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A coil of wire having inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current I₁(t) starts flowing through the coil. If I₂(t) is the current induced in the ring, and B(t) is the magnetic field at the axis of the coil due to I₁(t), then as a function of time (t > 0), the product I₂(t) B(t)

(a)	increases with time	(b)	decreases with time
(c)	does not vary with time	(d)	passes through a maximum

Chemistry

The edge length of unit cell of a metal having molecular weight 75 g/mol is 5

which crystallizes in cubic lattice. If the density is 2 g/cc then find the radius of metal atom (N_A = 6 x 10²³). Give the answer in pm.

Mathematics

Let f (x) = Ax² + Bx + C where A, B, C are real numbers. Prove that if f (x) is an integer whenever x is an integer, then the numbers 2A, A + B and C are all integers. Conversely, prove that if the numbers 2A, A + B and C are all integers then f (x) is an integer whenever x is an integer.

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