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

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.

Solve the following differential equations:

x²ydx – (x³ – y³)dy = 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` = ______.

Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.

`int 1/(4x^2 - 1) 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`

If y = x . log x then `dy/dx` = ______.

If y = (log x)² the `dy/dx` = ______.

Graphical solution set of the inequations x ≥ 0 and y ≤ 0 lies in ______ quadrant.

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.

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

Find `dy/dx  "if",y=x^(e^x) `

FInd `dy/dx` if,`x=e^(3t), y=e^sqrtt`

Find `dy/dx  "if",  y = x^(e^x)`

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

Evaluate :

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

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