Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E . The energy stored in B , when spring constants \(k _{ A }, k _{ B }\) of A and \(B\), respectively satisfy the relation \(4 k _{ A }=3 k _{ B }\), is :

Given below are two statements Statement \(I:\) The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement \(II\) : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be

A bowl filled with very hot soup cools from \(98^{\circ}\,C\) to \(86^{\circ}\,C\) in \(2\) minutes when the room temperature is \(22^{\circ}\,C\). \(..........\,minutes\) long it will take to cool from \(75^{\circ}\,C\) to \(69^{\circ}\,C\) ?

A butterfly is flying with a velocity \(4 \sqrt{2} \,{m} / {s}\) in North-East direction. Wind is slowly blowing at \(1\) \({m} / {s}\) from North to South. The resultant displacement of the butterfly in \(3\, seconds\) is \(....\,{m}.\)

A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

Given below in the left column are different modes of communication using the kinds of waves given in the right column

\(A.\) Optical Fiber Communication	\(P.\) Ultrasound
\(B.\) Radar	\(Q.\) Infrared Light
\(C.\) Sonar	\(R.\) Microwaves
\(D.\) Mobile Phones	\(S.\) Radio Waves

From the options given below, find the most appropriate match between entries in the left and the right column

Two cars \({X}\) and \({Y}\) are approaching each other with velocities \(36\; {km} / {h}\) and \(72\; {km} / {h}\) respectively. The frequency of a whistle sound as emitted by a passenger in car \({X}\), heard by the passenger in car \({Y}\) is \(1320 \;{Hz}\). If the velocity of sound in air is \(340\; {m} / {s}\), the actual frequency of the whistle sound produced is ........ \(Hz.\)

A spherical soap bubble of radius \(3\,cm\) is formed inside another spherical soap bubble of radius \(6\,cm\). If the internal pressure of the smaller bubble of radius \(3\,cm\) in the above system is equal to the internal pressure of the another single soap bubble of radius \(r\,cm\). The value of \(r\) is.......

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are \(50\) divisions on the circular scale, and the main scale moves by \(0.5 \,{mm}\) on a complete rotation. For a particular observation the reading on the main scale is \(5\, {mm}\) and the \(20^{\text {th }}\) division of the circular scale coincides with reference line. Calculate the true reading. (in \({mm}\))

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \(5\,\Omega\). The internal resistance of each cell will be \(.............\,\Omega\).

The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is