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

Choose the correct answer from the given alternatives in the following question:

The inverse of `[(0,1),(1,0)]` is

Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is

An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes number of black balls drawn. What are possible values of X?

Find expected value and variance of X, where X is number obtained on uppermost face when a fair die is thrown.

Choose the correct option from the given alternatives:

The differential equation `"y" "dy"/"dx" + "x" = 0` represents family of

Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

20 white rats are available for an experiment. Twelve rats are male. Scientist randomly selects 5 rats number of female rats selected on a specific day

Solve the following:

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

A highway safety group is interested in studying the speed (km/hrs) of a car at a check point.

The p.d.f. of a continuous r.v. X is given by

f (x) = `1/ (2a)` , for 0 < x < 2a and = 0, otherwise. Show that `P [X < a/ 2] = P [X >( 3a)/ 2]` .

The p.d.f. of r.v. of X is given by

f (x) = `k /sqrtx` , for 0 < x < 4 and = 0, otherwise. Determine k .

Determine c.d.f. of X and hence P (X ≤ 2) and P(X ≤ 1).

A random variable X has the following probability distribution :

Determine (i) k

(ii) P(X> 6)

(iii) P(0<X<3).

Solve the following problem :

Following is the probability distribution of a r.v.X.

Find the probability that X is positive.

Solve the following problem:

Following is the probability distribution of a r.v.X.

Find the probability that X is odd.

The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.

If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A² 

If A = `[(-2, 4),(-1, 2)]` then find A² 

Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`

Find A⁻¹ using column transformations:

A = `[(5, 3),(3, -2)]`

Find A⁻¹ using column transformations:

A = `[(2, -3),(-1, 2)]`

If A = `[(1, 2, -1),(3, -2, 5)]`, apply R₁ ↔ R₂ and then C₁ → C₁ + 2C₃ on A