HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`

Form the differential equation of family of standard circle

Form the differential equation of y = (c₁ + c₂)e^x 

Find the differential equation of family of all ellipse whose major axis is twice the minor axis

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Find the differential equation by eliminating arbitrary constants from the relation y = (c₁ + c₂x)e^x 

Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0

Find the differential equation from the relation x² + 4y² = 4b² 

If X denotes the number on the uppermost face of cubic die when it is tossed, then E(X) is ______

If a d.r.v. X takes values 0, 1, 2, 3, … with probability P(X = x) = k(x + 1) × 5^–x, where k is a constant, then P(X = 0) = ______

The p.m.f. of a d.r.v. X is P(X = x) = `{{:(((5),(x))/2^5",", "for"  x = 0","  1","  2","  3","  4","  5),(0",", "otherwise"):}` If a = P(X ≤ 2) and b = P(X ≥ 3), then

If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(x/("n"("n" + 1))",", "for"  x = 1","  2","  3","  .... "," "n"),(0",", "otherwise"):}`, then E(X) = ______

If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(("c")/x^3",", "for"  x = 1","  2","  3","),(0",", "otherwise"):}` then E(X) = ______

If a d.r.v. X has the following probability distribution:

then P(X = –1) is ______

If a d.r.v. X has the following probability distribution:

then k = ______

Find mean for the following probability distribution.

Find the expected value and variance of r.v. X whose p.m.f. is given below.

The probability distribution of X is as follows:

Find k and P[X < 2]

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as number greater than 4 appears on at least one die.

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