A scooter accelerates from rest for time \(t_{1}\) at constant rate \(a _{1}\) and then retards at constant rate \(a _{2}\) for time \(t _{2}\) and comes to rest. The correct value of \(\frac{t_{1}}{t_{2}}\) will be ..... .

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. \(T_1\) and \(T_2\) are the total flying times of first and second ball, respectively, then the ratio of \(T_1\) and \(T_2\) is :

A particle of mass \(m\) is moving along the \(x\) -axis with initial velocity \(u \hat i\). It collides elastically with a particle of mass \(10\, m\) at rest and then moves with half its initial kinetic energy (see figure). If \(\sin \theta_{1}=\sqrt{n} \sin \theta_{2}\) then value of \(n\) is.....

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

A pendulum of length \(2 \; m\) consists of a wooden bob of mass \(50 \; g\). A bullet of mass \(75 \; g\) is fired towards the stationary bob with a speed \(v\). The bullet emerges out of the bob with a speed \(\frac{v}{3}\) and the bob just completes the vertical circle. The value of \(v\) is \(\dots \; ms ^{-1}\). (if \(g =10 \; m / s ^{2}\) )

Given below are two statement : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a rod lying freely is heated, no thermal stress is developed in it. Reason \(R :\) On heating the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below

In a hypothetical fission reaction \({ }_{92} \mathrm{X}^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} \mathrm{Z}^{92}+3 \mathrm{R}\) The identity of emitted particles \((R)\) is _______.

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

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

For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:

Four resistances \(40 \ \Omega, 60\  \Omega, 90\  \Omega\) and \(110\  \Omega\) make the arms of a quadrilateral \(A,B,C,D\). Across \(AC\) is a battery of emf \(40\, V\) and internal resistance negligible. The potential difference across \(BD\) is \(V\) is...... 

A water spray gun is attached to a hose of cross sectional area \(30\) cm\(^2\). The gun comprises of \(10\) perforations each of cross sectional area \(15\) mm\(^2\). If the water flows in the hose with the speed of \(50\) cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)