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MATHS Assertion (A) & Reason (B) MCQ

Playing with Numbers · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 8 questions.

Questions

Assertion (A) & Reason (B) MCQ

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8 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): If a number is divisible by 18 it is divisible by each one of 2, 3, 6 and 9. Reason (R): A number divisible by $n$ is divisible by each of the factors of $n$.
  • ✓
    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
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MCQ 21 Mark
Assertion (A): If $31 a 2$ is divisible by 6 then $a$ has 3 possible values.
Reason (R): For a number to be divisible by 6 it must be divisible by both 2 and 3 .
  • 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)
$31 a 2$ is divisible by 6
$\Rightarrow 31 a 2$ is divisible by both 2 and 3
$\Rightarrow 31 a 2$ is divisible by 2 for all values of $a$.
But, $31 a 2$ is divisible by 3 for $a=0,3,6$ or 9 .
Thus, $a$ has 4 possible values.
So, A is false. But R is true.
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MCQ 31 Mark
Assertion (A): If $N \div 5$ leaves remainder 3 and $N \div 2$ leaves remainder 0 then $N \div 10$ leaves remainder 4.
Reason (R): $N$ is a multiple of 2 and leaves remainder 3 when divided by 5.
  • 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)
$N \div 2$ leaves remainder $2 \Rightarrow N$ is even.
$N \div 5$ leaves remainder $3 \Rightarrow N$ is 3 more than a multiple of 5 .
So, units digit of $N$ is 8 .
Hence, $N \div 10$ leaves remainder 8 .
So, A is false but R is true.
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MCQ 41 Mark
Assertion (A): The sum of a two-digit number and the number obtained by reversing the digits is always divisible by 11.
Reason (R): The difference of a two-digit number and the number obtained by reversing the digits is always divisible by 9.
  • 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)
Let the given two-digit number be $10 a+b$.
Then, number obtained by reversing the digits $=10 b+a$.
Now, $(10 a+b)+(10 b+a)=11 a+11 b=11(a+b)$, which is clearly divisible by 11 .
So, $A$ is true.
And, $(10 a+b)-(10 b+a)=9 a-9 b=9(a-b)$, which is clearly divisible by 9.
So, R is true.
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MCQ 51 Mark
Assertion (A): Every three-digit number consisting of three identical digits is divisible by each one of 3, 37 and 111 .
Reason (R): $100 a+10 a+a=111 a$, which is clearly divisible by each one of 3, 37 and 111.
  • ✓
    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
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MCQ 61 Mark
Assertion (A): For $4 y 5$ to be divisible by $3, y$ can have at the most 3 possible values.
Reason (R): Every number divisible by 9 must be divisible by 3 .
  • 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)
$4 y 5$ is divisible by $3 \Leftrightarrow(4+y+5)$ is divisible by 3
$\begin{array}{l}\Leftrightarrow(9+y) \text { is divisible by } 3 \\ \Leftrightarrow y=0,3,6 \text { or } 9 .\end{array}$
So, $y$ has 4 possible values.
Thus, A is false. Clearly, R is true.
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MCQ 71 Mark
Assertion (A): If $23 x$ is divisible by 9 then $x=6$.
Reason (R): A number is divisible by 9 if the sum of its digits is divisible by 9.
  • 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)
$23 x$ is divisible by $9 \Leftrightarrow(2+3+x)$ is divisible by 9
$\Leftrightarrow x=4$
So, A is false. Clearly, R is true.
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MCQ 81 Mark
Assertion (A): The generalised form of a three-digit number $a b c$ is $100 a+10 b+c$.
Reason (R): $100 a+10 b+c$ denotes the sum of the place values of the digits of the 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
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