HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

State the truth value of (p ˅ ∼p)

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.

Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

Examine whether the statement pattern

[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.

Use quantifiers to convert the given open sentence defined on N into a true statement

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement

Y + 4 > 6

The negation of p ^ (q → r) is ______.

Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q

Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q

Simplify the given circuit by writing its logical expression. Also, write your conclusion.

Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p

The dual of statement t ∨ (p ∨ q) is ______.

Apply the given elementary transformation of the following matrix.

A = `[(1,0),(-1,3)]`, R₁↔ R₂

If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A⁻¹ by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`

Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row transformations.

Express the following equations in matrix form and solve them by the method of reduction:

x − y + z = 1, 2x − y = 1, 3x + 3y − 4z = 2