JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f ( x )=2 x ^{ n }+\lambda, \lambda \in R , n \in N\), and \(f (4)=133\), \(f(5)=255\). Then the sum of all the positive integer divisors of \(( f (3)- f (2))\) is
- A \(61\)
- B \(60\)
- C \(58\)
- D \(59\)
Answer & Solution
Correct Answer
(B) \(60\)
Step-by-step Solution
Detailed explanation
\(f(x)=2 x^{ n }+\lambda\) \(f(4)=133\) \(f(5)=255\) \(133=2 \times 4^{ n }+\lambda......(1)\) \(255=2 \times 5^{ n }+\lambda......(2)\) \((2) -(1)\) \(122=2\left(5^{ n }-4^{ n }\right)\) \(\Rightarrow 5^{ n }-4^{ n }=61\) \(\therefore n =3\, and\, \lambda=5\) Now,…
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