Mathematics
Assertion (A) : 49 is a perfect square, when divided by 3 remainder is 1.
Reason (R) : When each of the perfect square numbers 1, 4, 9, …………. is divided by 3, the remainder is always 1.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Sq & Sq Roots
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Answer
Finding prime factors of 49, we get :
⇒ 49 = (7 x 7)
Since all prime factors are in pair.
∴ 49 is a perfect square.
49 divided by 3 leaves quotient 16 and remainder 1.
⇒ 49 = 3 x 16 + 1
So, assertion (A) is true.
For each perfect squares,
1 divided by 3 leaves quotient 0 and remainder 1.
⇒ 1 = 3 x 0 + 1
4 divided by 3 leaves quotient 1 and remainder 1.
⇒ 4 = 3 x 1 + 1
16 divided by 3 leaves quotient 5 and remainder 1.
⇒ 16 = 3 x 5 + 1
25 divided by 3 leaves quotient 8 and remainder 1.
⇒ 25 = 3 x 8 + 1
36 divided by 3 leaves quotient 12 and remainder 0.
⇒ 36 = 3 x 12 + 0
Therefore when each of the perfect square numbers 1, 4, 9, …………. is divided by 3, the remainder is not always 1.
So, reason (R) is false.
Hence, option 3 is the correct option.
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Related Questions
Statement 1: 3675 is not a perfect square.
Statement 2: After grouping into pairs of equal factors of 3675, if we multiply or divide by the unpaired factor (if any) then the product or the quotient becomes a perfect square.
Which of the following options is correct ?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
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Assertion (A) :
Reason (R) : The square root of a number n is that number which when multiplied by itself gives n as the product.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : Natural numbers 5, 12 and 13 are Pythagorean triplets as 122 + 52 = 132.
Reason (R) : For any natural number n, (n + 1)2 - n2 = (n + 1) + n.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : 1 + 3 + 5 + 7 + ……. + 21 = 102.
Reason (R) : The sum of first n odd natural numbers = n2.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.