JEE Main 2023MathematicsBinomial TheoremMediumNumerical

JEE Main 2023 — Binomial Theorem Question with Solution

JEE Main 2023 (08 Apr Shift 1)

Question

Let t denote the greatest integer ≤t. if the constant term in the expansion of 3x2-12x57 is α then α is equal to _____

Enter your answer

Show full solutionCorrect answer: 1275
Correct answer
1275

Step-by-step explanation

The given expansion is 3x2-12x57.

The general term in the binomial expansion of x+an is given by Tr+1=Crnxn-rar.

⇒Tr+1=Cr73x27-r-12x5r

=Cr7-1r37-r2rx14-2r-5r

Now for term independent of x⇒14-2r-5r=0

⇒r=2

Coefficient of x0 is C27-12×37-222

=7×62×3522.

⇒α=51034

⇒α=1275

Hence this is the required answer.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Binomial Theorem chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, covering the Binomial Theorem 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.