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 negation of the proposition “if a quadrilateral is a square, then it is a rhombus “ is
  • A
    if a quadrilateral is a square , then it is not a rhombus
  • B
    a quadrilateral is not a square and it is a rhombus
  • C
    a quadrilateral is a square and it is not a rhombus
    Correct
  • D
    if a quadrilateral is not a square , then it is a rhombus
2
The contrapositive of \((p \vee q) \to r\) is
  • A
    \( \sim r \to ( \sim p \wedge \sim q)\)
  • B
    \( \sim r \to \sim (p \vee q)\)
    Correct
  • C
    \(p \to (p \wedge q)\)
  • D
    \( \sim r \to (p \wedge q)\)
3
The contrapositive of \(p \to ( \sim q \to \sim r)\) is
  • A
    \(( \sim q \wedge r) \to \sim p\)
    Correct
  • B
    \((q \wedge \sim r) \to \sim p\)
  • C
    \((q \wedge \sim r) \to p\)
  • D
    \((q \vee \sim r) \vee p\)
4
The contrapositive of the statement “ if \({2^2} = 5,\) then I get first class” is
  • A
    If I do not get a first class , then \({2^2} = 5,\)
  • B
    If I do not get a first class , then \({2^2} \ne 5,\)
    Correct
  • C
    If I get a first class , then \({2^2} = 5,\)
  • D
    none of these
5
If x = 5 and y = - 2 , then x – 2y = 9 . The contrapositive of this proposition is
  • A
    If x – 2y = 9 , then x \( \ne \) 5 or y \( \ne \) - 2
    Correct
  • B
    x – 2y = 9 iff x = 5 and y = - 2
  • C
    If x – 2y = 9 , x \( \ne \) 5 and y \( \ne \) - 2
  • D
    none of these
6
“The diagonals of a rhombus are perpendicular “. The contrapositive of the above statement is
  • A
    If the diagonals are not perpendicular, then the figure is a rhombus
  • B
    If the diagonals are perpendicular, then the figure is a rhombus
  • C
    If the figure is not a rhombus, then its diagonals are not perpendicular
  • D
    If the diagonals are not perpendicular, then the figure is not a rhombus
    Correct
7
Which of the following statement is a tautology ?
  • A
    \((p \wedge q) \wedge \left( { \sim \left( {p \wedge q} \right)} \right)\)
  • B
    \(( \sim q \wedge p) \wedge (p \wedge \sim p)\)
  • C
    \(( \sim q \wedge p) \wedge q\)
  • D
    \(( \sim q \wedge p) \vee (p \vee \sim p)\)
    Correct
8
The statement \(p \to (q \to p)\) is equivalent to
  • A
    \(p \to (p \vee q)\)
    Correct
  • B
    \(p \to (p \to q)\)
  • C
    \(p \to (p \leftrightarrow q)\)
  • D
    \(p \to (p \wedge q)\)
9
The inverse of the proposition \((p \wedge \sim q) \to r\) is
  • A
    none of these
  • B
    \( \sim r \to \sim p \vee q\)
  • C
    \(r \to p \wedge \sim q\)
  • D
    \(( \sim p \vee q) \to \sim r\)
    Correct
10
Logical equivalent proposition to the proposition \( \sim \left( {p \vee q} \right)\) is
  • A
    \( \sim p \leftrightarrow \sim q\)
  • B
    \( \sim p \to \sim q\)
  • C
    \( \sim p \wedge \sim q\)
    Correct
  • D
    \( \sim p \vee \sim q\)
11
Let p and q be two propositions. Then the inverse of the implication \(p \to q\) is
  • A
    \( \sim p \to \sim q\)
    Correct
  • B
    \( \sim q \to p\)
  • C
    \(p \to \sim q\)
  • D
    \( \sim p \to q\)
12
Let p and q be two propositions. Then the contrapositive of the implication \(p \to q\) is
  • A
    \(p \leftrightarrow q\)
  • B
    \( \sim p \to \sim q\)
  • C
    \( \sim q \to p\)
  • D
    \( \sim q \to \sim p\)
    Correct
13
Let p and q be two propositions. Then the implication \(p \to q\) is false ,when
  • A
    p is true and q is false
    Correct
  • B
    p is false and q is true
  • C
    both p and q are false
  • D
    p is true and q is true
14
Let p and q be two propositions. Then the implication \(p \leftrightarrow \sim q\) is true ,when
  • A
    both p and q are false
  • B
    p is false and q is true
    Correct
  • C
    p is true and q is true
  • D
    p is true and q is false
15
For any three propositions p , q , and r , the proposition \(\left( {p \wedge q} \right) \wedge \left( {q \wedge r} \right)\) is true , when
  • A
    p,q , r are all true
    Correct
  • B
    p, q are true and r is false
  • C
    p is true and q, r are false
  • D
    p, q , r are all false