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Daily Question Banks for Engineering Entrance and Board Exams

Questions
Physics
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 (NA = 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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