JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let

p

and

p + 2

be prime numbers and let

\Delta = \begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \end{vmatrix}

Then the sum of the maximum values of

\alpha

and

\beta

, such that

p^{\alpha}

and

(p + 2)^{\beta}

divide

\Delta

, is __________.

Official answer

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Quick Identification via Proportionality

Same topic in other shifts

All Cramer's Rule questions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.