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 $1.95 \mathrm{eV}$. If the photoelectric threshold wavelength for the target metal is $310 \mathrm{nm}$, the value of $Z$ is _____.
[Given $hc=1240 \mathrm{eV}-\mathrm{nm}$ and $Rhc=13.6 \mathrm{eV}$, where $R$ is the Rydberg constant, $h$ is the Planck’s constant and $c$ is the speed of light in vacuum]

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$ . Which of the following statements is (are) true?

A projectile of mass 200 g is launched in a viscous medium at an angle \(60^{\circ}\) with the horizontal, with an initial velocity of \(270 \mathrm{~m} / \mathrm{s}\). It experiences a viscous drag force \(\vec{F}=-c \vec{v}\) where the drag coefficient \(c=0.1 \mathrm{~kg} / \mathrm{s}\) and \(\vec{v}\) is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s . Taking \(e=2.7\), the horizontal distance of the wall from the point of projection (in m ) is

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Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS Maglev system.
There are coils on both sides of wheels. Due to motion of train, current induces in the coil of track which levitate it. This is in accordance with Lenz's law. If trains lower down then due to Lenz's law a repulsive force increases due to which train gets uplifted and if it goes much high then there is a net downward force disc to gravity. The advantage of Maglev train is that there is no friction between the train and the track, thereby reducing power consumption and enabling the train to attain very high speeds.
Disadvantage of Maglev train is that as it slows down the electromagnetic forces decreases and it becomes difficult to keep it leviated and as it moves forward according to Lenz law, there is an electromagnetic drag force.
Question:
What is the disadvantage of this system?

A cubical region of side \(a\) has its centre at the origin. It encloses three fixed point charges, \(-q\) at \((0,-a / 4,0),+3 q\) at \((0,0,0)\) and \(-q\) at \((0,+a / 4,0)\). Choose the correct options(s)

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and ${\mathrm{U}}_0$ are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

	Column I		Column II
A.	${\mathrm{U}}_1\left(\mathrm{x}\right)=\frac{{\mathrm{U}}_0}{2}{\left[1-{\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^2\right]}^2$	P.	The force acting on the particle is zero at $\mathrm{x}\mathrm{}=\mathrm{}\mathrm{a}$
B.	${\mathrm{U}}_2\left(\mathrm{x}\right)=\frac{{\mathrm{U}}_0}{2}{\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^2$	Q.	The force acting on the particle is zero at $\mathrm{x}\mathrm{}=\mathrm{}0$ .
C.	${\mathrm{U}}_3\left(\mathrm{x}\right)=\frac{{\mathrm{U}}_0}{2}{\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^2\exp \left[-{\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^2\right]$	R.	The force acting on the particle is zero at $\mathrm{x}=\mathrm{}-\mathrm{a}$
D.	${\mathrm{U}}_4\left(\mathrm{x}\right)=\frac{{\mathrm{U}}_0}{2}\left[\frac{\mathrm{x}}{\mathrm{a}}-\frac{1}{3}{\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^3\right]$	S.	The particle experiences an attractive force towards $\mathrm{x}\mathrm{}=\mathrm{}0$ in the region $\left|\mathrm{x}\right|<\mathrm{a}$
		T.	The particle with total energy $\frac{{\mathrm{U}}_0}{4}$ can oscillate about the point $\mathrm{x}=\mathrm{}-\mathrm{a}$

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S₁ is pressed first to fully charge the capacitor C₁ and the released. The switch S₂ is then pressed to charge the capacitor C₂. After some time, S₂ is released and then is S₃ pressed. After some time,

In the following reactions, $\mathbf{P},\mathbf{Q},\mathbf{R}$, and $\mathbf{S}$ are the major products.




The correct statement(s) about $\mathbf{P},\mathbf{Q},\mathbf{R}$, and $\mathbf{S}$ is(are)

Let \(f:(-1,1) \rightarrow I R\) be such that \(f(\cos 4 \theta)=\frac{2}{2-\sec ^{2} \theta}\) for \(\theta \in\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\). Then the value (s) of \(f\left(\frac{1}{3}\right)\) is (are)

Match the transformation in Column I with appropriate options in Column II.

Column I	Column II
A. \(CO _2(s) \rightarrow CO _2(g)\)	p. Phase transition
B. \(CaCO _3(s) \rightarrow CaO (s)\) \(+~ CO _2(g)\)	q. Allotropic change
C. \(2 H \rightarrow H _2(g)\)	r. \(\Delta\text{H}\) is positive
D. \(P _{\text {(white, solid) }} \rightarrow P _{\text {(red, solid) }}\)	s. \(\Delta\text{S}\) is positive
	t. \(\Delta\text{S}\) is negative

Which of the following statement(s) is (are) correct about the spectrum of hydrogen atom?

In a neutral or faintly alkaline solution, $8$ moles of permanganate anion quantitatively oxidize thiosulphate anions to produce $\mathrm{X}$ moles of a sulphur containing product. The magnitude of $\mathrm{X}$ is:

Let $f:R\to R$ be defined by $f\left(x\right)=\frac{x^2-3x-6}{x^2+2x+4}$ Then which of the following statements is(are) TRUE?