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

State whether the following statement is True or False:

In sequencing problem the processing times are dependent of order of processing the jobs on machine

Solve the following problem of sequencing for minimizing the total elapsed time and idle time for both the machines.

The optimal sequence of the jobs as follows:

Total elasped time is obtained as follows:

Total elapsed time T = `square` minutes

Idle time for Machine A = T – `square` = `square` minutes

Idle time for Machine B = `square`

Complete the following activity to find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as:

E_c = (0.0003)I² + (0.075)I²

when I = 1000

Find `(d^2y)/(dy^2)`, if y = e^4x

If elasticity of demand η = 0 then demand is ______.

If f(x) = x³ – 3x² + 3x – 100, x ∈ R then f"(x) is ______.

If 0 < η < 1 then the demand is ______.

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

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

`"If" log(x+y) = log(xy)+a  "then show that", dy/dx=(-y^2)/x^2`

If log(x+y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

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

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

In a factory, for production of Q articles, standing charges are ₹500, labour charges are ₹700 and processing charges are 50Q. The price of an article is 1700 - 3Q. Complete the following activity to find the values of Q for which the profit is increasing.

Solution: Let C be the cost of production of Q articles.

Then C = standing charges + labour charges + processing charges

∴ C = `square` 

Revenue R = P·Q = (1700 - 3Q)Q = 1700Q- 3Q²

Profit `pi = R - C = square`

 Differentiating w.r.t. Q, we get

`(dpi)/(dQ) = square`

If profit is increasing , then `(dpi)/(dQ) >0`

∴ `Q < square` 

Hence, profit is increasing for `Q < square` 

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

If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`

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

If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`

Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010:

Fit the trend line to the above data by the method of least squares.