HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`

Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`

Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`

Integrate the following w.r.t.x : log (log x)+(log x)^–2 

Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`

Integrate the following w.r.t.x : log (x² + 1)

Integrate the following w.r.t.x : e^2x sin x cos x

Integrate the following w.r.t.x : sec⁴x cosec²x

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

x² + 3x - 10 = 0 

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