HSC Science (Electronics) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve: `tan^-1 ("1 - x"/"1 + x") = 1/2 (tan^-1 "x")`, for x > 0.

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes. 

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that all the five cards are spades.

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 cards are spades

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that none is a spade.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that none of the floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly two floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.

Choose the correct option from the given alternatives:

A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is ______.

Choose the correct option from the given alternatives:

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Choose the correct option from the given alternatives:

For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______

For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______.

If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.

Choose the correct option from the given alternatives:

The probability of a shooter hitting a target is `3/4` How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.

Let X ~ B(10, 0.2). Find P(X = 1).