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

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` 

The consumption expenditure E_c of a person with the income x. is given by E_c = 0.0006x² + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.

Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4 

= 10 for x = 4  at x = 4

Find `dy/dx,if e^x+e^y=e^(x-y)`

Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q 

Evaluate :`int Sinx/(sqrt(cos^2 x-2 cos x-3)) dx`

A shop valued at ₹ 2,40,000 is insured for 75% of its value. If the rate of premium is 90 paise percent, find the premium paid by the owner of the shop. 

 If `Σd_i^2` = 25, n = 6 find rank correlation coefficient where d_i, is the difference between the ranks of i^th values.

The following table gives the ages of husbands and wives 

Find : (i) The marginal frequency distribution of the age of husbands.
(ii) The conditional frequency distribution of the age of husbands when the age of wives lies between
25 - 35.

The regression equation of Y on X is y = `2/9` x and the regression equation of X on Y is `x=y/2+7/6` 

Find:

1.  The correlation coefficient between X and Y. 
2.  `σ_y^2 if σ _x^2=4`

Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0 

Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X. 

Ramesh, Vivek, and Sunil started a business by investing capital in the ratio 4 : 5 : 6. After 3 months Vivek withdrew all his capital and after 6 months Sunil withdrew all his capital from the business. At the end of the year, Ramesh received ₹ 6,400 as profit. Find the profit earned by Vivek.

Solve the following minimal assignment problem and hence find the minimum value : 

A bill was drawn on 12th April for 3,500 and was discounted on 4th July at 5% p.a. If the banker paid 3,465 for the bill. Find period of the bill. 

Solve the following inequation :
– 8 < – (3x – 5) < 13.