A point particle of charge \(Q\) is located at \(P\) along the axis of an electric dipole 1 at a distance \(r\) as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance \(2 a\). For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

The specific heats, \(C_P\) and \(C_V\) of a gas of diatomic molecules, \(A\), are given (in units of \(J\, mol^{-1}\, K^{-1}\)) by \(29\) and \(22\), respectively. Another gas of diatomic molecules \(B\), has the corresponding values \(30\) and \(21\). If they are treated as ideal gases, then

A capacitor C is first charged fully with potential difference of \( V_{0} \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In time t, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is

A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
Choose the correct answer from the options given below:

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______.

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity \(\omega\) as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, \(I_A-I_B\), for the given Amperian loops is:

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below

Three persons enter in a lift at the ground floor. The lift will go up to \(10^{\text {th }}\) floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ___ .

Charges \(-q\) and \(+ q\) located at \(A\) and \(B\), respectively, constitute an electric dipole. Distance \(AB = 2a\), \(O\) is the mid point of the dipole and \(OP\) is perpendicular to \(AB\). A charge \(Q\) is placed at \(P\) where \(OP = y\) and \(y >> 2a\). The charge \(Q\) experiences an electrostatic force \(F\). If \(Q\) is now moved along the equatorial line to \(P'\) such that \(OP' = \frac{y}{3}\), the force on \(Q\) will be close to: \(\left( {\frac{y}{3} >  > 2a} \right)\)

Two circles with equal radii intersecting at the points \((0, 1)\) and \((0, -1).\) The tangent at the point \((0, 1)\) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is

If \(m\) and \(M\) are the minimum and the maximum values of \(4 + \frac{1}{2}\,{\sin ^2}\,2x - 2\,{\cos ^4}\,x\,,x\, \in R,\)  then \(M - m\) is equal to

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

List\(-I\)	List\(-II\)
\(A\)  Microwaves	\(I\) Physiotherapy
\(B\) \(UV\) rays	\(II\) Treatment of cancer
\(C\) Infra-red rays	\(III\) Lasik eye surgery
\(D\) \(X\)-rays	\(IV\) Aircraft navigation

Choose the correct answer from the option given below:

Let \(f:[0, \infty) \rightarrow[0, \infty)\) be defined as \(\mathrm{f}(\mathrm{x})= \int_{0}^{x}[y] \,d y\) Where \([x]\) is the greatest integer less than or equal to \(x\). Which of the following is true?