A block of mass M moving on a frictionless horizontal surface collides with a spring of spring constant K, as shown in the figure. If the spring compresses by a length \(\mathrm{L}\), then the maximum momentum of the block after the collision is.

Twelve cells, each having emf \(E\) volts are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with an ammeter, an external resistance \(R\) ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the circuit when the 12-cell battery and 2-cell battery aid each other is 3A and is \(2 \mathrm{~A}\) when they oppose each other. Then, the number of cells in 12-cell battery that are connected wrongly is :

The work done to assemble the three charges in a configuration as shown in the figure below is

Which of the following statement is incorrect?

If $E$ and $E_0$ denote energies at time $t$ and $t_0$ respectively, and $L$ and $L_0$ distance from some point at $t$ and $t_0$ respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) $E=\frac{2E_{0}L}{L_0}$ (B) $E=E_0{e}^{-\frac{2L}{L_0}}$ (C) $E=2L{e}^{\frac{-L}{E_0}}$ (D) $E=2\left(\frac{E_0}{L_0}\right)\times e^{\frac{-L}{L_0}}$

In the logic circuit given below; if \(X=1\) and \(Y=1\) then the values of \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) are

The operation of a nuclear reactor is said to be critical when the value of neutron multiplication factor \(K\) is

A ball is allowed to fall freely from a height of 42 m from the ground. If the coefficient of restitution between the ball and the ground is 0.4, then the total distance travelled by the ball before it comes to rest is

A cell of emf \(10 \mathrm{~V}\) and internal resistance \(3 \Omega\) is connected in parallel with another cell of emf \(7 \mathrm{~V}\) and internal resistance \(\frac{3}{5} \Omega\), such that their positive terminals are joined together and so their are negative terminals. Their positive terminals are joined with the negative terminal and their negative terminal is joined with the positive terminal of a third cell of emf \(20 \mathrm{~V}\) with internal resistance \(2 \Omega\). The combination can be replaced by a battery of emf \(E\) and internal resistance \(r\), then the values of \(E\) and \(R\) are respectively

An elastic spring of wnstretched length \(L\) and force constant \(k\) is stretched by a small length \(x\). It is further stretched by another small length \(y\). Work done dwring the second stretching is

The energy released by the fission of one uranium nucleus is 200 MeV . The number of fissions per second required to produce 128 W power is

If the light from Balmer series of hydrogen is used to eject photoelectrons from a metal, then the maximum work function of the metal can be

A constant horizontal force \(\overrightarrow{\mathrm{F}}\) of magnitude \(10 \mathrm{~N}\) is applied to a block \(\mathrm{A}\) and this produces an acceleration of magnitude \(20 \mathrm{~m} / \mathrm{s}^2\). If this block \(A\) is then kept against another block B of mass \(1.5 \mathrm{~kg}\) as shown in figure and a force \(\mathrm{F}^{\prime}\) of \(20 \mathrm{~N}\) is applied, find the force on the block B. Neglect friction.