Mathematical Reasoning CBSE Questions & Answers

Mathematical Reasoning

This is Mathematics Class 11 Mathematical Reasoning CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The contrapositive of \(( \sim p \wedge q) \to \sim r\) is
  • A
    \((p \wedge q) \to r\)
  • B
    \((p \vee q) \to r\)
  • C
    none of these
  • D
    \(r \to (p \vee \sim q)\)
    Correct
2
The negation of \(p \wedge \sim (q \wedge r)\)is
  • A
    \(p \vee (q \wedge r)\)
  • B
    \( \sim p \to (q \vee \sim r)\)
  • C
    \( \sim p \to (q \wedge r)\)
  • D
    \( \sim p \vee (q \wedge r)\)
    Correct
3
The negation of \(q \vee \sim (p \wedge r)\) is
  • A
    \( \sim q \wedge (p \wedge r)\)
    Correct
  • B
    \( \sim q \wedge (p \vee r)\)
  • C
    \(q \vee (p \vee r)\)
  • D
    \( \sim q \vee (p \vee r)\)
4
Consider the proposition: “If we control population growth, we prosper “. Negative of this proposition is
  • A
    If we do not control population growth but we prosper
  • B
    If we control population, we do not prosper
  • C
    We control population but we do not prosper
    Correct
  • D
    We do not control population but we prosper
5
Consider the proposition: “If the pressure increases, the volume decreases “. Negative of this proposition is
  • A
    If the volume decreases, then the pressure increases
  • B
    If the volume increases, the pressure decreases
  • C
    If the volume does not decrease, the pressure does not increase
    Correct
  • D
    If the pressure does not increase the volume does not decrease
6
Which of the following is a contradiction?
  • A
    \(\left( {p \wedge q} \right) \wedge \left( { \sim \left( {p \vee q} \right)} \right)\)
    Correct
  • B
    none of these
  • C
    \((p \to q) \to p\)
  • D
    \(p \vee ( \sim p \wedge q)\)
7
Which of the following is logically equivalent to \(p \wedge q\) ?
  • A
    \( \sim (p \to \sim q)\)
    Correct
  • B
    \( \sim ( \sim p \wedge \sim q)\)
  • C
    \((p \wedge \sim q)\)
  • D
    none of these
8
The negation of the proposition \(q \vee \sim \left( {p \wedge r} \right)\) is
  • A
    \( \sim q \wedge \left( { \sim p \wedge \sim r} \right)\)
  • B
    none of these
  • C
    \( \sim q \wedge \left( {p \wedge r} \right)\)
    Correct
  • D
    \(q \wedge \left( {p \wedge r} \right)\)
9
If \(p \to (q \vee r)\) is false , then the truth values of p , q and r, are respectively
  • A
    T,T,T
  • B
    T,F,F
    Correct
  • C
    F,T,T
  • D
    F,F,F
10
Which of the following connectives satisfy commutative law ?
  • A
    \( \Leftrightarrow \)
  • B
    all of these
    Correct
  • C
    \( \wedge \)
  • D
    \( \vee \)
11
The statement \(p \Rightarrow p \vee q\) is
  • A
    neither a contradiction nor a tautology
  • B
    both a tautology and contradiction
  • C
    a contradiction
  • D
    a tautology
    Correct
12
The statement \(p \vee q\) is
  • A
    contingency
    Correct
  • B
    a contradiction
  • C
    a tautology
  • D
    none of these
13
Which of the following pairs is logically equivalent ?
  • A
    Inverse , Contrapositive
  • B
    Contrapositive , Converse
  • C
    Conditional , Inverse
  • D
    Conditional , Contrapositive
    Correct
14
Which of the following sentences is a statement ?
  • A
    Oh ! It is amazing
  • B
    What are you doing ?
  • C
    2 is the smallest prime number
    Correct
  • D
    Aarushi is a pretty girl
15
Which of the following is logically equivalent to \( \sim ( \sim p \to q)\) ?
  • A
    \(p \wedge q\)
  • B
    \( \sim p \wedge \sim q\)
    Correct
  • C
    \( \sim p \wedge q\)
  • D
    \(p \wedge \sim q\)