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

Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.

Write the negation of the following statement.

10 > 5 and 3 < 8

Write the negation of the following statement.

I will have tea or coffee.

Write the negation of the following statement.

∀ n ∈ N, n + 3 > 9.

Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10x + 25x² 

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 18x + log(x - 4).

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25x + log(1 + x²)

Find the marginal demand of a commodity where demand is x and price is y.

y = `"x"*"e"^-"x" + 7`

Find the marginal demand of a commodity where demand is x and price is y.

y = `("x + 2")/("x"^2 + 1)`

Find the marginal demand of a commodity where demand is x and price is y.

y = `(5x + 9)/(2x - 10)`

State whether the following is True or False:

If f′ is the derivative of f, then the derivative of the inverse of f is the inverse of f′.

If y = `"x"^3 + 3"xy"^2 + 3"x"^2"y"` Find `"dy"/"dx"`

If `"x"^3 + "y"^2 + "xy" = 7` Find `"dy"/"dx"`

If `"x"^3"y"^3 = "x"^2 - "y"^2`, Find `"dy"/"dx"`

Test whether the following function is increasing or decreasing.

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0

Find the value of x, such that f(x) is increasing function.

f(x) = 2x³ - 15x² + 36x + 1 

Find the value of x, such that f(x) is increasing function.

f(x) = x² + 2x - 5 

Find the value of x, such that f(x) is increasing function.

f(x) = 2x³ - 15x² - 144x - 7 

Find the value of x, such that f(x) is decreasing function.

f(x) = 2x³ - 15x² - 144x - 7