HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0 

Using the rules of negation, write the negatlon of the following: 

(a) p ∧ (q → r)

(b)  ~P ∨ ~q

Write the Truth Value of the Negation of the Following Statement :

The Sun sets in the East. 

Find the feasible solution for the following system of linear inequations:
0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≤ 5, 2x + y ≥ 4

Write the truth value of the negation of the following statement : 

cos² θ + sin² θ = 1, for all θ ∈ R 

If Σ_x1 = 56 Σ_y1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σ_x1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.