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

Solve the following :

Find the area of the ellipse `x^2/(25) + y^2/(16)` = 1 using integration

Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution:

k = 

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

An economist is interested the number of unemployed graduate in the town of population 1 lakh.

Which of the following is not a statement?

Choose the correct alternative :

Which of the following is an open statement?

Which of the following statements is false?

Choose the correct alternative :

For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.

Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.

Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is

Choose the correct alternative:

Which of the following is always true?

Choose the correct alternative :

∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.

The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.

Then show that P (X ≤ 2) = P (X ≥ 3).

Choose the correct alternative :

If p is the sentence ‘This statement is false’ then

Choose the correct alternative :

Conditional p → q is equivalent to

Choose the correct alternative :

Negation of the statement “This is false or That is true” is

Fill in the blanks :

The statement q → p is called as the ––––––––– of the statement p → q.

If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.

Fill in the blanks :

Truth value of if x = 2, then x2 = − 4 is –––––––––.