HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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.

Find the value of c for which the conclusion of the mean value theorem holds for the function f(x) = log x on the interval [1, 3]

If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.

An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.

Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X denote the sum of numbers. Find expected value of the sum.

The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.

For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.

Find `dy/dx`, if y = (log x)^x.

Evaluate:

`int log x dx`

The dual of statement t ∨ (p ∨ q) is ______.

If y=e^ax ,show that  `xdy/dx=ylogy`

Price P for demand D is given as P = 183 +120D - 3D² Find D for which the price is increasing

Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.

If x^py^q = (x + y)^p+q then Prove that `dy/dx = y/x`

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

Find dy/dx if x sin y + y sin x = 0.