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MATHS Assertion (A) & Reason (B) MCQ

Integers · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 6 questions.

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Assertion (A) & Reason (B) MCQ

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6 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): $(a \div b) \div c \neq a \div(b \div c)$ for all integers $a, b$ and $c$.
Reason (R): Division on integers is not associative.
  • 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): If $c=1$ then we have,
$(a \div b) \div c=(a \div b) \div 1=(a \div b) \text { and } a \div(b \div c)=a \div(b \div 1)=(a \div b)$
$\therefore$ in that case, $(a \div b) \div c=a+(b \div c)$.
Hence, A is false. R is true since division on integers is not assoclative.
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MCQ 21 Mark
Assertion (A): For any three integers $a, b, c$, we have $a \times(b+c)=(a \times b)+(a \times c)$.
Reason (R): The associative law of multiplication holds for integers.
  • 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): For any three integers $a, b, c$, we have $a \times(b+c)=(a \times b)+(a \times c)$, by the distributive law of multiplication over addition.
$\therefore A$ is true.
It is also true that associative law of multiplication holds for integers.
$\therefore R$ is also true but R is not the correct explanation of A .
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MCQ 31 Mark
Assertion ( A ): (-7)+(-3)=-10)
Reason (R): If the sum of two integers is negative then both the integers must be 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).
  • ✓
    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): The sum of two negative integers is always negative.
$\therefore A$ is true.
Consider two integers $a=-7, b=+3$. We have, $a+b=-7+3=-4$.
So, it is not necessary that if the sum of two integers is negative then both the integers must be negative.
$\therefore R$ is false.
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MCQ 41 Mark
Assertion (A): Consider the integers -6 and +7, we have $-6-(+7)=-6-7=-13$
Reason (R): The difference between two integers with opposite signs is always 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).
  • ✓
    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): A is clearly true.
The difference between two integers with opposite signs can be positive.
For example, $+8-(-5)=8+5=13$.
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MCQ 51 Mark
Assertion (A): The multiplicative inverse of -3 is $\frac{1}{-3}$.
Reason (R): $(-3) \times\left(-\frac{1}{3}\right)=1$.

  • ✓
    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): The multiplicative inverse of an integer $a$ is $\frac{1}{a}$, because $a \times \frac{1}{a}=\frac{1}{a} \times a=1$.
$\therefore A$ and R are both true and R is the correct explanation of A .
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MCQ 61 Mark
Assertion (A): -23< -20.
Reason (R): On a number line, the value of numbers increases as we move towards the left.
  • 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): $-23<-20$ is true.
On a number line, as we move towards the left, the value of numbers goes on decreasing.
$\therefore A$ is true but R is false.
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Assertion (A) & Reason (B) MCQ - MATHS STD 7 Questions - Vidyadip