Mathematics
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.
Answer
We know that,
The sum of first n odd natural numbers = n2.
So, reason (R) is true.
According to assertion :
1 + 3 + 5 + 7 + ……. + 21 = 102
Solving the L.H.S. of above equation, we get :
⇒ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21
The above is a sum of the first 11 odd natural numbers. So, by formula
⇒ 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 112 = 121.
So, assertion (A) is false.
Hence, option 4 is the correct option.
Related Questions
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.
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.
Express 212 as the sum of two consecutive whole numbers.