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MATHS 2 Marks Questions

Number Play · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 14 questions.

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2 Marks Questions

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14 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Make conjectures by examining if there are any patterns or relations between
(i) the parity of a number and its digital root.
(ii) the digital root of a number and the remainder obtained when the number is divided by 3 or 9.
Answer
self
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Question 32 Marks
Write any number. Generate a sequence of numbers by repeatedly adding 11. What would be the digital roots of this sequence of numbers? Share your observations.
Answer
self
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Question 42 Marks
The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
Answer
self
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Question 82 Marks
When divided by 7 , the number 661 leaves a remainder of 3 , and 4779 leaves a remainder of 5. Without calculating, can you say what remainders the following expressions will leave when divided by 7 ? Show the solution both algebraically and visually.
(i) $4779+661$
(ii) $4779-661$
Answer
(i) $4779+661$
= Remainder 5 + Remainder 3
= Remainder 8
8 divided by $7 \rightarrow$ remainder 1 .
(ii) $4779-661$
= Remainder 5 - Remainder 3
= Remainder 2
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Question 92 Marks
Find a few numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4. Write an algebraic expression to describe all such numbers.
Answer
L.C.M of 3 and $4=12$.
All such numbers are given by the expression $=12 a+2$.
Examples :
(i) $12 \times 1+2=12+2=14$.
(ii) $12 \times 2+2=24+2=26$.
(iii) $12 \times 3+2=36+2=38$.
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Question 102 Marks
For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
The sum of a multiple of 6 and a multiple of 3 is a multiple of 9.
Answer
Let multiple of 6 be 6 a, multiple of 3 be 3b.
Sum : $6 a +3 b=3(2 a + b )$.
For it to divisible by $9,2 a+b$ must be divisible by 3 .
Example :
$6(6 \times 1)+3(3 \times 1)=9 \rightarrow$ divisible by 9
$6+6=12 \rightarrow$ not divisible by 9
Conclusion : Sometimes true.
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Question 112 Marks
For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
The sum of a multiple of 6 and a multiple of 9 is a multiple of 3.
Answer
Let the multiple of 6 be 6 a , the multiple of 9 be 9 b .
Sum : $6 a+9 b=3(2 a+3 b) \rightarrow$ clearly divisible by 3 .
Example :
$6+9=15 \rightarrow$ divisible by 3 .
$12+18=30 \rightarrow$ divisible by 3 .
Conclusion : Always true.
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Question 122 Marks
For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
If two numbers are not divisible by 6, then their sum is not divisible by 6.
Answer
Let the two numbers be $a$ and $b$.
Not divisible by 6 means they do not satisfy 6|a or 6|b.
But their sum can still be divisible by 6 .
Example : 2 and $4 \rightarrow$ both not divisible by 6 .
But, $2+4=6 \rightarrow$ divisible by 6 .
Conclusion : Sometimes true.
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Question 132 Marks
For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
If a number is not divisible by 18, then it is also not divisible by 9.
Answer
If a number is divisible by 18 , then it is also divisible by 9 because 9 is a factor of 18 . $18 a \div 9=2 a \rightarrow$ divisible by 9 .
But if a number is divisible by 9 , it is not always divisible by 18 . $9 b \div 18= b / 2 \rightarrow$ not divisible by 9 .
Example : 9 is divisible by 9 but not divisible by 18 .
27 is divisible by 9 but not 18 .
Conclusion : Sometimes true.
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Question 142 Marks
For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
The sum of two even numbers is a multiple of 3.
Answer
Let the two even numbers be $2 a+2 b$
$\text { Sum }=2 a+2 b=2(a+b)$
For $2(a+b)$ to be a multiple of $3,(a+b)$ must be multiple of 3 .
Example :
$2+4=6 \rightarrow \text { divisible by } 3$
$2+8=10 \rightarrow$ not divisible by 3
Conclusion : Sometimes true.
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2 Marks Questions - MATHS STD 8 Questions - Vidyadip