MCQ

MCQ 11 Mark

The contrapositive of the statement
"If Chandigarh is capital of Haryana, then Chandigarh is in India" is :

A
If Chandigarh is in India, then Chandigarh is capital of Haryana.
✓
If Chandigarh is not in India, then Chandigarh is not the capital of Haryana.
C
If Chandigarh is capital of Haryana, then Chandigarh is not in India.
D
If Chandigarh is not in India, then Chandigarh is capital of Haryana.

Answer

Correct option: B.

If Chandigarh is not in India, then Chandigarh is not the capital of Haryana.

(B) If Chandigarh is not in India, then Chandigarh is not the capital of Haryana.
Explanation : Let
$p$ : Chadigarh is capital of Haryana
$q$ : Chandigarh is in India
$\sim p$ : Chandigarh is not capital of Haryana
$\sim q$ : Chandigarh is not in India
Since, Contrapositive of "If $p$ then $q$ " is
If $(\sim q)$, then $(\sim p)$
Therefore,
If Chandigarh is not in India, then Chandigarh is not capital of Haryana.

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MCQ 21 Mark

The negation of the statement " 42 is divisible by 2 and $3^{\prime \prime}$ is :

A
42 is not divisible by 2 and 42 is not divisible by 3 .
✓
42 is not divisible by 2 or 42 is not divisible by 3
C
42 is not divisible by 2 and 42 is divisible by 3
D
42 is divisible by 2 and 42 is not divisible by 3 .

Answer

Correct option: B.

42 is not divisible by 2 or 42 is not divisible by 3

(B) 42 is not divisible by 2 or 42 is not divisible by 3
Explanation : Let
$p: 42$ is divisible by 2
$q: 42$ is divisible by 3
$\sim p: 42$ is not divisible by 2
$\sim q: 42$ is not divisible by 3$
\sim(p \wedge q)=\sim p \vee \sim q
$
i.e., 42 is not divisible by 2 or 42 is not divisible by 3 .

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MCQ 31 Mark

The contrapositive of the statement "If $p$, then $q$ " is :

A
If $q$, then $\sim p$
B
If $\sim p$, then $\sim q$
C
If $p$, then $\sim q$
✓
If $\sim q$, then $\sim p$

Answer

Correct option: D.

If $\sim q$, then $\sim p$

(D) If $\sim q$, then $\sim p$
Explanation : If $p$ and $q$ are two statements, then the contrapositive of the implication "if $p$ then $q$ " is :
$
\text { "if } \sim q \text { then } \sim p^{\prime \prime}
$

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MCQ 41 Mark

The converse of the statement "If $x>y$, then $x+a>y+a^{\prime \prime}$ is :

A
If $x > y$, then $x+a < y+a$
B
If $x < y$, then $x+a > y+a$
✓
If $x+a > y+a$, then $x > y$
D
If $x < y$, then $x+a < y+a$

Answer

Correct option: C.

If $x+a > y+a$, then $x > y$

(C) If $x+a>y+a$, then $x>y$
Explanation : Let
$
\begin{array}{l}
p: x>y \\
q: x+a>y+a
\end{array}
$
Therefore, $p \rightarrow q$
Converse of the above statement is $q \rightarrow p$
i.e., if $x+a>y+a$, then $x>y$.

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MCQ 51 Mark

The connective in the statement " $3+5>9$ or $3+5<9^{\prime \prime}$ is

A
>
B
<
✓
or
D
and

Answer

Correct option: C.

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MCQ 61 Mark

The negation of the statement " 6 is greater than 8 " is

A
8 is less than 6
B
6 is equal to 8
✓
6 is not greater than 8
D
None of these

Answer

Correct option: C.

6 is not greater than 8

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MCQ 71 Mark

The connective in the statement "Earth revolves round the Sun and Moon is a satellite of Earth" is

A
Earth
B
or
C
Moon
✓
and

Answer

Correct option: D.

and

(D) and
Explanation : The connective of the given compound statement is 'and' because two simple statements i.e., "Earth revolves round the Sun" & "Moon is a satellite of Earth" are connected with word "and".

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MCQ 81 Mark

Which of the following is a statement:

A
$n$ is a real numbers
B
let us go
C
switch off the fan
✓
3 is a natural number

Answer

Correct option: D.

3 is a natural number

(D) 3 is a natural number
Explanation : We know that, statement is a sentence which is either true or false. Here, 3 is a natural number is a true sentence, hence it is a statement.

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