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

Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra

Choose the correct alternative:

What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x³.

Choose the correct alternative:

What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`

Choose the correct alternative:

If x^m. yⁿ = `("x" + "y")^(("m" + "n"))`, then `("dy")/("dx")` = ?

Choose the correct alternative:

If x = at², y = 2at, then `("d"^2y)/("d"x^2)` = ?

The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = 5 + x²e^–x + 2x

The rate of change of demand (x) of a commodity with respect to its price (y) is ______ if y = xe^–x + 7

State whether the following statement is True or False:

If y = 10^x + 1, then `("d"y)/("d"x)` = 10^x.log10

State whether the following statement is True or False:

If y = 7x + 1, then the rate of change of demand (x) of a commodity with respect to its price (y) is 7

State whether the following statement is True or False:

If y = x², then the rate of change of demand (x) of a commodity with respect to its price (y) is `1/(2x)`

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 5 + x²e^–x + 2x

Find rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`

The rate of change of demand (x) of a commodity with respect to its price (y), if y = 20 + 15x + x³.

Solution: Let y = 20 + 15x + x³

Diff. w.r.to x, we get

`("d"y)/("d"x) = square + square  + square`

∴ `("d"y)/("d"x)` = 15 + 3x²

∴ By derivative of the inverse function,

`("d"x)/("d"y)  1/square, ("d"y)/("d"x) ≠ 0`

∴ Rate of change of demand with respect to price = `1/(square + square)`

Choose the correct alternative:

The function f(x) = x³ – 3x² + 3x – 100, x ∈ R is

The price P for the demand D is given as P = 183 + 120D − 3D², then the value of D for which price is increasing, is ______.

The slope of tangent at any point (a, b) is also called as ______.

If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______

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

State whether the following statement is True or False: 

The function f(x) = `3/x` + 10, x ≠ 0 is decreasing

The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing