A long solenoid of radius R carries a time (t) - dependent current
I(t)=I₀t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 $$ \le $$ t $$ \le $$ 1, the induced current (I_R) and the induced EMF(V_R) in the ring change as :

Two moles of an ideal gas with $${{{C_P}} \over {{C_V}}} = {5 \over 3}$$ are mixed with 3 moles of another ideal gas with $${{{C_P}} \over {{C_V}}} = {4 \over 3}$$. The value of $${{{C_P}} \over {{C_V}}}$$ for the mixture is :

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30^o. The electric field in the region shown between them is given by :

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 $$ \times $$ 10¹¹ Nm^-2, the extension of wire over its natural length is :