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HSC Commerce (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] - Maharashtra State Board Important Questions for Mathematics and Statistics

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Mathematics and Statistics
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Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

Appears in 3 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

Appears in 3 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? ("Given" sqrt(3/2) = 1.2247)

Appears in 3 question papers
Chapter: [0.018000000000000002] Differential Equation and Applications
Concept: Application of Differential Equations

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Choose the correct alternative:

int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x, then p = ?

Appears in 2 question papers
Chapter: [0.015] Integration
Concept: Methods of Integration: Integration Using Partial Fractions

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Examine whether the statement pattern

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

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Complete the truth table.

 p q r q → r r → p (q → r) ˅ (r → p) T T T T square T T T F F square square T F T T square T T F F T square square F T T square F T F T F square T square F F T square F T F F F square T square

The given statement pattern is a square

Appears in 1 question paper
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

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

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

Choose the correct alternative:

The false statement in the following is

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Logical Connective, Simple and Compound Statements

Examine whether the statement pattern

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

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

Complete the truth table.

 p q r q → r r → p (q → r) ˅ (r → p) T T T T square T T T F F square square T F T T square T T F F T square square F T T square F T F T F square T square F F T square F T F F F square T square

The given statement pattern is a square

Appears in 1 question paper
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

The total cost of 3 T.V. and 2 V.C.R. is ₹ 35,000. The shopkeeper wants profit of ₹1000 per television and ₹ 500 per V.C.R. He can sell 2 T.V. and 1 V.C.R. and get the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. and a V.C.R.

Appears in 1 question paper
Chapter: [0.012] Matrices
Concept: Application of Matrices

The sum of three numbers is 6. If we multiply third number by 3 and add it to the second number we get 11. By adding the first and third number we get a number which is double the second number. Use this information and find a system of linear equations. Find the three numbers using matrices.

Appears in 1 question paper
Chapter: [0.012] Matrices
Concept: Application of Matrices

Find matrices A and B, if 2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]

Appears in 1 question paper
Chapter: [0.012] Matrices
Concept: Algebra of Matrices
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