An elastic spring under tension of \(3 \mathrm{~N}\) has a lengtha. Its length is \(b\) under tension \(2 \mathrm{~N}\). For its length\((3 a-2 b)\), the value of tension will be_______. \(\mathrm{N}\).

A solenoid of \(1000\) turns per metre has a core with relative permeability \(500\). Insulated windings of the solenoid carry an electric current of \(5\, A\). The magnetic flux density produced by the solenoid is (permeability of free space \(\left.=4 \pi \times 10^{-7} H / m \right)\)

At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ......

The r.m.s speed of oxygen molecules at \(47^{\circ} C\) is equal to that of the hydrogen molecules kept at _________ \({ }^{\circ} C\). (Mass of oxygen molecule/mass of hydrogen molecule \(=32 / 2\) )

Given below are two statements :
Statement-I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement-II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below.

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field \((\vec{E})\) at the center O of the pentagon due to these five positive charges are:

Solid sphere \(A\) is rotating about an axis \(PQ\). If the radius of the sphere is \(5\,cm\) then its radius of gyration about \(P Q\) will be \(\sqrt{x} \;cm\). The value of \(x\) is \(................\).

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is _______.

A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

A proton (mass \(m\) ) accelerated by a potential difference \(V\)  flies through a uniform transverse magnetic field \(B.\) The field occupies a region of space by width \('d'\). If \(\alpha \) be the angle of deviation of proton from initial direction of motion (see figure), the value of \(sin\,\alpha \) will be

In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is \(1/8^{th}\) of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to