What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3$$\Omega$$ ?

(Given resistivities of iron and copper-nickel alloy wire are 12 $$\mu$$$$\Omega$$ and 51 $$\mu$$$$\Omega$$ cm respectively)

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms^-2. The gases come out at a relative speed of 500 ms^$$-$$1 with respect to the rocket : [Use g = 10 m/s²]

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^$$-$$5G^$$-$$2 are :

The material filled between the plates of a parallel plate capacitor has resistivity 200 $$\Omega$$m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permittivity of material is 50)