JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 75

If the system of linear equations :
$x+y+z=6,\qquad x+2y+5z=10,\qquad 2x+3y+\lambda z=\mu$
has infinitely many solutions, then the value of $\lambda+\mu$ equals :

Answer and worked solution

Official answer: C

Infinitely many solutions. The third equation must be $p(\text{eq}_1)+q(\text{eq}_2)$ : $p+q=2$ and $p+2q=3$ , so $p=q=1$ .

So $\lambda=1+5=6$ , $\mu=6+10=16$ , and $\lambda+\mu=22$ .

(C)

Topics:Systems of linear equations

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 3