The specific heat of water \(=4200\, J\, kg ^{-1}\, K ^{-1}\) and the latent heat of ice \(=3.4 \times 10^{5}\, J\, kg ^{-1}.\) \(100\) grams of ice at \(0^{\circ} C\) is placed in \(200\, g\) of water at \(25^{\circ} C\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ} C\) is close to (in \(grams\)) 

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is:

Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) \(EM\) waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason \(R\) : Infrared \(EM\) waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below:

A potentiometer wire \(AB\) having length \(L\) and resistance \(12\, r\) is joined to a cell \(D\) of \(emf\) \(\varepsilon \) and internal resistance \(r\). A cell \(C\) having \(emf\) \(\varepsilon /2\) and internal resistance \(3r\) is connected. The length \(AJ\) at which the galvanometer as shown in figure shows no deflection is

Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)

A beam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^o \) relative to that of \(A\). The intensity of the emergent light is _______.

A train starting from rest first accelerates uniformly up to a speed of \(80 \mathrm{~km} / \mathrm{h}\) for time \(t\), then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in \(\mathrm{km} / \mathrm{h}\) ) _______.

A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........

The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).)

A small spherical ball of radius \(r\), falling through a viscous medium of negligible density has terminal velocity ' \(v\) '. Another ball of the same mass but of radius \(2 r\), falling through the same viscous medium will have terminal velocity _______.

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is __________ m/s.