combination of \( 5 \) identical convex lenses which are kept in contact along the principal axis is \( 25 \, \text{D} \). Focal length of each of the convex lens is:

39.

A metal wire of uniform mass density having length \( L \) and mass \( M \) is bent to form a semicircular arc and a particle of mass \( m \) is placed at the centre of the arc. The gravitational force on the particle by the wire is:

40.

Which of the following nuclear fragments corresponding to nuclear fission between neutron \(( ^{1}_{0}\mathrm{n}) \) and uranium isotope \(( ^{235}_{92}\mathrm{U} \)) is correct:

41.

Which figure shows the correct variation of applied potential difference \( V \) with photoelectric current \( I \) at two different intensities of light \( (I_{1} < I_{2}) \) of same wavelengths:

42.

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

43.

On celcius scale the temperature of body increases by \( 40^\circ \text{C} \). The increase in temperature on Fahrenheit scale is:

44.

Given below are two statements:
Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \( P_1 - P_2 = \rho g (h_2 - h_1) \)
Statement II: In ventury tube shown \( 2gh = v_1^2 - v_2^2 \).

In the light of the above statements, choose the most appropriate answer from the options given below:

45.

The electric field in an electromagnetic wave is given by \( \vec{E} = \hat{\imath} \, 40 \cos \omega \!\left( t - \frac{z}{c} \right) \, \text{N C}^{-1} \). The magnetic field induction of this wave is (in SI unit):

46.

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to:
A. Pure inductor.
B. Pure capacitor.
C. Pure resistor.
D. Combination of an inductor and capacitor.
Choose the correct answer from the options given below:

47.

The equation of stationary wave is: \( y = 2a \sin\!\left( \dfrac{2\pi n t}{\lambda} \right)\cos\!\left( \dfrac{2\pi x}{\lambda} \right) \). Which of the following is NOT correct:

48.

The value of net resistance of the network as shown in the given figure is:

49.

In an experiment to measure focal length \( (f) \) of convex lens, the least counts of the measuring scales for the position of object \( (u) \) and for the position of image \( (v) \) are \( \Delta u \) and \( \Delta v \), respectively. The error in the measurement of the focal length of the convex lens will be:

50.

P–T diagram of an ideal gas having three different densities \( \rho_{1}, \rho_{2}, \rho_{3} \) (in three different cases) is shown in the figure. Which of the following is correct:

51.

Two wavelengths \( \lambda_{1} \) and \( \lambda_{2} \) are used in Young’s double slit experiment. \( \lambda_{1} = 450 \, \text{nm} \) and \( \lambda_{2} = 650 \, \text{nm} \). The minimum order of fringe produced by \( \lambda_{2} \) which overlaps with the fringe produced by \( \lambda_{1} \) is \( n \). The value of \( n \) is ________.

52.

Two forces \( \vec{F}_{1} \) and \( \vec{F}_{2} \) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \( \vec{F}_{1} \) and \( \vec{F}_{2} \) is \( \cos^{-1}\!\left( \frac{1}{n} \right) \). The value of \( |n| \) is ________.

53.

An infinite plane sheet of charge having uniform surface charge density \( +\sigma_{s} \, \text{C} \, /\text{m}^{2} \) is placed on x–y plane. Another infinitely long line charge having uniform linear charge density \( +\lambda_{\ell} \, \text{C} \,/ \text{m} \) is placed at \( z = 4 \, \text{m} \) plane and parallel to y-axis. If the magnitude values \( |\sigma_{s}| = 2|\lambda_{e}| \) then at point \( (0, 0, 2) \), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \( \pi \sqrt{n} : 1 \). The value of \( n \) is __________.

54.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed \( v \). The sphere and the cylinder reaches upto maximum heights \( h_{1} \) and \( h_{2} \), respectively, above the initial level. The ratio \( h_{1} : h_{2} \) is \( \frac{n}{10} \). The value of \( n \) is __________.

55.

A alternating current at any instant is given by \( i = \left[ 6 + \sqrt{56}\,\sin\!\left(100\pi t + \frac{\pi}{3}\right) \right] \,\text{A} \). The rms value of the current is _______ \( \text{A} \).

56.

Twelve wires each having resistance \( 2\,\Omega \) are joined to form a cube. A battery of \( 6 \,\text{V} \) emf is joined across point \( a \) and \( c \). The voltage difference between \( e \) and \( f \) is _______ \( \text{V} \).

57.

The magnetic field existing in a region is given by \( \vec{B} = 0.2\,(1 + 2x)\,\hat{k}\; \text{T} \). A square loop of edge \( 50 \) \( \text{cm} \) carrying \( 0.5 \) \( \text{A} \) current is placed in \( x-\!y \) plane with its edges parallel to the \( x-\!y \) axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _______ \( \text{mN} \).

58.

A soap bubble is blown to a diameter of \( 7 \) \( \text{cm} \). \( 36960 \) \( \text{erg} \) of work is done in blowing it further. If surface tension of soap solution is \( 40 \) \( \text{dyne/cm} \) then the new radius is _________ \( \text{cm} \). Take \( \left( \pi = \frac{22}{7} \right) \).

59.

An elastic spring under tension of \( 3\,\text{N} \) has a length \( a \). Its length is \( b \) under tension \( 2\,\text{N} \). For its length \( (3a - 2b) \), the value of tension will be _________ \( \text{N} \).

60.

A hydrogen atom changes its state from \( n = 3 \) to \( n = 2 \). Due to recoil, the percentage change in the wavelength of emitted light is approximately \( 1 \times 10^{-n} \). The value of \( n \) is _______________.
[Given \( R h c = 13.6 \, \text{eV} \), \( h c = 1242 \, \text{eV}\,\text{nm} \), \( h = 6.6 \times 10^{-34} \, \text{J}\,\text{s} \), mass of the hydrogen atom \( = 1.6 \times 10^{-27} \, \text{kg} \)]

JEE Main 2024 4th April Morning Shift

Mathematics Physics Chemistry

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An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

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