PROPERTIES OF FUNCTIONS AND PROBABILITY IN JEE ADVANCED QUESTIONS AND ANSWERS What functional property does the function f:R → R satisfy? - ANS-f(x+y) = f(x) + f(y) for all x, y in R. If f(x) is differentiable at x = 0, which of the following statements are true? - ANS-(B) f(x) is continuous for all x in R and (C) f'(x) is constant for all x in R. What is the solution form for the equations (2x)² = (3y)^(1/3) and 3ln(x) = 2ln(y)? - ANS-Let (x, y) be the solution of the equations. What is the integral expression involving sin(x)? - ANS-The expression is ∫(x sin x) dx. What is the probability of drawing a white ball from urn U₂ after transferring balls from urn U₁? - ANS-The probability is calculated based on the conditions of the coin toss and the contents of the urns. What are the contents of urn U₁ and urn U₂? - ANS-Urn U₁ contains 3 white and 2 red balls, while urn U₂ contains 1 white ball. What happens if heads appears when tossing a coin regarding the balls? ...
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