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

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

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"

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)`

Concept: Application of Differential Equations

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Concept: Statement Patterns and Logical Equivalence

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

(p ∧ ~ q) → (~ p ∧ ~ q)

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 = ?

Concept: Methods of Integration: Integration Using Partial Fractions

**Choose the correct alternative:**

Negation of p → (p ˅ ~q) is

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°”

Concept: Logical Connective, Simple and Compound Statements

**Examine whether the statement pattern**

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

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`

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

Concept: Truth Value of Statement

**Choose the correct alternative:**

The false statement in the following is

Concept: Truth Value of Statement

**Choose the correct alternative:**

Negation of p → (p ˅ ~q) is

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°”

Concept: Logical Connective, Simple and Compound Statements

**Examine whether the statement pattern**

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

Concept: Statement Patterns and Logical Equivalence

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

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`

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.

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.

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)]`

Concept: Algebra of Matrices

Maharashtra State Board HSC Commerce (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] Important Questions |
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Important Questions for Maharashtra State Board HSC Commerce (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] English |

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