Straight Lines · JEE Main previous year questions

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2024 13 questions

Q152024 · 8 Apr 2024 · Shift 1
The equations of two sides AB and AC of a triangle ABC are $4 x + y = 14$ and $3 x - 2 y = 5$ , respectively. The point $(2, - \frac{4}{3})$ divides the third side BC internally in the ratio $2 : 1$ , the equation of the side BC is
1. A. $x + 6 y + 6 = 0$
2. B. $x - 3 y - 6 = 0$
3. C. $x + 3 y + 2 = 0$
4. D. $x - 6 y - 10 = 0$
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Answer: C
Q212024 · 8 Apr 2024 · Shift 1· Numerical answer
If the orthocentre of the triangle formed by the lines $2 x + 3 y - 1 = 0, x + 2 y - 1 = 0$ and $a x + b y - 1 = 0$ , is the centroid of another triangle, whose circumcentre and orthocentre respectively are $(3, 4)$ and $(- 6, - 8)$ , then the value of $∣ a - b ∣$ is ________.
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Answer: 16
Q302024 · 8 Apr 2024 · Shift 2· Numerical answer
Let a ray of light passing through the point $(3, 10)$ reflects on the line $2 x + y = 6$ and the reflected ray passes through the point $(7, 2)$ . If the equation of the incident ray is $a x + b y + 1 = 0$ , then $a^{2} + b^{2} + 3 ab$ is equal to ____.
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Answer: 1
Q82024 · 5 Apr 2024 · Shift 2
Let $A (- 1, 1)$ and $B (2, 3)$ be two points and P be a variable point above the line AB such that the area of $△ PAB$ is 10. If the locus of P is $a x + b y = 15$ , then $5 a + 2 b$ is :
1. A. $- \frac{12}{5}$
2. B. $- \frac{6}{5}$
3. C.6
4. D.4
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Answer: A
Q152024 · 1 Feb 2024 · Shift 2
Let $P$ and $Q$ be the points on the line $\frac{x + 3}{8} = \frac{y - 4}{2} = \frac{z + 1}{2}$ which are at a distance of 6 units from the point $R (1, 2, 3)$ . If the centroid of the triangle $PQR$ is $(α, β, γ)$ , then $α^{2} + β^{2} + γ^{2}$ is :
1. A.18
2. B.24
3. C.26
4. D.36
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Answer: A
Q192024 · 31 Jan 2024 · Shift 2
Let $A (a, b), B (3, 4)$ and $C (- 6, - 8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P (2 a + 3, 7 b + 5)$ from the line $2 x + 3 y - 4 = 0$ measured parallel to the line $x - 2 y - 1 = 0$ is
1. A. $\frac{17 5}{6}$
2. B. $\frac{15 5}{7}$
3. C. $\frac{17 5}{7}$
4. D. $\frac{5}{17}$
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Answer: C
Q242024 · 31 Jan 2024 · Shift 2· Numerical answer
Let $A (- 2, - 1), B (1, 0), C (α, β)$ and $D (γ, δ)$ be the vertices of a parallelogram $A B C D$ . If the point $C$ lies on $2 x - y = 5$ and the point $D$ lies on $3 x - 2 y = 6$ , then the value of $∣ α + β + γ + δ ∣$ is equal to ____.
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Answer: 32
Q302024 · 31 Jan 2024 · Shift 2· Numerical answer
A line passes through $A (4, - 6, - 2)$ and $B (16, - 2, 4)$ . The point $P (a, b, c)$ , where $a, b, c$ are non-negative integers, on the line $A B$ lies at a distance of 21 units, from the point $A$ . The distance between the points $P (a, b, c)$ and $Q (4, - 12, 3)$ is equal to ____.
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Answer: 22
Q122024 · 29 Jan 2024 · Shift 1
In a $△ A B C$ , suppose $y = x$ is the equation of the bisector of the angle $B$ and the equation of the side $A C$ is $2 x - y = 2$ . If $2 A B = B C$ and the points $A$ and $B$ are respectively $(4, 6)$ and $(α, β)$ , then $α + 2 β$ is equal to
1. A. $42$
2. B. $39$
3. C. $48$
4. D. $45$
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Answer: A
Q172024 · 29 Jan 2024 · Shift 1
Let $P QR$ be a triangle with $R (- 1, 4, 2)$ . Suppose $M (2, 1, 2)$ is the mid point of PQ. The distance of the centroid of $△ PQR$ from the point of intersection of the lines $\frac{x - 2}{0} = \frac{y}{2} = \frac{z + 3}{- 1}$ and $\frac{x - 1}{1} = \frac{y + 3}{- 3} = \frac{z + 1}{1}$ is
1. A. $69$
2. B. $99$
3. C. $69$
4. D. $9$
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Answer: C
Q22024 · 29 Jan 2024 · Shift 2
Let A be the point of intersection of the lines $3 x + 2 y = 14, 5 x - y = 6$ and B be the point of intersection of the lines $4 x + 3 y = 8, 6 x + y = 5$ . The distance of the point $P (5, - 2)$ from the line AB is
1. A. $\frac{13}{2}$
2. B.8
3. C. $\frac{5}{2}$
4. D.6
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Answer: D
Q42024 · 29 Jan 2024 · Shift 2
The distance of the point $(2, 3)$ from the line $2 x - 3 y + 28 = 0$ , measured parallel to the line $3 x - y + 1 = 0$ , is equal to
1. A. $3 + 42$
2. B. $63$
3. C. $4 + 63$
4. D. $42$
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Answer: C
Q52024 · 27 Jan 2024 · Shift 1
If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2)$ , $(2, 3)$ and $(3, 1)$ , and $I_{1} = a \int b x sin (4 x - x^{2}) d x$ , $I_{2} = a \int b sin (4 x - x^{2}) d x$ , then $36 \frac{I _{1}}{I _{2}}$ is equal to :
1. A.80
2. B.72
3. C.66
4. D.88
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Answer: B