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

Evaluate.

`int (5x^2 - 6x + 3) / (2x -3) dx`

Find `dy / dx` if, x = `e^(3t), y = e^sqrt t` 

Solve the following.

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

Find `dy/dx` if, x = e^3t, y = `e^sqrtt`

Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`

Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

If log(x + y) = log(xy) + a then show that, `dy/dx = (−y^2)/x^2`

If log(x + y) = log(xy) + a then show that, `dy/dx=(-y^2)/x^2`

Find `dy/dx"if", x= e^(3t), y=e^sqrtt`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

Find `dy/(dx)  "if" , x = e^(3t), y = e^sqrtt`. 

Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`

Evaluate.

`int (5x^2 - 6x + 3)/(2x - 3)dx`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

If log(x + y) = log(xy) + a, then show that `dy/dx = (-y^2)/x^2`

The negation of p ∧ (q → r) is ______________.

The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.

Find:

(a) Correlation coefficient

(b) `sigma_x/sigma_y`

Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)

If A = {2, 3, 4, 5, 6}, then which of the following is not true?

(A) ∃ x ∈ A such that x + 3 = 8

(B) ∃ x ∈ A such that x + 2 < 5

(C) ∃ x ∈ A such that x + 2 < 9

(D) ∀ x ∈ A such that x + 6 ≥ 9