M.C.Q (1 Marks)

MCQ 11 Mark

The negation of the statement “The product of $3$ and $4$ is $9”$ is.

✓
It is false that the product of $3$ and $4$ is $9.$
B
The product of $3$ and $4$ is $12.$
C
The product of $3$ and $4$ is not $12.$
D
It is false that the product of $3$ and $4$ is not $9.$

Answer

Correct option: A.

It is false that the product of $3$ and $4$ is $9.$

The negation of the statement is “It is false that the product of $3$ and $4$ is $9”.$

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MCQ 21 Mark

The negation of the statement. $“101$ is not a multiple of $3”$ is.

✓
$101$ is a multiple of $3.$
B
$101$ is a multiple of $2$.
C
$101$ is an odd number.
D
$101$ is an even number.

Answer

Correct option: A.

$101$ is a multiple of $3.$

Let $p: 101$ is not multiple of $3.$
$~p: 101$ is a multiple of $3.$

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MCQ 31 Mark

Which of the following is the conditional $p \rightarrow q?$

A
$q$ is sufficient for $p.$
B
$p$ is necessary for $q.$
✓
$p$ only if $q.$
D
if $q,$ then $p.$

Answer

Correct option: C.

$p$ only if $q.$

We know that $p \rightarrow q$ is same as $p$ only if $q.$

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MCQ 41 Mark

Which of the following is a statement.

A
$x$ is a real number.
B
Switch off the fan.
✓
$6$ is a natural number.
D
Let me go.

Answer

Correct option: C.

$6$ is a natural number.

Since, statement is a sentence which is ether true or false.
So, $6$ is a natural number which is true.

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MCQ 51 Mark

The negation of the statement. $“72$ is divisible by $2$ and $3”$ is.

✓
$72$ is not divisible by $2$ or $72$ is not divisible by $3.$
B
$72$ is not divisible by $2$ and $72$ is not divisible by $3.$
C
$72$ is divisible by $2$ and $72$ is not divisible by $3.$
D
$72$ is not divisible by $2$ and $72$ is divisible by $3.$

Answer

Correct option: A.

$72$ is not divisible by $2$ or $72$ is not divisible by $3.$

We have, $p: 72$ is divisible by $2$ and $3.$
Let $q: 72$ is divisible by $2.$
$r: 72$ is divisible by $3.$
$~q: 72$ is not divisible by $2.$
$~r. 72$ is not divisible by $3.$
$~{(q ⋀ f ) -~q v ~r}$
$\Rightarrow 72$ is not divisible by $2$ or $72$ is not divisible by $3.$

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MCQ 61 Mark

The statement “If $x^2$ is not even, then $x$ is not even” is converse of the statement.

A
If $x^2$ is odd, then $x$ is even.
✓
If $x$ is not even, then $x^2$ is not even.
C
If $x$ is even, then $x^2$ is even.
D
If $x$ is odd, then $x^2$ is even.

Answer

Correct option: B.

If $x$ is not even, then $x^2$ is not even.

Let $p: x^2$ is not even.
$q: x$ is not even. So, the converse of the statement $p \rightarrow q is q \rightarrow p$
i.e., If $x$ is not even, then $x^2$ is not even.

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MCQ 71 Mark

The converse of the statement. “If $x > y,$ then $x + a > y + a”$ is.

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

Answer

Correct option: B.

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

Let $p: x > y$
$q: x + a > y + a$
$P \rightarrow q$
Converse of the above statement is:
$q \rightarrow P$
i.e., If $x + a > y + a,$ then $x > y$

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MCQ 81 Mark

The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is.

✓
If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
B
If Chandigarh is in India, then Chandigarh is Capital of Punjab.
C
If Chandigarh is not capital of Punjab, then Chandigarh is not capital of India.
D
If Chandigarh is capital of Punjab, then Chandigarh is not in India.

Answer

Correct option: A.

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

Let $p:$ Chandigarh is capital of Punjab.
and $q:$ Chandigarh is in India.
$\sim p:$ Chandigarh is not capital of Punjab.
$\sim q:$ Chandigarh is not in India.
Contra positive of the statement $p \rightarrow q$
if $(\sim q),$ then $(\sim p)$.
It Chandigarh is not in India, then Chandigarh is not the capital of Punjab.

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MCQ 91 Mark

The negation of the statement. “A circle is an ellipse” is.

A
An ellipse is a circle.
B
An ellipse is not a circle.
✓
A circle is not an ellipse.
D
A circle is an ellipse.

Answer

Correct option: C.

A circle is not an ellipse.

Let $p:$ A circle is an ellipse.
$\sim p:$ A circle is not an ellipse.

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MCQ 101 Mark

The contrapositive of the statement. “If $p,$ then $q”,$ is.

A
If $q,$ then $p.$
B
If $p,$ then $\sim q.$
✓
If $\sim q,$ then $\sim p.$
D
If $\sim p,$ then $\sim q.$

Answer

Correct option: C.

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

$p \rightarrow q$
If $p,$ then $q$
Contra positive of the statement $p \rightarrow q$ is $(\sim q) \rightarrow (\sim p).$
If $\sim q,$ then $\sim p.$

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MCQ 111 Mark

The connective in the statement. “Earth revolves round the Sun and Moon is a satellite of earth” is.

A
or.
B
Earth.
C
Sun.
✓
and.

Answer

Correct option: D.

and.

Connective word is “and”.

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MCQ 121 Mark

The connective in the statement. $“2 + 7 > 9$ or $2 + 7 < 9”$ is

A
and
✓
or
C
$ > $
D
$ < $

Answer

Correct option: B.

In $‘2 + 7 > 9$ or $2 + 7 < 9\ ’$ the connective is ‘or’.

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MCQ 131 Mark

Which of the following is not a negation of “A natural number is greater than zero”.

A
A natural number is not greater than zero.
B
It is false that a natural number is greater than zero.
✓
It is false that a natural number is not greater than zero.
D
None of the above.

Answer

Correct option: C.

It is false that a natural number is not greater than zero.

The negation of the given statement is false.
i.e., It is false that a natural number is not greater than zero.

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MCQ 141 Mark

Which of the following is not a statement.

A
Smoking is injurious to health.
B
$2 + 2 = 4.$
C
$2$ is the only even prime number.
✓
Come here.

Answer

Correct option: D.

Come here.

To given order cannot be a statement.
So ‘Come here’ is not a statement.

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MCQ 151 Mark

The negation of the statement. $“7$ is greater than $8”$ is.

A
$7$ is equal to $8.$
✓
$7$ is not greater than $8.$
C
$8$ is less than $7.$
D
none of these.

Answer

Correct option: B.

$7$ is not greater than $8.$

Let $p: 7$ is greater than $8.$
$\sim p: 7$ is not greater than $8.$

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MCQ 161 Mark

The negation of the statement. Plants take in $CO_{2 }$ and give out $O_2 $ is.

A
Plants do not take in $CO_2$ and do not give out $O_2$.
✓
Plants do not take in $CO_2$ or do not give out $O_2$.
C
Plants take in $CO_2$ and do not give out $O_2.$
D
Plants take in $CO_2$ or do not give out $O_2.$

Answer

Correct option: B.

Plants do not take in $CO_2$ or do not give out $O_2$.

Plants do not take in $CO_2$ or do not give out $O_2$.
Let $p:$ Plants take in $CO_2$ and give out $O_2.$
$q:$ Plants take in $CO_2.$
$r:$ Plants give out $O_2$
$~q:$ Plants do not take in $CO_2.$
$~r:$ Plants do not give out $O_2.$
$\therefore ~(q ^ r) = (~q ^ r)$: plants do not take in $CO_2$ or do not give out $O_2.$

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MCQ 171 Mark

Which of the following statement is a conjunction?

A
Ram and Shyam are friends.
B
Both Ram and Shyam are tall.
C
Both Ram and Shyam are enemies.
✓
None of the above.

Answer

Correct option: D.

None of the above.

If two simple statements $p$ and $q$ are connected by the word ‘and’, then the resulting compound statement $p$ and $q$ is called a conjunction of $p$ and $q.$
Here, none of the given statement is conjunction.

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MCQ 181 Mark

The negation of the statement. “Rajesh or Rajni lived in Bangalore” is.

A
Rajesh did not live in Bangalore or Rajni lives in Bangalore.
B
Rajesh lives in Bangalore and Rajni did not live in Bangalore.
✓
Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
D
Rajesh did not live in Bangalore or Rajni did not live in Bangalore.

Answer

Correct option: C.

Rajesh did not live in Bangalore and Rajni did not live in Bangalore.

We have, $p:$ Rajesh or Rajni lived in Bangalore.
and $q:$ Rajesh lived in Bangalore.
$r:$ Rajni lived in Bangalore.
$\sim q:$ Rajesh did not live in Bangalore.
$\sim r.$ Rajni did not live in Bangalore.
$\sim (q v r):$ Rajesh did not live in Bangalore and Rajni did not live in Bangalore.

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MCQ 191 Mark

The contrapositive of the statement. “If $7$ is greater than $5$, then $8$ is greater than $6”$ is.

A
If $8$ is greater than $6$, then $7$ is greater than $5.$
B
If $8$ is not greater than $6,$ then $7$ is greater than $5.$
✓
If $8$ is not greater than $6$, then $7$ is not greater than $5.$
D
If $8$ is greater than $6$, then $7$ is not greater than $5.$

Answer

Correct option: C.

If $8$ is not greater than $6$, then $7$ is not greater than $5.$

Let $p: 7$ is greater than $5.$
and $q: 8$ is greater than $6.$
$\therefore p \rightarrow q$
$\sim p: 7$ is not greater than $5.$
$\sim q: 8$ is not greater than $6.$
$(\sim q) \rightarrow (\sim p)$ i.e., if $8$ is not greater than $6$, then $7$ is not greater than $5.$

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MCQ 201 Mark

The converse of the statement. “If sun is not shining, then sky is filled with clouds” is.

✓
If sky is filled with clouds, then the sun is not shining.
B
If sun is shining, then sky is filled with clouds.
C
If sky is clear, then sun is shining.
D
If sun is not shining, then sky is not filled with clouds.

Answer

Correct option: A.

If sky is filled with clouds, then the sun is not shining.

Let $p:$ Sun is not shining.
$q:$ Sky is filled with clouds.
So, the converse of the statement $p \rightarrow q$ is $q \rightarrow p.$
i.e., If Sky is filled with clouds, then the Sun is not shining.

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Maths M.C.Q (1 Marks)

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