Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|=$
MathematicsDeterminantsTS EAMCETTS EAMCET 2023 (12 May Shift 2)
Options:
  • A $5 \sqrt{2}-3 \sqrt{3}$
  • B $5 \sqrt{3}-3 \sqrt{5}$
  • C $10 \sqrt{3}-15 \sqrt{2}$
  • D $15 \sqrt{2}-25 \sqrt{3}$
Solution:
2662 Upvotes Verified Answer
The correct answer is: $15 \sqrt{2}-25 \sqrt{3}$
$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|$
$\begin{aligned} & =\sqrt{3}(25-\sqrt{150})-2 \sqrt{5}(5 \sqrt{15}-3 \sqrt{10})+\sqrt{5}(15-15) \\ & =25 \sqrt{3}-15 \sqrt{2}-50 \sqrt{3}+30 \sqrt{2} \\ & =15 \sqrt{2}-25 \sqrt{3}\end{aligned}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.