Straight Lines · JEE Main previous year questions

2021 6 questions

1. Q202021 · 26 Aug 2021 · Shift 2
   
   1. A.${\tan }^{-1}\left(\frac{3}{4}\right)$
   2. B.${\tan }^{-1}(1)$
   3. C.${\tan }^{-1}\left(\frac{4}{3}\right)$
   4. D.${\tan }^{-1}\left(\frac{1}{2}\right)$
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   Answer: A

2. Q202021 · 25 Jul 2021 · Shift 2

   Let the equation of the pair of lines, y = px and y = qx, can be written as $(y-px)(y-qx)=0$. Then the equation of the pair of the angle bisectors of the lines $x^2-4xy-5y^2=0$ is :

   1. A.$x^2-3xy+y^2=0$
   2. B.$x^2+4xy-y^2=0$
   3. C.$x^2+3xy-y^2=0$
   4. D.$x^2-3xy-y^2=0$
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   Answer: C

3. Q292021 · 25 Jul 2021 · Shift 2· Numerical answer

   Let a curve y = f(x) pass through the point $(2,({\log }_{e}2{)}^2)$ and have slope $\frac{2y}{x{\log }_{e}x}$ for all positive real value of x. Then the value of f(e) is equal to ____.

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   Answer: 1

4. Q52021 · 18 Mar 2021 · Shift 1

   The equation of one of the straight lines which passes through the point $(1,3)$ and makes an angles ${\tan }^{-1}\left(\sqrt{2}\right)$ with the straight line, $y+1=3\sqrt{2}x$ is :

   1. A.$4\sqrt{2}x+5y-\left(15+4\sqrt{2}\right)=0$
   2. B.$5\sqrt{2}x+4y-\left(15+4\sqrt{2}\right)=0$
   3. C.$4\sqrt{2}x+5y-4\sqrt{2}=0$
   4. D.$4\sqrt{2}x-5y-\left(5+4\sqrt{2}\right)=0$
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   Answer: A

5. Q192021 · 18 Mar 2021 · Shift 1

   If $\alpha ,\beta$ are natural numbers such that $100^{\alpha }-199\beta =(100)(100)+(99)(101)+(98)(102)+\cdots +(1)(199)$, then the slope of the line passing through $(\alpha ,\beta )$ and origin is :

   1. A.540
   2. B.550
   3. C.530
   4. D.510
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   Answer: B

6. Q82021 · 26 Feb 2021 · Shift 1

   The intersection of three lines $x-y=0$, $x+2y=3$ and $2x+y=6$ is a :

   1. A.Right angled triangle
   2. B.Equilateral triangle
   3. C.None of the above
   4. D.Isosceles triangle
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   Answer: D