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

If a fair coin is tossed 10 times. Find the probability of getting at most six heads.

Find the vector equation of the lines passing through the point having position vector `(-hati - hatj + 2hatk)` and parallel to the line `vecr = (hati + 2hatj + 3hatk) + λ(3hati + 2hatj + hatk)`.

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

The dual of statement p ∧ [∼ q ∨ (p ∧ q) ∨∼ r] is ______.

Find `dy/dx`, if y = (sin x)^{tan x} – x^{log x}.

Bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 3 hours, find in how many hours the number of bacteria will be 4N?

Write the dual of `(p → q) ∨ (q → p)`. 

If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`

In a single throw of a die, a random variable X is defined as the prime number on its upper face. Find the variance of X.

Find the acute angle between the lines `(x - 1)/1 = (y - 2)/-1 = (z - 3)/2` and `barr = (hati + 2hatj + 3hatk) + λ(2hati + hatj + hatk)`.

Two number are selected at random (without replacement but with different arrangement) from the first four positive integers. Let X denote the larger of the two numbers obtained. Find expectation of X.

The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.

If y = `9^(log_3x)`, find `dy/dx`.

In three throws with a pair of dice find the chance of throwing doublets at least twice.

A fair coin is tossed 8 times. Find the probability that it shows heads at most once.

The probability distribution of a r.v. X is given below:

Find the standard deviation of X.

A fair coin is tossed 3 times. A person receives ₹ X² if he gets X number of heads in all. Find his expected gain.

A student is given a quiz with 10 true or false questions and he answers by sheer guessing. If X is the number of questions answered correctly write the p.m.f. of X. If the student passes the quiz by getting 7 or more correct answers what is the probability that the student passes the quiz?

A fair coin is tossed 6 times. Find the probability of getting heads 4 times.

If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.