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

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

Use quantifiers to convert the following open sentences defined on N, into a true statement.

2n - 1 = 5

Use quantifiers to convert the following open sentences defined on N, into a true statement.

y + 4 > 6

Use quantifiers to convert the following open sentences defined on N, into a true statement.

3y - 2 ≤ 9

If B = {2, 3, 5, 6, 7} determine the truth value of ∀ x ∈ B such that x is prime number.

If B = {2, 3, 5, 6, 7} determine the truth value of
∃ n ∈ B, such that n + 6 > 12.

If B = {2, 3, 5, 6, 7} determine the truth value of
∃ n ∈ B, such that 2n + 2 < 4.

If B = {2, 3, 5, 6, 7} determine the truth value of
∀ y ∈ B, such that y² is negative.

If B = {2, 3, 5, 6, 7} determine the truth value of
∀ y ∈ B, such that (y - 5) ∈ N

Which of the following sentence is a statement? In case of a statement, write down the truth value.

What is happy ending?

Obtain the differential equation by eliminating arbitrary constants from the following equations.

y = Ae^3x + Be^−3x

Obtain the differential equations by eliminating arbitrary constants from the following equation.

`y = c_2 + c_1/x`

Obtain the differential equation by eliminating arbitrary constants from the following equations.

y = (c₁ + c₂ x) e^x

Obtain the differential equations by eliminating arbitrary constants from the following equations.

y = c₁e ^3x + c₂e ^2x

Obtain the differential equation by eliminating arbitrary constants from the following equation.

y² = (x + c)³

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Form the differential equation by eliminating arbitrary constants from the relation

bx + ay = ab.

Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`

Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`

Solve the following differential equation.

(x² − yx² ) dy + (y² + xy²) dx = 0