If two metallic plates of equal thicknesses and thermal conductivities \({K_1}\) and \({K_2}\) are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

A radio-active material is reduced to \(1 / 8\) of its original amount in \(3\) days. If \(8 \times 10^{-3}\,kg\) of the material is left after \(5\) days. The initial amount of the material is \(.......\,g\)

A current carrying rectangular loop PQRS is made of uniform wire. The length \(PR = QS =5\,cm\) and \(PQ = RS =100\,cm\). If ammeter current reading changes from I to \(2 I\), the ratio of magnetic forces per unit length on the wire \(P Q\) due to wire RS in the two cases respectively \(f_{ PQ }^{ I }: f_{ PQ }^{2 I }\) is :

Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are

The energy dissipated by a resistor is \(10 \,mJ\) in \(1\,s\) when an electric current of \(2\, mA\) flows through it. The resistance is \(....... \Omega\) (Round off to the Nearest Integer)

In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).

Two identical positive charges \(Q\) each are fixed at a distance of ' \(2 a\) ' apart from each other. Another point charge qo with mass ' \(m\) ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \(q_{0}\) executes \(SHM\). The time period of oscillation of charge \(q_{0}\) will be.

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0= 10\, m\). What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v = 20\, m/s\), on a horizontal surface ......... \(^o.\) \((g = 10\, m/s^2)\)

On interchanging the resistances, the balance point of a meter bridge shifts to the left by \(10\ cm\). The resistance of their series combination is \(1\ k\Omega\). How much was the resistance on the left slot before interchanging the resistances?  ..................  \(\Omega\)

What is the position and nature of image formed by lens combination shown in figure? (\(f_1, f_2\) are focal lengths)

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: