Consider the nuclear fission \(Ne^{20} \to 2He^4 + C^{12}\) .Given that the binding energy / nucleon of \(Ne^{20}, He^4\) and \(C^{12}\) are, respectively, \(8.03\, MeV\), \(7.07\, MeV\), and \(7.86\, MeV\), identify the correct statement

A particle of mass \(m\) moves in a circular orbit in a central potential field \(U\left( r \right) = \frac{1}{2}k{r^2}\). If Bohr’s quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number \(n\) as

In the given figure, the charge stored in \(6 \ \mu \mathrm{F}\) capacitor, when points \(A\) and \(B\) are joined by a connecting wire is _______ \(\mu \mathrm{C}\).

An alternating voltage \(v\left( t \right) = 220\,\sin \,100\pi l\,volt\) is applied to a purely resistive load of \(50\,\Omega \) . The time taken for the current to rise from half of the peak value of the peak value is.....\(ms\)

Two cylindrical vessels of equal cross-sectional area \(16\,cm ^{2}\) contain water upto herghts \(100\,cm\) and \(150\,cm\) respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is \(......J\) [Take density of water \(=10^{3}\,kg / m ^{3}\) and \(g =10\,ms ^{-2}\) ]

The time period of a simple harmonic oscillator is \(T =2 \pi \sqrt{\frac{ k }{ m }}\). The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg , and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant( \(k\) ) is ___________ %.

A bar magnet has total length \(2 l=20\) units and the field point \(P\) is at a distance \(\mathrm{d}=10\) units from the centre of the magnet. If the relative uncertainty of length measurement is \(1 \%\), then uncertainty of the magnetic field at point P is :

For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _______.

Match List \(-I\) with List \(-II\).

	List \(-I\)		List \(-II\)
\(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
\(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
\(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
\(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). The \(n_2\) material is replaced by another material having refractive index \(n_3\) such that the critical angle at the interface between \(n_1\) and \(n_3\) materials is \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is :

Two identical parallel plate capacitors, of capacitance \(C\) each, have plates of area \(A\), separated by a distance \(d\). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \(K_1\) , \(K_2\) and \(K_3\) . The first capacitor is filled as shown in fig. \(I\), and the second one is filled as shown in fig. \(II\). If these two modified capacitors are charged by the same potential \(V\), the ratio of the energy stored in the two, would be ( \(E_1\) refers to capacitor \((I)\) and \(E_2\) to capacitor \((II)\))