If $$'f$$ is a continuous function with $$\int\limits_0^x {f\left( t \right)dt \to \infty } $$ as $$\left| x \right| \to \infty ,$$ then show that every line $$y=mx$$
intersects the curve $${y^2} + \int\limits_0^x {f\left( t \right)dt = 2!} $$

If the mean and the variance of binomial variate $$X$$ are $$2$$ and $$1$$ respectively, then the probability that $$X$$ takes a value greater than one is equal to ...............

For any two events $$A$$ and $$B$$ in a simple space

In a test an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he make a guess is $$1/3$$ and the probability that he copies the answer is $$1/6$$. The probability that his answer is correct given that he copied it, is $$1/8$$. Find the probability that he knew the answer to the questions given that he correctly answered it.