JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

If two straight lines whose direction cosines are given by the relations $l+m-n=0$ , $3l^2+m^2+cnl=0$ are parallel, then the positive value of $c$ is :

Answer and worked solution

Official answer: A

Eliminate n. $n=l+m$ gives $(3+c)l^2+clm+m^2=0$ , a quadratic in $\frac lm$ .

Parallel lines mean equal roots: $c^2=4(3+c)$ , so $c=6$ (positive).

(A)

Topics:Direction cosines and ratios Nature of roots

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JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 14