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JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(A=\{n \in N: n\) is a \(3 -\) digit number \(\}\) \(B =\{9 k +2: k \in N \}\) and \(C=\{9 k+l: k \in N\}\) for some \(l(0< l< 9)\) If the sum of all the elements of the set \(A \cap(B \cup C)\) is \(274 \times 400,\) then \(l\) is equal to ..............
- A \(2\)
- B \(3\)
- C \(1\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(B\) and \(C\) will contain three digit numbers of the form \(9 k +2\) and \(9 k +\ell\) respectively. We need to find sum of all elements in the set \(B \cup C\) effectively. Now, \(S(B \cup C)=S(B)+S(C)-S(B \cap C)\) where \(S ( k )\) denotes sum of elements of set \(k\).…
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