Question Bank Solutions for HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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)

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)` 

The price P for demand D is given as P = 183 + 120 D – 3D².
Find D for which the price is increasing.

Evaluate`int (1)/(x(3+log x))dx` 

Find cofactors of the elements of the matrix A = `[[-1,2],[-3,4]]`

Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0

                     = k                    for x = 0

is continuous at x = 0. 

If x = cos2 θ and y = cot θ then find `dy/dx  at  θ=pi/4`