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Physics

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: [Assume $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ m_e = 9.0 \times 10^{-31} \, \text{kg} $ and $ m_p = 1836 $ times $ m_e $]

32.

Correct Bernoulli’s equation is: [Symbols have their usual meaning]

33.

Average force exerted on a non-reflecting surface at normal incidence is $ 2.4 \times 10^{-4} \, \text{N} $. If $ 360 \, \text{W}/\text{cm}^{2} $ is the light energy flux during span of $ 1 $ hour $ 30 $ minutes. Then the area of the surface is:

34.

A clock has $ 75 \, \text{cm} $, $ 60 \, \text{cm} $ long second hand and minute hand respectively. In $ 30 $ minutes duration the tip of second hand will travel $ x $ distance more than the tip of minute hand. The value of $ x $ in meter is nearly. [Take : $ \pi = 3.14 $]

35.

Paramagnetic substances.
A. Align themselves along the directions of external magnetic field.
B. Attract strongly towards external magnetic field.
C. Has susceptibility little more than zero.
D. Move from a region of strong magnetic field to weak magnetic field.
Choose the most appropriate answer from the options given below:

36.

Two planets $ A $ and $ B $ having masses $ m_{1} $ and $ m_{2} $ move around the sun in circular orbits of $ r_{1} $ and $ r_{2} $ radii respectively. If angular momentum of $ A $ is $ L $ and that of $ B $ is $ 3L $, the ratio of time period $ \left( \frac{T_A}{T_B} \right) $ is:

37.

Young's modulus is determined by the equation given by $ Y = 49000 \, \frac{m}{l} \, \text{dyne} / \text{cm}^2 $ where $ M $ is the mass and $ l $ is the extension of wire used in the experiment. Now error in young modules ($ Y $) is estimated by taking data from $ M\text{–}l $ plot in graph paper. The smallest scale divisions are $ 5 \, \text{g} $ and $ 0.02 \, \text{cm} $ along load axis and extension axis respectively. If the value of $ M $ and $ l $ are $ 500 \, \text{g} $ and $ 2 \, \text{cm} $ respectively then percentage error of $ Y $ is:

38.

A $ \text{LCR} $ circuit is at resonance for a capacitor $ C $, inductance $ L $ and resistance $ R $. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

39.

Two charged conducting spheres of radii $ a $ and $ b $ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

40.

Three bodies $ A $, $ B $ and $ C $ have equal kinetic energies and their masses are $ 400 \, \text{g} $, $ 1.2 \, \text{kg} $ and $ 1.6 \, \text{kg} $ respectively. The ratio of their linear momenta is:

41.

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $ 27^{\circ}\text{C} $. The ratio of specific heat of gases at constant volume respectively is:

42.

A stationary particle breaks into two parts of masses $ m_A $ and $ m_B $ which move with velocities $ v_A $ and $ v_B $ respectively. The ratio of their kinetic energies $ (K_B : K_A) $ is:

43.

A player caught a cricket ball of mass $ 150 \, \text{g} $ moving at a speed of $ 20 \, \text{m/s} $. If the catching process is completed in $ 0.1 \, \text{s} $, the magnitude of force exerted by the ball on the hand of the player is:

44.

Critical angle of incidence for a pair of optical media is $ 45^\circ $. The refractive indices of first and second media are in the ratio:

45.

The diameter of a sphere is measured using a vernier caliper whose $ 9 $ divisions of main scale are equal to $ 10 $ divisions of vernier scale. The shortest division on the main scale is equal to $ 1 \, \text{mm} $. The main scale reading is $ 2 \, \text{cm} $ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $ 8.635 \, \text{g} $, the density of the sphere is:

46.

The output $ Y $ of following circuit for given inputs is:

47.

Binding energy of a certain nucleus is $ 18 \times 10^{8} \, \text{J} $. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

48.

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P–V diagram. The relation between the ratio $ \dfrac{V_a}{V_d} $ and the ratio $ \dfrac{V_b}{V_c} $ is:

49.

In the given circuit, the terminal potential difference of the cell is:

50.

In an expression $ a \times 10^{b} $.

51.

Three vectors $ \overrightarrow{OP} $, $ \overrightarrow{OQ} $ and $ \overrightarrow{OR} $ each of magnitude $ A $ are acting as shown in figure. The resultant of the three vectors is $ A\sqrt{x} $. The value of $ x $ is _______.

52.

A liquid column of height $ 0.04 \, \text{cm} $ balances excess pressure of a soap bubble of certain radius. If density of liquid is $ 8 \times 10^{3} \, \text{kg m}^{-3} $ and surface tension of soap solution is $ 0.28 \, \text{N m}^{-1} $, then diameter of the soap bubble is ______ $ \text{cm} $.
[If $ g = 10 \, \text{m s}^{-2} $]

53.

In an alpha particle scattering experiment distance of closest approach for the $ \alpha $ particle is $ 4.5 \times 10^{-14} \, \text{m} $. If target nucleus has atomic number $ 80 $, then maximum velocity of $ \alpha $-particle is ______ $ \times 10^{5} \, \text{m} / \text{s} $ approximately.
[$ \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{9} $ SI unit, mass of $ \alpha $ particle $ = 6.72 \times 10^{-27} \, \text{kg} $]

54.

A square loop $ PQRS $ having $ 10 $ turns, area $ 3.6 \times 10^{-3} \, \text{m}^{2} $ and resistance $ 100 \, \Omega $ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $ B = 0.5 \, \text{T} $ as shown. Work done in pulling the loop out of the field in $ 1.0 \, \text{s} $ is ______ $ \times 10^{-6} \, \text{J} $.

55.

A parallel beam of monochromatic light of wavelength $ 600 \, \text{nm} $ passes through single slit of $ 0.4 \, \text{mm} $ width. Angular divergence corresponding to second order minima would be ______ $ \times 10^{-3} \, \text{rad} $.

56.

An electron with kinetic energy $ 5 \, \text{eV} $ enters a region of uniform magnetic field of $ 3 \, \mu \text{T} $ perpendicular to its direction. An electric field $ E $ is applied perpendicular to the direction of velocity and magnetic field. The value of $ E $, so that electron moves along the same path, is ______ $ \text{N C}^{-1} $.
[Given, mass of electron $ = 9 \times 10^{-31} \, \text{kg} $, electric charge $ = 1.6 \times 10^{-19} \, \text{C} $]

57.

Resistance of a wire at $ 0^\circ \text{C} $, $ 100^\circ \text{C} $ and $ t^\circ \text{C} $ is found to be $ 10 \, \Omega $, $ 10.2 \, \Omega $ and $ 10.95 \, \Omega $ respectively. The temperature $ t $ in Kelvin scale is ______.

58.

A uniform thin metal plate of mass $ 10 \, \text{kg} $ with dimensions is shown. The ratio of x and y coordinates of center of mass of plate is $ \frac{n}{9} $. The value of $ n $ is ______.

59.

An electronic field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\text{ m}^2$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ $\text{V m}$.

60.

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $ \left( \dfrac{a-1}{a} \right) $ then the value of $ a $ is ______.

JEE Main 2024 8th April Morning Shift

Mathematics Physics Chemistry

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A liquid column of height $ 0.04 \, \text{cm} $ balances excess pressure of a soap bubble of certain radius. If density of liquid is $ 8 \times 10^{3} \, \text{kg m}^{-3} $ and surface tension of soap solution is $ 0.28 \, \text{N m}^{-1} $, then diameter of the soap bubble is ______ $ \text{cm} $.
[If $ g = 10 \, \text{m s}^{-2} $]

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ