HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the truth values of the following.

4 is odd or 1 is prime.

Write the truth values of the following.

64 is a perfect square and 46 is a prime number.

Write the truth values of the following.

5 is a prime number and 7 divides 94.

Find the combined equation of the following pair of lines:

Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 0.

Write the truth values of the following.

It is not true that 5−3i is a real number.

Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.

Write the truth value of the following.

Milk is white if and only if sky is blue.

Find the combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0

Write the truth values of the following.

24 is a composite number or 17 is a prime number.

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

p ∨ (q ∧ r)

Find the separate equation of the line represented by the following equation:

3y² + 7xy = 0 

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∨ (r → s)

Find the separate equation of the line represented by the following equation:

x² - 4xy = 0 

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(q ∧ r) ∨ (∼ p ∧ s)

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∧ ∼ r

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(∼ r ↔ p) → ∼ q

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]

Find the separate equation of the line represented by the following equation:

`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

[(∼ p ∧ q) ∧ ∼ r] ∨ [(q → p) → (∼ s ∨ r)]

Find the separate equation of the line represented by the following equation:

x² + 2(cosec α)xy + y² = 0