A block '\(A\)' takes \(2\,s\) to slide down a frictionless incline of \(30^{\circ}\) and length ' \(l\) ', kept inside a lift going up with uniform velocity ' \(v\) '. If the incline is changed to \(45^{\circ}\), the time taken by the block, to slide down the incline, will be approximately \(........\,s\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

In the given figure switches \(S_{1}\) and \(S_{2}\) are in open condition. The resistance across \(a b\) when the switches \(S_{1}\) and \(S_{2}\) are closed is \(...\,\Omega\)

If one mole of the polyatomic gas is having two vibrational modes and \(\beta\) is the ratio of molar specific heats for polyatomic gas \(\left(\beta=\frac{ C _{ P }}{ C _{ v }}\right)\) then the value of \(\beta\) is:

A lead bullet penetrates into a solid object and melts. Assuming that \(40 \%\) of its kinetic energy is used to heat it, the initial speed of bullet is ............ \(ms ^{-1}\) (Given, initial temperature of the bullet \(=127^{\circ} C\), Melting point of the bullet \(=327^{\circ} C\), Latent heat of fusion of lead \(=2.5 \times 10^{4} \,J Kg ^{-1}\), Specific heat capacity of lead \(=125 \,J / kg K\) )

The relationship between the magnetic susceptibility \((\chi)\) and the magnetic permeability \((\mu)\) is given by :
(\(\mu_0\) is the permeability of free space and \(\mu_{\mathrm{r}}\) is relative permeability)

A person pushes a box on a rough horizontal platform surface. He applies a force of \(200\, N\) over a distance of \(15\, m .\) Thereafter, he gets progressively tired and his applied force reduces linearly with distance of \(100\, N\). The total distance through which the box has been moved is \(30\, m\). What is the work done by the person during the total movement of the box\(........J\)\(?\)

A closed circular tube of average radius \(15\,cm\), whose inner walls are rough, is kept in vertical plane. A block of mass \(1\,kg\) just fit inside the tube. The speed of block is \(22\,m / s\), when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is \(......J\). [Given \(g=10\,m / s ^2\) ]

To find the resistance of a galvanometer by the half deflection method the following circuit is used with resistances \(R_1 = 9970\,\Omega,\) \(R_2 = 30\,\Omega\) and \(R_3 = 0\,\Omega.\) The deflection in the galvanometer is \(d\). With \(R_3 = 107\,\Omega\) the deflection changed to \(\frac {d}{2}\)The galvanometer resistance is approximately ............... \(\Omega\)

A transverse wave is represented by \(y=2 \sin\) \((\omega t - kx ) cm\). The value of wavelength (in \(cm\) ) for which the wave velocity becomes equal to the maximum particle velocity, will be.

If the circle \(x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in R\) passes through the point \((6,1)\) and its centre lies on the line \(x-2 c y=8\), then the length of intercept made by the circle on \(x\)-axis is.

Surface tension of two liquids (having same densities), \(T_1\) and \(T_2\), are measured using capillary rise method utilizing two tubes with inner radii of \(r_1\) and \(r_2\) where \(r_1>r_2\). The measured liquid heights in these tubes are \(h_1\) and \(h_2\) respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights \(h _1\) and \(h _2\) and surface tensions \(T _1\) and \(T _2\) satisfy the relation :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor