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A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height \( 3h \) from the ground, as shown in the figure. A spherical ball of mass \( m \) is released on the slide from rest at a height \( h \) from the top of the terrace. The ball leaves the slide with a velocity \( \,\vec{u}_0 = u_0 \hat{x} \, \) and falls on the ground at a distance \( d \) from the building making an angle \( \theta \) with the horizontal. It bounces off with a velocity \( \vec{v} \) and reaches a maximum height \( h_1 \). The acceleration due to gravity is \( g \) and the coefficient of restitution of the ground is \( \dfrac{1}{\sqrt{3}} \). Which of the following statement(s) is(are) correct?

2.

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is \( \delta = 60^\circ \) (see Figure-\( 1 \)). The angle of minimum deviation for red light from the same prism is \( \delta_{\min} = 30^\circ \) (see Figure-\( 2 \)). The refractive index of the prism material for blue light is \( \sqrt{3} \). Which of the following statement(s) is(are) correct?

3.

In a circuit shown in the figure, the capacitor \( C \) is initially uncharged and the key \( K \) is open. In this condition, a current of \( 1 \, \text{A} \) flows through the \( 1 \, \Omega \) resistor. The key is closed at time \( t = t_0 \). Which of the following statement(s) is(are) correct? [Given: \( e^{-1} = 0.36 \)]

4.

A bar of mass \( M = 1.00 \, \text{kg} \) and length \( L = 0.20 \, \text{m} \) is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass \( m = 0.10 \, \text{kg} \) is moving on the same horizontal surface with \( 5.00 \, \text{m s}^{-1} \) speed on a path perpendicular to the bar. It hits the bar at a distance \( L/2 \) from the pivoted end and returns back on the same path with speed \( v \). After this elastic collision, the bar rotates with an angular velocity \( \omega \). Which of the following statement is correct?

5.

A container has a base of \( 50 \, \text{cm} \times 5 \, \text{cm} \) and height \( 50 \, \text{cm} \), as shown in the figure. It has two parallel electrically conducting walls each of area \( 50 \, \text{cm} \times 50 \, \text{cm} \). The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant \( 3 \) at a uniform rate of \( 250 \, \text{cm}^3 \, \text{s}^{-1} \). What is the value of the capacitance of the container after \( 10 \) seconds?
[Given: Permittivity of free space \( \varepsilon_0 = 9 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2} \), the effects of the non-conducting wall on the capacitance are negligible]

6.

One mole of an ideal gas expands adiabatically from an initial state \( (T_A, V_0) \) to final state \( (T_f, 5V_0) \). Another mole of the same gas expands isothermally from a different initial state \( (T_B, V_0) \) to the same final state \( (T_f, 5V_0) \). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is \( \gamma \). What is the ratio \( T_A / T_B \)?

7.

Two satellites \( P \) and \( Q \) are moving in different circular orbits around the Earth (radius \( R \)). The heights of \( P \) and \( Q \) from the Earth surface are \( h_P \) and \( h_Q \), respectively, where \( h_P = R/3 \). The accelerations of \( P \) and \( Q \) due to Earth’s gravity are \( g_P \) and \( g_Q \), respectively. If \( g_P / g_Q = 36 / 25 \), what is the value of \( h_Q \)?

8.

A Hydrogen-like atom has atomic number \( Z \). Photons emitted in the electronic transitions from level \( n = 4 \) to level \( n = 3 \) in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is \( 1.95 \, \text{eV} \). If the photoelectric threshold wavelength for the target metal is \( 310 \, \text{nm} \), the value of \( Z \) is ______.
[Given: \( hc = 1240 \, \text{eV} \! \cdot \! \text{nm} \) and \( Rhc = 13.6 \, \text{eV} \), where \( R \) is the Rydberg constant, \( h \) is the Planck’s constant and \( c \) is the speed of light in vacuum]

9.

An optical arrangement consists of two concave mirrors \( M_1 \) and \( M_2 \), and a convex lens \( L \) with a common principal axis, as shown in the figure. The focal length of \( L \) is \( 10 \, \text{cm} \). The radii of curvature of \( M_1 \) and \( M_2 \) are \( 20 \, \text{cm} \) and \( 24 \, \text{cm} \), respectively. The distance between \( L \) and \( M_2 \) is \( 20 \, \text{cm} \). A point object \( S \) is placed at the mid-point between \( L \) and \( M_2 \) on the axis. When the distance between \( L \) and \( M_1 \) is \( n/7 \, \text{cm} \), one of the images coincides with \( S \). The value of \( n \) is _______.

10.

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is \( 10 \pm 0.1 \, \text{cm} \) and the distance of its real image from the lens is \( 20 \pm 0.2 \, \text{cm} \). The error in the determination of focal length of the lens is \( n\% \). The value of \( n \) is __________.

11.

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas \( (\gamma = \frac{5}{3}) \) and one mole of an ideal diatomic gas \( (\gamma = \frac{7}{5}) \). Here, \( \gamma \) is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of \( 66 \, \text{Joule} \) when heated at constant pressure. The change in its internal energy is __________ Joule.

12.

A person of height \( 1.6 \, \text{m} \) is walking away from a lamp post of height \( 4 \, \text{m} \) along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is \( 60 \, \text{cm s}^{-1} \), the speed of the tip of the person’s shadow on the ground with respect to the person is __________ \( \text{cm s}^{-1} \).

13.

Two point-like objects of masses \( 20 \, \text{gm} \) and \( 30 \, \text{gm} \) are fixed at the two ends of a rigid massless rod of length \( 10 \, \text{cm} \). This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is \( 1.2 \times 10^{-8} \, \text{N m rad}^{-1} \). The angular frequency of the oscillations in \( n \times 10^{-3} \, \text{rad s}^{-1} \). The value of \( n \) is _______.

14.

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

15.

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien’s constant as \( 2.9 \times 10^{-3} \, \text{m-K} \) and \( \dfrac{hc}{e} = 1.24 \times 10^{-6} \, \text{eV-m} \) ]

16.

A series LCR circuit is connected to a \( 45\sin(\omega t) \) Volt source. The resonant angular frequency of the circuit is \( 10^{5} \, \text{rad} \, \text{s}^{-1} \) and current amplitude at resonance is \( I_{0} \). When the angular frequency of the source is \( \omega = 8 \times 10^{4} \, \text{rad} \, \text{s}^{-1} \), the current amplitude in the circuit is \( 0.05 I_{0} \). If \( L = 50 \, \text{mH} \), match each entry in List-I with an appropriate value of from List-II and choose the correct option.

17.

A thin conducting rod MN of mass \( 20 \, \text{gm} \), length \( 25 \, \text{cm} \) and resistance \( 10 \, \Omega \) is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field \( B_{0} = 4 \, \text{T} \) directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time \( t = 0 \) and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option.
[Given: The acceleration due to gravity \( g = 10 \, \text{m} \, \text{s}^{-2} \) and \( e^{-1} = 0.4 \)]

JEE Advanced 2023 Paper - 1

Physics Chemistry Mathematics

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List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

JEE MainsJEE AdvanceBITSATJEE Advance | PYQ

JEE Mains JEE Advance BITSAT
JEE Advance | PYQ