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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Determinants

NDA 2021 · Mathematics · Determinants

Let A=| array lr p & q r & s array | where p, q, r and s are any...

Let A=\left|pqrs\begin{array}{lr}p & q \\ r & s\end{array}\right| where p,q,rp, q, r and ss are any four different prime numbers less than 20. What is the maximum value of the determinant?

Options

  1. A215215
  2. B311311
  3. C317317
  4. D323323

Correct answer

C. 317317

Step-by-step solution

A=\left|pqrs\begin{array}{ll}p & q \\ r & s\end{array}\right|, where (p,q,r,s)(p, q, r, s) prime number <20∴(p,q,r,s)=(2,3,5,7,11,13,17 and 19)< 20\therefore(p, q, r, s)=(2,3,5,7,11,13,17 \text{ and } 19) Now, A=p⋅s−q⋅rA=p \cdot s-q \cdot r. For Amax A_{\text{max }}, product (p.s)(p. s) should be max. and product (q.r) should be min. ∴Amax⁡.=p⋅s−q⋅r=19×17−2×3=317\therefore A_{\max.}=p \cdot s-q \cdot r=19 \times 17-2 \times 3=317
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