Straight Lines · JEE Main previous year questions

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2023 8 questions

Q92023 · 13 Apr 2023 · Shift 2
Let $(α, β)$ be the centroid of the triangle formed by the lines $15 x - y = 82$ , $6 x - 5 y = - 4$ and $9 x + 4 y = 17$ . Then $α + 2 β$ and $2 α - β$ are the roots of the equation :
1. A. $x^{2} - 7 x + 12 = 0$
2. B. $x^{2} - 13 x + 42 = 0$
3. C. $x^{2} - 14 x + 48 = 0$
4. D. $x^{2} - 10 x + 25 = 0$
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Answer: B
Q302023 · 11 Apr 2023 · Shift 2· Numerical answer
If the line $l_{1} : 3 y - 2 x = 3$ is the angular bisector of the lines $l_{2} : x - y + 1 = 0$ and $l_{3} : α x + β y + 17 = 0$ , then $α^{2} + β^{2} - α - β$ is equal to _________.
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Answer: 348
Q102023 · 8 Apr 2023 · Shift 1
Let $C (α, β)$ be the circumcenter of the triangle formed by the lines $4 x + 3 y = 69$ $4 y - 3 x = 17$ , and $x + 7 y = 61$ . Then $(α - β)^{2} + α + β$ is equal to :
1. A. $15$
2. B. $17$
3. C. $16$
4. D. $18$
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Answer: B
Q32023 · 6 Apr 2023 · Shift 1
The straight lines $l_{1}$ and $l_{2}$ pass through the origin and trisect the line segment of the line L : $9 x + 5 y = 45$ between the axes. If $m_{1}$ and $m_{2}$ are the slopes of the lines $l_{1}$ and $l_{2}$ , then the point of intersection of the line $y = (m_{1} + m_{2}) x$ with L lies on :
1. A. $6 x - y = 15$
2. B. $6 x + y = 10$
3. C. $y - x = 5$
4. D. $y - 2 x = 5$
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Answer: C
Q132023 · 31 Jan 2023 · Shift 1
For all $z \in C$ on the curve $C_{1} : ∣ z ∣ = 4$ , let the locus of the point $z + \frac{1}{z}$ be the curve $C_{2}$ . Then :
1. A.the curves $C_{1}$ and $C_{2}$ intersect at 4 points
2. B.the curve $C_{2}$ lies inside $C_{1}$
3. C.the curve $C_{1}$ lies inside $C_{2}$
4. D.the curves $C_{1}$ and $C_{2}$ intersect at 2 points
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Answer: A
Q132023 · 30 Jan 2023 · Shift 1
A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$ -axis and $y$ axis respectively. If the perpendicular from origin $O$ to this line makes an angle of $\frac{π}{6}$ with positive direction of $y$ -axis and the area of $△ OAB$ is $\frac{98}{3} 3$ , then $a^{2} - b^{2}$ is equal to :
1. A. $\frac{392}{3}$
2. B.98
3. C.196
4. D. $\frac{196}{3}$
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Answer: A
Q92023 · 29 Jan 2023 · Shift 1
A light ray emits from the origin making an angle $3 0^{\circ}$ with the positive $x$ -axis. After getting reflected by the line $x + y = 1$ , if this ray intersects $x$ -axis at Q, then the abscissa of Q is :
1. A. $\frac{2}{( 3 - 1 )}$
2. B. $\frac{2}{3 - 3}$
3. C. $\frac{3}{2 ( 3 + 1 )}$
4. D. $\frac{2}{3 + 3}$
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Answer: D
Q252023 · 24 Jan 2023 · Shift 2· Numerical answer
The equations of the sides AB, BC and CA of a triangle ABC are : $2 x + y = 0, x + p y = 21 a, (a \neq = 0)$ and $x - y = 3$ respectively. Let P(2, a) be the centroid of $Δ ABC$ . Then $(BC)^{2}$ is equal to _______.
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Answer: 122