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

Write the negation of the following statement:

(p `rightarrow` q) ∨ (p `rightarrow` r)

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`

Show that the following statement pattern is a contingency:

(p→q)∧(p→r)

Examine whether the following statement pattern is a tautology or a contradiction or a contingency:

(∼p ∧ ∼q) → (p → q)

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` 

If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______

The converse of contrapositive of ∼p → q is ______.

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

In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

1. `bar(PR)`  
2. `bar(PM)`
3. `bar(QM)`

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.