JEE Main 2023MathematicsPermutation CombinationHardMCQ

JEE Main 2023 — Permutation Combination Question with Solution

JEE Main 2023 (25 Jan Shift 2)

Question

Let f(x)=2xn+λ,λ∈ℝ,n∈ℕ, and f(4)=133, f(5)=255. Then the sum of all the positive integer divisors of (f(3)-f(2)) is

Choose an option

Show full solutionCorrect option: B
Correct answer
B60

Step-by-step explanation

f(x) is given as

f(x)=2xn+λ, λ∈R, n∈N

∵ f(4)=133

⇒133=2×4n+λ              ...(1)

∵ f(5)=255

⇒255=2×5n+λ              ...(2)

Now, (2)-(1)

122=25n-4n

⇒5n-4n=61

∴n=3 & λ=5

Now f(3)-f(2)=233-23=38

Number of divisors =1, 2,19, 38 and their sum is 60

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About this question

This is a previous-year question from JEE Main 2023, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.