Straight Line – JEE Advanced Previous Year Questions with Solutions

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Q. Let $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ be the points on the plane with position vectors $-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}, 4 \hat{\mathrm{i}}, 3 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $-3 \hat{\mathrm{j}}$ and $-3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$ respectively. The quadrilateral PQRS must be a (A) parallelogram, which is neither a rhombus nor a rectangle (B) square (C) rectangle, but not a square (D) rhombus, but not a square [JEE 2010, 3]

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Sol. (A) $\Rightarrow$ PQRS is a parallelogram but neither a rhombus nor a rectangle.

Q. A straight line L through the point $(3,-2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If $L$ also intersect the x-axis, then the equation of $L$ is (A) $y+\sqrt{3} x+2-3 \sqrt{3}=0$ (B) $\mathrm{y}-\sqrt{3} \mathrm{x}+2+3 \sqrt{3}=0$ (C) $\sqrt{3} y-x+3+2 \sqrt{3}=0$ (D) $\sqrt{3} y+x-3+2 \sqrt{3}=0$ [JEE 2011, 3 (–1)]

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Sol. (B)

Q. For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines $a x+b y+c=0$ and $b x+a y+c=0$ is less than $2 \sqrt{2} .$ Then (A) a + b – c > 0 (B) a – b + c < 0 (C) a – b + c > 0 (D) a + b – c < 0 [JEE-Advanced 2013, 2]

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Sol. (A or C or A,C) Point of intersection of both lines is $\left(-\frac{c}{(a+b)},-\frac{c}{(a+b)}\right)$ Distance between $\left(-\frac{c}{(a+b)},-\frac{c}{(a+b)}\right) \&(1,1)$ is Distance $=\sqrt{\frac{(a+b+c)^{2}}{(a+b)^{2}} \times 2}<2 \sqrt{2}$ $a+b+c<2(a+b)$ $a+b-c>0$ According to given condition option (C) also correct.

Q. For a point $P$ in the plane, let $d_{1}(P)$ and $d_{2}(P)$ be the distances of the point $P$ from the lines $x-y=0$ and $x+y=0$ respectively. The area of the region $R$ consisting of all points $P$ lying in the first quadrant of the plane and satisfying $2 \leq d_{1}(P)+d_{2}(P) \leq 4,$ is [JEE(Advanced)-2014, 3]

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Sol. 6

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Comments
  • May 11, 2021 at 8:14 pm

    I suggest esaral to add more questions. I am unsatisfied from this😑.

    0
  • March 31, 2021 at 8:25 pm

    Very few but challenging questions please edit more questions 👍

    0
  • October 13, 2020 at 1:07 am

    Btwlast question is fantastic..

    0
  • October 13, 2020 at 12:44 am

    Is that it? …only this much questions from straight lines ?

    0
  • September 24, 2020 at 7:59 pm

    Put more questions please sir and solution very clarity

    0
  • September 22, 2020 at 2:33 pm

    abe yrr sirf 4 hi question??

    0
  • September 15, 2020 at 5:16 pm

    Aur question daalo be… Sirf 4….

    0