Straight Lines · JEE Main previous year questions

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2026 10 questions

Q102026 · 8 Apr 2026 · Shift 2
If a straight line drawn through the point of intersection of the lines $4 x + 3 y - 1 = 0$ and $3 x + 4 y - 1 = 0$ , meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is :
1. A. $x + y - 7 = 0$
2. B. $x + y - 14 x y = 0$
3. C. $2 x + y + 14 x y = 0$
4. D. $x + 2 y - 14 x y = 0$
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Answer: B
Q162026 · 6 Apr 2026 · Shift 1
Given below are two statements : Statement I : 3-phenylpropene reacts with HBr and gives secondary alkyl bromide having a chiral carbon atom as the major product. Statement II : Aryl chlorides and aryl cyanides can be prepared by Sandmeyer reaction as well as Gattermann reaction. In the light of the above statements, choose the correct answer from the options given below
1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true
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Answer: B
Q112026 · 5 Apr 2026 · Shift 1
In an equilateral triangle $PQR$ , let the vertex $P$ be at $(3, 5)$ and the side $QR$ be along the line $x + y = 4$ . If the orthocentre of the triangle $PQR$ is $(α, β)$ , then $9 (α + β)$ is equal to:
1. A.16
2. B.27
3. C.36
4. D.48
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Answer: D
Q142026 · 5 Apr 2026 · Shift 2
Let a triangle $PQR$ be such that $P$ and $Q$ lie on the line $\frac{x + 3}{8} = \frac{y - 4}{2} = \frac{z + 1}{2}$ and are at a distance of 6 units from $R (1, 2, 3)$ . If $(α, β, γ)$ is the centroid of $Δ PQR$ , then $α + β + γ$ is equal to :
1. A. $4$
2. B. $5$
3. C. $6$
4. D. $8$
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Answer: C
Q222026 · 5 Apr 2026 · Shift 2· Numerical answer
From the point $(- 1, - 1)$ , two rays are sent making angles of $4 5^{\circ}$ with the line $x + y = 0$ . These rays get reflected from the mirror $x + 2 y = 1$ . If the equations of the reflected rays are $a x + b y = 9$ and $c x + d y = 7$ , $a, b, c, d \in Z$ , then the value of $a d + b c$ is ____.
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Answer: 7
Q112026 · 4 Apr 2026 · Shift 1
Let the line $L_{1} : x + 3 = 0$ intersect the lines $L_{2} : x - y = 0$ and $L_{3} : 3 x + y = 0$ at the points A and B, respectively. Let the bisector of the obtuse angle between the lines $L_{2}$ and $L_{3}$ intersect the line $L_{1}$ at the point C. Then $BC^{2} : AC^{2}$ is equal to:
1. A. $5 : 1$
2. B. $1 : 5$
3. C. $2 : 3$
4. D. $3 : 2$
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Answer: A
Q122026 · 4 Apr 2026 · Shift 1
Let the vertex A of a triangle ABC be $(1, 2)$ , and the mid-point of the side AB be $(5, - 1)$ . If the centroid of this triangle is $(3, 4)$ and its circumcenter is $(α, β)$ , then $21 (α + β)$ is equal to:
1. A.309
2. B.403
3. C.497
4. D.524
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Answer: C
Q92026 · 2 Apr 2026 · Shift 1
Given below are two statements : Statement (I) : The first ionisation enthalpy of the elements Na, Mg, Cl and Ar follows the order Na > Mg > Cl > Ar. Statement (II) : Among Ca, Al, Fe and B, the third ionisation enthalpy is very high for Ca. In the light of the above statements, choose the correct answer from the options given below :
1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true
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Answer: C
Q22026 · 24 Jan 2026 · Shift 1
Let $A (1, 0), B (2, - 1)$ and $C (\frac{7}{3}, \frac{4}{3})$ be three points. If the equation of the bisector of the angle ABC is $α x + β y = 5$ , then the value of $α^{2} + β^{2}$ is
1. A.5
2. B.10
3. C.8
4. D.13
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Answer: B
Q102026 · 23 Jan 2026 · Shift 2
Let A(1, 2) and C(-3, -6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7 x - y = 14$ . If $B (α, β)$ and $D (γ, δ)$ are the other two vertices, then $∣ α + β + γ + δ ∣$ is equal to :
1. A.3
2. B.6
3. C.1
4. D.9
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Answer: B