IIT-JEE Exam

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

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IIT-JEE Other Question

The line 2x + y = 1 is tangent to the hyperbola x^2/a^2 - y^2/b^2 = 1 If this line passes through the point of
intersection of the nearest directrix and the x–axis, then the eccentricity of the hyperbola is 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.