Straight Lines · JEE Main previous year questions

2025 9 questions

1. Q52025 · 8 Apr 2025 · Shift 2

   A line passing through the point $P(a,0)$ makes an acute angle $\alpha$ with the positive x-axis. Let this line be rotated about the point $P$ through an angle $\frac{\alpha }{2}$ in the clockwise direction. If in the new position, the slope of the line is $2-\sqrt{3}$ and its distance from the origin is $\frac{1}{\sqrt{2}}$, then the value of $3a^2{\tan }^2\alpha -2\sqrt{3}$ is :

   1. A.$8$
   2. B.$4$
   3. C.$5$
   4. D.$6$
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   Answer: B

2. Q242025 · 8 Apr 2025 · Shift 2· Numerical answer

   Let the area of the triangle formed by the lines $x+2=y-1=z$, $\frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^2$ is equal to $\underline{}$.

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   Answer: 56

3. Q182025 · 4 Apr 2025 · Shift 1

   Let the three sides of a triangle lie on the lines $4x-7y+10=0,x+y=5$ and $7x+4y=15$. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $x=0,y=0$ and $x+y=1$ is

   1. A.$\sqrt{20}$
   2. B.$20$
   3. C.$\sqrt{5}$
   4. D.$5$
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   Answer: C

4. Q192025 · 3 Apr 2025 · Shift 1

   A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines ${\mathrm{L}}_1:2x+y+6=0$ and ${\mathrm{L}}_2:4x+2y-p=0$, $p>0$, at the points A and B , respectively. If $AB=\frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\frac{AM}{BM}$ is equal to

   1. A.5
   2. B.3
   3. C.2
   4. D.4
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   Answer: B

5. Q42025 · 3 Apr 2025 · Shift 2

   If $z_1,z_2,z_3\in \mathbb{C}$ are the vertices of an equilateral triangle whose centroid is $z_0$, then ${\sum }_{k=1}^3(z_k-z_0{)}^2$ is equal to

   1. A.$0$
   2. B.$1$
   3. C.$\mathrm{i}$
   4. D.$-\mathrm{i}$
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   Answer: A

6. Q122025 · 2 Apr 2025 · Shift 2

   Let the area of the triangle formed by a straight line $L:x+by+c=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $45^{\circ }$ with the positive $x$-axis, then the value of $b^2+c^2$ is :

   1. A.90
   2. B.83
   3. C.93
   4. D.97
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   Answer: D

7. Q182025 · 24 Jan 2025 · Shift 1

   Let the lines $3x-4y-\alpha =0,8x-11y-33=0$, and $2x-3y+\lambda =0$ be concurrent. If the image of the point $(1,2)$ in the line $2x-3y+\lambda =0$ is $\left(\frac{57}{13},\frac{-40}{13}\right)$, then $|\alpha \lambda |$ is equal to

   1. A.$91$
   2. B.$113$
   3. C.$101$
   4. D.$84$
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   Answer: A

8. Q152025 · 24 Jan 2025 · Shift 2

   Let the points $\left(\frac{11}{2},\alpha \right)$ lie on or inside the triangle with sides $x+y=11,x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

   1. A.22
   2. B.33
   3. C.55
   4. D.44
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   Answer: B

9. Q62025 · 22 Jan 2025 · Shift 1

   Let the triangle PQR be the image of the triangle with vertices $(1,3)$, $(3,1)$ and $(2,4)$ in the line $x+2y=2$. If the centroid of $△\mathrm{PQR}$ is the point $(\alpha ,\beta )$, then $15(\alpha -\beta )$ is equal to :

   1. A.21
   2. B.19
   3. C.22
   4. D.24
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   Answer: C