A resistance wire connected in the left gap of a metre bridge balances a $10 \ \Omega$ resistance in the right gap at a point which divides the bridge wire in the ratio $3 : 2$. If the length of the resistance wire is $1.5 \text{ m}$, then the length of $1 \ \Omega$ of the resistance wire is :

The solids which have the negative temperature coefficient of resistance are:

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of :

A short electric dipole has a dipole moment of $16 \times 10^{-9} C m$. The electric potential due to the dipole at a point at a distance of $0.6 m$ from the centre of the dipole, situated on a line making an angle of $60^{\circ}$ with the dipole axis is : ($\frac{1}{4\pi \epsilon_0} = 9 \times 10^9 N m^2/C^2$)

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

For the logic circuit shown, the truth table is:

A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is $\frac{\pi}{3}$. If instead C is removed from the circuit, the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is :

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to $L_1$ when mass M is suspended from its free end. The expression for Young's modulus is :

Light with an average flux of $20 \text{ W/cm}^2$ falls on a non-reflecting surface at normal incidence having surface area $20 \text{ cm}^2$. The energy received by the surface during time span of 1 minute is :