Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is

Given below are two statements: Statement \(I :\) A second's pendulum has a time period of \(1\) second. Statement \(II :\) It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below:

A parallel plate capacitor is made of two plates of length \(l\), width \(w\) and separated by distance \(d\). A dielectric slab ( dielectric constant \(K\)) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force \(F = -\frac{{\partial U}}{{\partial x}}\) where \(U\) is the energy of the capacitor when dielectric is inside the capacitor up to distance \(x\) (See figure). If the charge on the capacitor is \(Q\) then the force on the dielectric when it is near the edge is

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Body \('P'\) having mass \(M\) moving with speed \('u'\) has head-on collision elastically with another body \('Q'\) having mass \('m'\) initially at rest. If \(m< < M,\) body \('Q'\) will have a maximum speed equal to \('2u'\) after collision. Reason \(R\) : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

An electron in the hydrogen atom initially in the fourth excited state makes a transition to \(\mathrm{n}^{\text {th }}\) energy state by emitting a photon of energy 2.86 eV. The integer value of \(n\) will be ____.

The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.

If two vectors \(\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\vec{Q}=4 \hat{i}-2 \hat{j}+ mk\) are perpendicular to each other. Then, the value of \(m\) will be :

A particle starts moving from time \(t=0\) and its coordinate is given as \(x(t)=4t^{3}-3t.\)
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point.
C. Acceleration of the particle is non-negative.
D. The particle is 0.5 units away from origin at its turning point.
E. Particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below :

The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8\  \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is _______ \(\mathrm{A}\).