Match List - I with List - II. List I — Statement List II — Result A. Average…
2024
Match List - I with List - II.
List I — Statement | List II — Result |
|---|---|
A. Average of the squares of first 10 natural numbers | I. 13 |
B. Average of first 5 multiples of 5 | II. 45 |
C. Average of first 25 natural numbers | III. 38.5 |
D. Average of cubes of first 5 natural numbers | IV. 15 |
Choose the correct answer from the options given below :
Answer: D. A-III, B-IV, C-I, D-II — ConceptThe average of n values equals their sum divided by n. For consecutive arithmetic terms, the average is also the mean of the first and last terms.…
- A.
A-I, B-II, C-III, D-IV
- B.
A-II, B-III, C-IV, D-I
- C.
A-IV, B-I, C-II, D-III
- D.
A-III, B-IV, C-I, D-II
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Concept
The average of n values equals their sum divided by n. For consecutive arithmetic terms, the average is also the mean of the first and last terms. Standard sum formulas for natural numbers, their squares, and their cubes make each row directly computable.
Application
For A, the sum of the squares from 1 through 10 is 10 × 11 × 21 ÷ 6 = 385; dividing by 10 gives 38.5. Therefore A maps to III.
For B, the first five multiples of 5 are 5, 10, 15, 20, and 25. Their average is (5 + 25) ÷ 2 = 15. Therefore B maps to IV.
For C, the average of the natural numbers from 1 through 25 is (1 + 25) ÷ 2 = 13. Therefore C maps to I.
For D, the sum of the first five cubes is [5 × 6 ÷ 2]2 = 225; dividing by 5 gives 45. Therefore D maps to II.
Cross-check
Directly adding the five multiples of 5 gives 75, and 75 ÷ 5 = 15.
The natural numbers from 1 through 25 are paired symmetrically around 13, confirming the value for C.
Hence the complete matching is A-III, B-IV, C-I, D-II.