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

If E(X) = m and Var(X) = m then X follows ______.

Solve the following problem :

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X.

Solve the following problem :

If X follows Poisson distribution with parameter m such that
`("P"("X" = x + 1))/("P"("X" = x)) = (2)/(x + 1)`
Find mean and variance of X.

If y = sec (tan⁻¹x), then `dy/dx` at x = 1 is ______.

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0

Solve the following differential equation y²dx + (xy + x²) dy = 0

Choose the correct alternative :

Which of the following statement is true?

Choose the correct alternative :

Which of the following is not a statement?

The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.

State whether the following statement is True or False:

p → q is equivalent to p → ~ q

State whether the following statement is True or False:

Truth value of `sqrt(3)` is not an irrational number is F

State whether the following statement is True or False:

(p ˅ q) ˄ ~ p is a contradiction

State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values

State whether the following statement is True or False:

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q