Two cars are travelling towards each other at speed of \(20 \mathrm{~m} \mathrm{~s}^{-1}\) each. When the cars are \(300 \mathrm{~m}\) apart, both the drivers apply brakes and the cars retard at the rate of \(2 \mathrm{~m} \mathrm{~s}^{-2}\). The distance between them when they come to rest is _______.

A short bar magnet placed with its axis at \(30^{\circ}\) with an external field of 800 Gauss, experiences a torque of \(0.016 N . m\). The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3} J\). The value of \(\alpha\) is _________ .

Two identical capacitors have same capacitance \(C\). One of them is charged to the potential \(\mathrm{V}\) and other to the potential \(2 \mathrm{~V}\). The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is _______.

The electric field intensity produced by the radiation coming from a \(100\, W\) bulb at a distance of \(3\, m\) is \(E\). The electric field intensity produced by the radiation coming from \(60\, W\) at the same distance is \(\sqrt{\frac{x}{5}} E\). Where the value of \(x=......... .\)

A point charge of magnitude \(+ 1\,\mu C\) is fixed at \((0, 0, 0) \). An isolated uncharged spherical conductor, is fixed with its center at \((4, 0, 0).\) The potential and the induced electric field at the centre of the sphere is

The \(I-V\) characteristics of a \(p - n\) junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltages of \(2 \; V\) and \(4 \; V\) respectively, is

Given below are two statements : one is labeled as Assertion \(A\) and the other is labeled as Reason \(R\) Assertion \(A:\) Photodiodes are used in forward bias usually for measuring the light intensity. Reason \(R:\) For a \(p-n\) junction diode, at applied voltage \(V\) the current in the forward bias is more than the current in the reverse bias for \(\left|V_z\right| > \pm V \geq\left|V_0\right|\) where \(V_0\) is the threshold voltage and \(V _{ z }\) is the breakdown voltage. In the light of the above statements, choose the correct answer from the options given below

A radioactive nuclei with decay constant \(0.5/s\) is being produced at a constant rate of \(100\, nuclei/s\). If at \(t\, = 0\) there were no nuclei, the time when there are \(50\, nuclei\) is

In a vernier callipers, each \(cm\) on the main scale is divided into \(20\) equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be \(\dots \; \times 10^{-2} \;mm\)

The figure shows three circuits \(I, II\) and \(III\) which are connected to a \(3\,V\) battery. If the powers dissipated by the configurations \(I, II\) and \(III\) are \(P_1 , P_2\) and \(P_3\) respectively, then