JEE Main 2020MathematicsDeterminantsHardNumerical

JEE Main 2020 — Determinants Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

Let S be the set of all integer solutions x, y, z of the system of equations

x-2 y+5 z=0

-2 x+4 y+z=0

-7 x+14 y+9 z=0

such that 15≤x2+y2+z2≤150. Then, the number of elements in the set S is equal to ..........

Enter your answer

Show full solutionCorrect answer: 8
Correct answer
8

Step-by-step explanation

x-2y+5z=0 ...........i

-2x+4y+z=0 ..........ii

-7x+14y+9z=0 ..........iii

Applying 2× equation i+equation ii, we get

z=0

Putting z=0 in equation i, we get

x=2y

Given 15≤x2+y2+z2≤150

⇒15≤4y2+y2≤150

⇒3≤y2≤30

⇒y=±2, ±3, ±4, ±5

⇒8 solutions.

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About this question

This is a previous-year question from JEE Main 2020, covering the Determinants 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.