HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Calculate the cost of living index number for the following data by aggregative expenditure method:

For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year

∴ Rate of interest per quarter = `square/4` = 4

⇒ r = 4%

⇒ i = `square/100 = 4/100` = 0.04

n = Number of quarters

= 4 × 1

= `square`

⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`

⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`

= `(2000(square))/square [1 - (square)^-4]`

= 50,000`(square)`[1 – 0.8548]

= ₹ 7,550.40

A function f(x) is maximum at x = a when f'(a) > 0.

Area of the region bounded by y= x⁴, x = 1, x = 5 and the X-axis is ______.

`int 1/sqrt(x^2 - a^2)dx` = ______.

Obtain the differential equation by eliminating arbitrary constants from the following equation:

y = Ae^3x + Be^–3x

Solve: `int sqrt(4x^2 + 5)dx`

A marketing manager has list of salesmen and territories. Considering the travelling cost of the salesmen and the nature of territory, the marketing manager estimates the total of cost per month (in thousand rupees) for each salesman in each territory. Suppose these amounts are as follows:

Find the assignment of salesman to territories that will result in minimum cost.

Evaluate :

`int(4x - 6)/(x^2 - 3x + 5)^(3/2)  dx`

`int(1-x)^-2 dx` = ______

`int1/sqrt(x^2 - a^2) dx` = ______

`intsqrt(1+x)  dx` = ______

Solution of the equation `xdy/dx=y log y` is ______

Evaluate the following.

`int x^3 e^(x^2) dx`

Evaluate: 

`int(1+logx)/(x(3+logx)(2+3logx))  dx`

A metal wire of 36 cm long is bent to form a rectangle. Find its dimensions when its area is maximum.

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To solve the problem of maximization objective, all the elements in the matrix are subtracted from the largest element in the matrix.

Calculate the Cost of Living Index Number for the following data.

`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`