IIT-JEE Exam

An AC voltage source of variable angular frequency ω and fixed amplitude V0 is connected in series with a
capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased
(A) the bulb glows dimmer (B) the bulb glows brighter
(C) total impedance of the circuit is unchanged (D) total impedance of the circuit increases.

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IIT-JEE Other Question

Let f be a real–valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y–
intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P,
then the value of f(–3) is equal to
A thin flexible wire of length L is connected to two adjacent fixed
points and carries a current I in the clockwise direction, as shown in
the figure. When the system is put in a uniform magnetic field of
strength B going into the plane of the paper, the wire takes the shape
of a circle. The tension in the wire is