Mathematics Tes...

Two numbers x and y are chosen at random without replacement from the first 30 natural numbers. The probability that  x² - y² is divisible by 3 is

Three numbers are chosen at random from the first 20 natural numbers. The probability that the selected numbers form a G.P. is

The probability that in a group of 3 people, at least two will have the same birthday is

Past records show that on an average, 1 house out of 1000 in a certain district has a fire during a year. If there are 2000 houses in that district, the probability that 5 houses will have a fire is

Alex is taking readings of an experiment. He calculated the algebraic sum of deviation of 25 observations which were measured from 40 was found out to be 5. What is the mean of the readings?

A scientist was weighing each of 30 fishes. Their mean weight worked out is 30 g and standard deviation is 2 g. Later, it was found that the measuring scale was misaligned and always under-reported every fish's weight by 2 g. The correct mean and standard deviation (in g) of fishes, are respectively

If the standard deviation of x₁, x₂, …, x_n is 3.5, then the standard deviation of – 2x₁ – 3, – 2x₂ – 3, …, – 2x_n – 3 is:

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:

Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is: