Resistance of the wire is measured as \(2\,\Omega\) and \(3\,\Omega\) at \(10^{\circ}C\) and \(30^{\circ}C\) respectively. Temperature cocoefficient of resistance of the material of the wire is............\(^{\circ}C ^{-1}\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(\mathbf{R}\)
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below

A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\))

In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of \(40\,cm\) from \(A\). If a \(10\,\Omega \) resistor is connected in series with \(R_1\), the null point shifts by \(10\,cm\). The resistance that should be connected in parallel with \(\left( {{R_1} + 10} \right)\,\Omega \) such that the null point shifts back to its initial position is .............. \(\Omega\)

A spherical body of radius \(r\) and density \(\sigma\) falls freely through a viscous liquid having density \(\rho\) and viscosity \(\eta\) and attains a terminal velocity \(v _0\). Estimated maximum error in the quantity \(\eta\) is : (Ignore errors associated with \(\sigma, \rho\) and g , gravitational acceleration)

Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be:

The angular frequency of the damped oscillator is given by, \(\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} \) where \(k\) is the spring constant, \(m\) is the mass of the oscillator and \(r\) is the damping constant. If the ratio \(\frac{{{r^2}}}{{mk}}\) is \(8\%\), the change in time period compared to the undamped oscillator is approximately as follows

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))

A fighter jet is flying horizontally at a certain altitude with a speed of \(200 \; ms ^{-1}\). When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If the bullet speed is \(400 \; m / s\), the value of \(\theta\) will be \(\dots \; {}^o\)