The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

If $$\int {{{dx} \over {{x^3}{{(1 + {x^6})}^{2/3}}}} = xf(x){{(1 + {x^6})}^{{1 \over 3}}} + C} $$
where C is a constant of integration, then the function ƒ(x) is equal to

A student scores the following marks in five tests :

45, 54, 41, 57, 43.

His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is :