HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A warehouse valued at Rs. 10,000 contained goods worth Rs. 60,000. The warehouse was insured against fire for Rs. 4,000 and the goods to the extent of 90% of their value. A fire broke out and goods worth Rs. 20,000 were completely destroyed, while the remainder was damaged and reduced to 80% of its value. The damage to the warehouse was to the extent of Rs. 2,000. Find the total amount that can be claimed.

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

 How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Evaluate : `intlogx/(1+logx)^2dx`

For the bivariate data r = 0.3, cov(X, Y) = 18, σ_x = 3, find σ_y .

Evaluate : `intsec^nxtanxdx`

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 

If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`

(A) 1

(B) 2

(C) –1

(D) –2

Find the probability distribution of number of heads in two tosses of a coin.

Find the probability distribution of number of tails in the simultaneous tosses of three coins.

Find the probability distribution of number of heads in four tosses of a coin.

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).

In a bivariate data, n = 10, `bar x` = 25, `bary` = 30 and `sum xy` = 7900. Find cov(X,Y)

Let X represent the difference between the number of heads and the number of tails when a coin is tossed 6 times. What are the possible values of X?

Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.  

Examine the continuity of f(x)=`x^2-x+9  "for"  x<=3`

=`4x+3  "for"  x>3,  "at"  x=3` 

find `dy/dx, if y= cos ^-1 (sin 5x)`