HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of a given week.

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

Use quantifiers to convert the given open sentence defined on N into a true statement

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement

Y + 4 > 6

If f(x) = log_x (log x) then f'(e) is ______

If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.

If y = log [cos(x⁵)] then find `("d"y)/("d"x)`

If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`

If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`

If log₅ `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`

If y = 5^x. x⁵. x^x. 5⁵ , find `("d"y)/("d"x)`

If x⁷ . y⁵ = (x + y)¹², show that `("d"y)/("d"x) = y/x`

Find the acute angle between the lines x = y, z = 0 and x = 0, z = 0

Find acute angle between the lines `(x - 1)/1 = (y - 2)/(-1) = (z - 3)/2` and `(x - 1)/2 = (y - 1)/1 = (z - 3)/1`

In a Binomial distribution with n = 4, if 2P(X = 3) = 3P(X = 2), then value of p is ______.

If X ~ B(n, p) with n = 10, p = 0.4, then find E(X²).

Verify Lagrange’s mean value theorem for the function f(x) = `sqrt(x + 4)` on the interval [0, 5].