Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): There exists a unique rational number whose additive inverse and multiplicative inverse do not exist.
Reason (R) : The additive inverse of 1 is -1 and its multiplicative inverse is 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).
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) Assertion (A) is false but Reason (R) is true.
0 is a unique rational number whose multiplicative inverse does not exist. But every rational number including 0 has an additive inverse. So, A is false.

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MCQ 21 Mark

Assertion (A): Addition and multiplication of rational numbers is both commutative and associative.
Reason (R): The rational numbers may be added or multiplied in any order or by grouping in any order. The sum or product remains the same.

✓
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) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
If $a, b$ and $c$ are rational numbers then by commutative law, we have
$a+b=b+a$ and $a \times b=b \times a$.
And, by associative law, we have
$a+(b+c)=(a+b)+c \text { and }(a \times b) \times c=a \times(b \times c)$

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MCQ 31 Mark

Assertion (A): The product of the additive inverse and multiplicative inverse of a rational number is -1 .
Reason (R): If $a$ is a rational number then its additive inverse is $(-a)$ and its multiplicative inverse is $\frac{1}{a}$.

✓
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).
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) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Clearly, $(-a) \times \frac{1}{a}=-1$

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MCQ 41 Mark

Assertion (A): Nonzero rational numbers are closed under addition, subtraction, multiplication and division.
Reason (R): The sum, difference and product of two rational numbers is a rational number but division by 0 is not defined.

✓
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).

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MCQ 51 Mark

Assertion (A): $\frac{2}{3} \times\left(\frac{4}{5}+\frac{6}{7}\right)=\frac{2}{3} \times \frac{4}{5}+\frac{2}{3} \times \frac{6}{7}$.
Reason (R): Multiplication is distributive over addition for rational numbers.

✓
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) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
According to distributive law of multiplication over addition of rational numbers, we have
$
\frac{a}{b} \times\left(\frac{c}{d}+\frac{e}{f}\right)=\left(\frac{a}{b} \times \frac{c}{d}\right)+\left(\frac{a}{b} \times \frac{e}{f}\right)
$
So, both A and R are true and R correctly explains A.

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MCQ 61 Mark

Assertion (A): There are three rational numbers which are their own reciprocals namely $-1,0$ and 1.
Reason (R): $\frac{b}{a}$ is called the reciprocal of $\frac{a}{b}$.

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) Assertion (A) is false but Reason (R) is true.
-1 and 1 are their own reciprocals, but reciprocal of 0 is not defined. So, A is false.
Clearly, R is true.

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MCQ 71 Mark

Assertion (A): Between every two rational numbers there exists a unique rational number.
Reason (R): If $x$ and $y$ be two rational numbers such that $x<y$ then $\frac{1}{2}(x+y)$ is a rational number between $x$ and $y$.

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) Assertion (A) is false but Reason (R) is true.
Between every two rational numbers there exist infinitely many rational numbers. So. A is false.
Clearly. R is true.

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MCQ 81 Mark

Assertion (A): The additive inverse of a rational number is always a negative rational number.
Reason (R) : If $a$ is a rational number then its additive inverse is $(-a)$.

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) Assertion (A) is false but Reason (R) is true.
The additive inverse of a rational number $a$ is $(-a)$. So, the additive inverse of a positive rational number is a negative rational number while the additive inverse of a negative rational number is a positive rational number.
Thus, A is false but R is true.

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MCQ 91 Mark

Assertion (A): Every whole number is a rational number.
Reason (R): 0 is a whole number which is not a rational number.

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) Assertion (A) is true but Reason (R) is false.
Clearly, A is true.
0 is both a whole number as well as a rational number. So, R is false.

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MCQ 101 Mark

Assertion (A): If $\frac{p}{q}$ is a rational number then $q$ cannot be equal to 0 .
Reason (R): Division by zero is not defined.

✓
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).

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MATHS Assertion (A) & Reason (B) MCQ

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