HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Determine the order and degree of the following differential equations.

`((d^3y)/dx^3)^(1/6) = 9`

Rewrite the following statement without using the connective ‘If ... then’.

If a quadrilateral is rhombus then it is not a square.

Rewrite the following statement without using the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.

Rewrite the following statement without using the connective ‘If ... then’.

If it rains then the principal declares a holiday.

Consider the following statements.

1. If D is dog, then D is very good.
2. If D is very good, then D is dog.
3. If D is not very good, then D is not a dog.
4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.

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.

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 

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

f(x) = 2x³ – 15x² – 84x – 7 

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

f(x) = x⁴ − 2x³ + 1

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the values of x for which Revenue is increasing.

Choose the correct alternative.

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

State whether the following statement is True or False:

The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.