Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): $a, b, c$ are said to be in continued proportion if $a: b:: b: c$.
Reason (R): If $a, b, c$ are in continued proportion then $b=a c$.

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 truе.

Answer

Correct option: C.

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

(c): A is true (by the definition of continued proportion).
Now, if $a, b, c$ are in continued proportion then $a: b:: b: c$.
And so, $b^2=a c \Rightarrow b=\sqrt{a c}$.
$\therefore R$ is false.

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MCQ 21 Mark

Assertion (A): If $a: b:: c: d$ then $a \times c=b \times d$.
Reason $( R )$ : In a proportion, the product of means $=$ product of extremes.

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.
D
Assertion (A) is false but Reason (R) is truе.

Answer

$( d ):$ In a proportion, the product of means $=$ the product of extremes.
$\therefore$ in the proportion $a: b:: c: d$, we have $b \times c=a \times d$.
Hence, A is false but R is true.

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MCQ 31 Mark

Assertion (A): The ratio between 15 kg and 20 km is $3: 4$.
Reason (R): Let $m$ be any nonzero number, then for any ratio $a: b$, we have $a: b=\frac{a}{m}: \frac{b}{m}$.

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 truе.

Answer

Correct option: D.

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

(d): There exists no ratio between quantities of different units. So, there is no ratio between 15 kg and 20 km .
$\therefore A$ is false. R is clearly true.

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MCQ 41 Mark

Assertion (A): The ratio $6: 4$ can be written in the simplest form as $3: 2$.
Reason (R): The ratio $a: b$ is said to be in the simplest form if $a$ and $b$ do not have any common factor.

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 truе.

Answer

Correct option: C.

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

(c): HCF of 6 and 4 is 2.
$
\therefore 6: 4=\frac{6}{4}=\frac{6+2}{4+2}=\frac{3}{2}=3: 2
$
Hence, $6: 4$ in the simplest form is $3: 2$.
$\therefore A$ is true.
R is false, since a ratio $a: b$ is said to be in the simplest form if HCF of $a$ and $b$ is 1 .

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MCQ 51 Mark

Assertion (A): The ratio $a: b$ is the same as the fraction $\frac{a}{b}$.
Reason (R): A ratio remains unchanged if both of its terms are multiplied by the same nonzero 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 truе.

Answer

Correct option: B.

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

(b): The fraction $\frac{a}{b}$ can be written as the ratio $a: b$.
$\therefore A$ is true.
Now, for any ratio $a: b$, we have $a: b=n a: n b$, where $n$ is any nonzero number.
$\therefore R$ is also true but R is not a correct explanation of A .

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MATHS Assertion (A) & Reason (B) MCQ

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