Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Statements/Expressions etc.) | (Values, etc.) | ||
| (A) | Find the sum of the first 20 odd natural numbers. | (I) | 285 |
| (B) | How many prime numbers are there between 100 and 200? | (II) | 0 |
| (C) | Find the sum of the squares of the digits from 1 to 9. | (III) | 400 |
| (D) | Find the unit's digit in the product 81 × 82 × 83 × ... × 89? | (IV) | 21 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
(A) Find the sum of the first 20 odd natural numbers. — this matches (III) 400. The sum of the first \(n\) odd numbers is the square of \(n\), the count of numbers added (1 + 3 = 4, 1 + 3 + 5 = 9, ...), so here it is \(20^{2}=400\).
(B) How many prime numbers are there between 100 and 200? — this matches (IV) 21. They are 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197 and 199, 21 primes.
(C) Find the sum of the squares of the digits from 1 to 9. — this matches (I) 285. By the formula \(\frac{n(n+1)(2n+1)}{6}\) for the sum of the first \(n\) squares, \(\frac{9\times10\times19}{6}=285\).
(D) Find the unit’s digit in the product 81 × 82 × 83 × ... × 89? — this matches (II) 0. The product contains 82 and 85, an even number and a multiple of 5, whose product ends in 0, so the whole product ends in 0.