Mathematics Tes...

The foot of the perpendicular drawn from the origin on the line 3x + y = λ (λ ≠ 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is:

If xlog_e(log_e x) - x² + y² = 4(y > 0), then dy/dx at x = e is equal to:

If |z - 3 + 2i| ≤ 4, then the difference between the greatest value and the least value of |z| is:

If the system of following linear equations has no solution, then:

x + ay + z = 3

x + 2y + 2z = 6

x + 5y + 3z = b

 then the matrix A^-50, when θ = π/12, is equal to:

Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families, so that no child gets more than one ticket. If the probability that all the tickets go to the children of family B is 1/12, then the number of children in each family is

The mean and the standard deviation (sd) of five observations are 9 and 0, respectively. If one of the observations is changed, such that the mean of the new set of five observations becomes 10, then their sd is

Consider the experiment of throwing a dice, if a multiple of '3' comes up, throw the dice again and if any other number comes, toss a coin. Find the conditional probability of the event coin shows the tail, given that at least one die shows a '3'.

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with the instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of the letter is mailed.