The figure represents the momentum time \((p-t)\) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If \(\left(t_3-t_2\right) < t_1\)

A block of mass \(m = 10\,kg\) rests on a horizontal table. The coefficient of friction between the block and the table is \(0.05.\) When hit by a bullet of mass \(50\,g\) moving with speed \(v,\) that gets embedded in it, the block moves and comes to stop after moving a distance of \(2\,m\) on the table. If a freely falling object were to acquire speed \(\frac {v}{10}\) after being dropped from height \(H,\) then neglecting energy losses and taking \(g = 10\,ms^{-2},\) the value of \(H\) is close to ................. \(\mathrm{km}\)

A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by

Calculate the amount of charge on capacitor of \(4\, \mu\, {F}\). The internal resistance of battery is \(1\, \Omega\) : (in \(\mu {C}\))

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of the third orbit will be

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy \(3\, {eV}\). The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength \(4000\, \mathring {{A}}\). What is the maximum kinetic energy of the emitted photoelectron ? (In \({eV}\))

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

Given below are two statements :
Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.
Statement (II) : Concave lens always forms a virtual and erect image.
In the light of the above statements, choose the correct answer from the options given below :

Let \([x]\) denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function \(f(x)=[x]+|x-2|,-2 \lt x \lt 3\), is not continuous and not differentiable. Then \(\mathrm{m}+\mathrm{n}\) is equal to :

A hall has a square floor of dimension \(10\, \mathrm{~m} \times 10\, \mathrm{~m}\) (see the figure) and vertical walls. If the angle \(GPH\) between the diagonals \(\mathrm{AG}\) and \(\mathrm{BH}\) is \(\cos ^{-1} \frac{1}{5}\), then the height of the hall (in \(meters\)) is :

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola \(\frac{{{x^2}}}{4} - \frac{{{y^2}}}{5} = 1\) , meet \(x-\) axis and \(y-\) axis at \(A\) and \(B\) respectively. Then \((OA)^2 - (OB)^2\) , where \(O\) is the origin, equals

An urn contains \(5\) red marbles, \(4\) black marbles and \(3\) white marbles. Then the number of ways in which \(4\) marbles can be drawn so that at the most three of them are red is

In the following nuclear rection, \(D \stackrel{\alpha}{\longrightarrow} D _{1} \stackrel{\beta-}{\longrightarrow} D _{2} \stackrel{\alpha}{\longrightarrow} D _{3} \stackrel{\gamma}{\longrightarrow} D _{4}\) Mass number of \(D\) is \(182\) and atomic number is \(74\) . Mass number and atomic number of \(D _{4}\) respectively will be