Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): $\frac{-3}{2} \times \frac{7}{-5}=\frac{21}{10}$.
Reason ( R ): Product of two rational numbers $=\frac{\text { product of their numerators }}{\text { product of their denominators }}$.

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(a): $\frac{7}{-5}=\frac{7 \times(-1)}{(-5) \times(-1)}=\frac{-7}{5}$.
$\therefore \frac{7}{-5}$ written in standard form is $\frac{-7}{5}$.
Now, $\frac{-3}{2} \times \frac{7}{-5}=\frac{-3}{2} \times \frac{-7}{5}=\frac{(-3) \times(-7)}{(2 \times 5)}=\frac{21}{10}$.
$\therefore A$ is true.
R is clearly true and R is the correct explanation of A .

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MCQ 21 Mark

Assertion (A): The rational number $\frac{-32}{-40}$ expressed in standard form is $\frac{4}{5}$.
Reason (R): A rational number $\frac{p}{q}$ is said to be in standard form if $p$ and $q$ are both positive and $p$ and $q$ have no common divisor other than 1.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(c): $\frac{-32}{-40}=\frac{(-32) \times(-1)}{(-40) \times(-1)}=\frac{32}{40}=\frac{32 \div 8}{40 \div 8}=\frac{4}{5} \quad[\because \quad \operatorname{HCF}(32,40)=8]$.
Thus, the rational number $\frac{-32}{-40}$ expressed in standard form is $\frac{4}{5}$.
$\therefore A$ is true.
R is false since we have to convert only the denominator into a positive integer so as to get a given rational number in its standard form.

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MCQ 31 Mark

Assertion (A): $\frac{4}{-7}$ and $\frac{-4}{7}$ are equivalent rational numbers.
Reason (R) : Two rational numbers are said to be equivalent if one can be obtained by multiplying or dividing the numerator and the denominator of the other by the same nonzero number.

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(a): $\frac{4}{-7}=\frac{4 \times(-1)}{(-7) \times(-1)}=\frac{-4}{7}$.
Thus, $\frac{4}{-7}$ and $\frac{-4}{7}$ are equivalent rational numbers.
$\therefore A$ is true.
R is clearly true (by the definition of equivalent rational numbers) and R is the correct explanation of $A$.

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MCQ 41 Mark

Assertion (A): $\frac{-7}{-2}$ is a negative rational number.
Reason (R) : A rational number is said to be positive if its numerator and denominator are either both positive or both negative.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(d): $\frac{-7}{-2}$ is a positive rational number as its numerator and denominator have the same signs.
$\therefore A$ is false.
R is clearly true (by the definition of positive rational numbers).

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MCQ 51 Mark

Assertion (A): $\frac{-8}{3}$ is a rational number.
Reason (R) : Every integer is a rational number.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation
of Assertion (A).

(b): $\frac{-8}{3}$ is a rational number as it is of the form $\frac{a}{b}$, where $a$ and $b$ are both integers.
$\therefore A$ is true.
Every integer is a rational number as an integer $m$ can be written as $\frac{m}{1}$, which is clearly a rational number.
$\therefore R$ is also true but R is not the correct explanation of A .

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MATHS Assertion (A) & Reason (B) MCQ

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