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

If the corner points of the feasible region are (0, 0), (3, 0), (2, 1) and `(0, 7/3)` the maximum value of z = 4x + 5y is ______.

The region represented by the inequality y ≤ 0 lies in _______ quadrants.

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.

Solve the problem for minimizing the total elapsed time.

The negation of p ∧ (q → r) is ______________.

Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.

[(p→q) ∧ q]→p

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)

Express the truth of each of the following statements by Venn diagram:

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls

Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`

Write the dual of the following statements: (p ∨ q) ∧ T

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

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.

Draw a Venn diagram for the truth of the following statement : 

All rational number are real numbers. 

Draw Venn diagram for the truth of the following statements : 

Some rectangles are squares. 

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )