Q86.Let A = {n ∈ N : H. C. F. (n, 45) = 1} and let B = {2k : k ∈{1, 2, … , 100}} . Then the sum of all the elements of A ∩B is _____.
What This Question Tests
This problem requires identifying elements in a set based on HCF conditions, then summing specific elements from an arithmetic progression using the principle of inclusion-exclusion related to divisibility.
Concepts Tested
Formulas Used
Sum of AP = (n/2)(a + l)
Number of terms not divisible by p and q = Total - (divisible by p) - (divisible by q) + (divisible by pq)
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📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Set operations, Number theory (HCF), Arithmetic Progression
- Year
- 2022
- Shift
- 26 Jun Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 1: Sets
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