JEE Mains · Maths · STD 11 - 7. binomial theoram
Let \( S=\{(m,n): m, n\in\{1,2,3,.....,50\}\} \). If the number of elements (m, n) in S such that \( 6^{m}+9^{n} \) is a multiple of 5 is p and the number of elements (m, n) in S such that \( m+n \) is a square of a prime number is q, then \( p+q \) is equal to :
- A 1333
- B 1250
- C 1350
- D 1283
Answer & Solution
Correct Answer
(A) 1333
Step-by-step Solution
Detailed explanation
\(S=\{1,2,3, \ldots .50\}\) \(p=\left(6^m+9^n\right)\) is divisible by 5 No. of ways \(6^{ m }=(5 \lambda+1)^{ m }=5 k +1\) \(9^{ n }=(10-1)^{ n }=10 \mu-1\) if n is odd ⇒ n must be odd \(10 \mu+1\) if n is even ⇒ No. of ways \(=50 \times 25=1250\) \(q \Rightarrow(m+n)\) is…
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