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

Choose the correct alternative.

If y = 5^x . x⁵, then `"dy"/"dx" = ?` 

Choose the correct alternative.

If ax² + 2hxy + by² = 0 then `"dy"/"dx" = ?` 

Choose the correct alternative.

If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?

Choose the correct alternative.

If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`  then `"dy"/"dx"` = ? 

If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.

State whether the following is True or False:

The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`

If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`

If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`

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

The demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.

The total cost function for production of x articles is given as C = 100 + 600x – 3x² . Find the values of x for which total cost is decreasing.

The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing

The total cost of manufacturing x articles C = 47x + 300x² – x⁴ . Find x, for which average cost is decreasing

Find the price, if the marginal revenue is 28 and elasticity of demand is 3.

If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.

Find the price for the demand function D = `((2"p" + 3)/(3"p" - 1))`, when elasticity of demand is `11/14`.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 5 comment on the result.

If the demand function is D = 50 – 3p – p². Find the elasticity of demand at p = 2 comment on the result

For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.

For the demand function D = 100 – `"p"^2/2`. Find the elasticity of demand at p = 6 and comment on the results.