Straight Lines · JEE Main previous year questions

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2022 12 questions

Q82022 · 29 Jul 2022 · Shift 1
Let the circumcentre of a triangle with vertices $A (a, 3)$ , $B (b, 5)$ and $C (a, b)$ , $ab > 0$ be $P (1, 1)$ . If the line $AP$ intersects the line $BC$ at the point $Q (k_{1}, k_{2})$ , then $k_{1} + k_{2}$ is equal to :
1. A.2
2. B. $\frac{4}{7}$
3. C. $\frac{2}{7}$
4. D.4
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Answer: B
Q102022 · 29 Jul 2022 · Shift 2
Let $A (α, - 2)$ , $B (α, 6)$ and $C (\frac{α}{4}, - 2)$ be vertices of a $△ ABC$ . If $(5, \frac{α}{4})$ is the circumcentre of $△ ABC$ , then which of the following is NOT correct about $△ ABC$ ?
1. A.area is 24
2. B.perimeter is 25
3. C.circumradius is 5
4. D.inradius is 2
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Answer: B
Q102022 · 27 Jul 2022 · Shift 2
The equations of the sides $AB$ , $BC$ and $CA$ of a triangle $ABC$ are $2 x + y = 0$ , $x + p y = 39$ and $x - y = 3$ respectively and $P (2, 3)$ is its circumcentre. Then which of the following is NOT true?
1. A. $(AC)^{2} = 9 p$
2. B. $(AC)^{2} + p^{2} = 136$
3. C. $32 < area (Δ ABC) < 36$
4. D. $34 < area (Δ ABC) < 38$
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Answer: D
Q102022 · 26 Jul 2022 · Shift 1
A point $P$ moves so that the sum of squares of its distances from the points $(1, 2)$ and $(- 2, 1)$ is 14. Let $f (x, y) = 0$ be the locus of P, which intersects the $x$ -axis at the points $A$ , B and the $y$ -axis at the points C, D. Then the area of the quadrilateral ACBD is equal to :
1. A. $\frac{9}{2}$
2. B. $\frac{3 17}{2}$
3. C. $\frac{3 17}{4}$
4. D.9
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Answer: B
Q252022 · 26 Jul 2022 · Shift 1· Numerical answer
The equations of the sides AB, BC and CA of a triangle ABC are $2 x + y = 0$ , $x + p y = 15 a$ and $x - y = 3$ respectively. If its orthocentre is $(2, a)$ , $- \frac{1}{2} < a < 2$ , then p is equal to ____ .
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Answer: 3
Q92022 · 30 Jun 2022 · Shift 1
Let $α_{1}, α_{2} (α_{1} < α_{2})$ be the values of $α$ for the points $(α, - 3)$ , $(2, 0)$ and $(1, α)$ to be collinear. Then the equation of the line, passing through $(α_{1}, α_{2})$ and making an angle of $\frac{π}{3}$ with the positive direction of the x-axis, is :
1. A. $x - 3 y - 33 + 1 = 0$
2. B. $3 x - y + 3 + 3 = 0$
3. C. $x - 3 y + 33 + 1 = 0$
4. D. $3 x - y + 3 - 3 = 0$
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Answer: B
Q122022 · 28 Jun 2022 · Shift 2
Let a triangle be bounded by the lines $L_{1} : 2 x + 5 y = 10$ ; $L_{2} : - 4 x + 3 y = 12$ and the line $L_{3}$ , which passes through the point $P (2, 3)$ , intersects $L_{2}$ at A and $L_{1}$ at B. If the point P divides the line-segment AB, internally in the ratio $1 : 3$ , then the area of the triangle is equal to :
1. A. $\frac{110}{13}$
2. B. $\frac{132}{13}$
3. C. $\frac{142}{13}$
4. D. $\frac{151}{13}$
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Answer: B
Q102022 · 27 Jun 2022 · Shift 1
In an isosceles triangle ABC, the vertex A is $(6, 1)$ and the equation of the base BC is $2 x + y = 4$ . Let the point B lie on the line $x + 3 y = 7$ . If $(α, β)$ is the centroid of $Δ ABC$ , then $15 (α + β)$ is equal to :
1. A.39
2. B.41
3. C.51
4. D.63
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Answer: C
Q92022 · 26 Jun 2022 · Shift 1
Let R be the point $(3, 7)$ and let P and Q be two points on the line $x + y = 5$ such that PQR is an equilateral triangle. Then the area of $Δ PQR$ is :
1. A. $\frac{25}{4 3}$
2. B. $\frac{25 3}{2}$
3. C. $\frac{25}{3}$
4. D. $\frac{25}{2 3}$
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Answer: D
Q102022 · 26 Jun 2022 · Shift 1
If the two lines $l_{1} : \frac{x - 2}{3} = \frac{y + 1}{- 2}, z = 2$ and $l_{2} : \frac{x - 1}{1} = \frac{2 y + 3}{α} = \frac{z + 5}{2}$ are perpendicular, then an angle between the lines $l_{2}$ and $l_{3} : \frac{1 - x}{3} = \frac{2 y - 1}{- 4} = \frac{z}{4}$ is :
1. A. $cos^{- 1} (\frac{29}{4})$
2. B. $sec^{- 1} (\frac{29}{4})$
3. C. $cos^{- 1} (\frac{2}{29})$
4. D. $cos^{- 1} (\frac{2}{29})$
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Answer: B
Q92022 · 24 Jun 2022 · Shift 2
Let the area of the triangle with vertices $A (1, α)$ , $B (α, 0)$ and $C (0, α)$ be 4 sq. units. If the points $(α, - α)$ , $(- α, α)$ and $(α^{2}, β)$ are collinear, then $β$ is equal to :
1. A.64
2. B. $- 8$
3. C. $- 64$
4. D.512
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Answer: C
Q202022 · 24 Jun 2022 · Shift 2
The slope of normal at any point $(x, y)$ , $x > 0$ , $y > 0$ on the curve $y = y (x)$ is given by $\frac{x ^{2}}{x y - x ^{2} y ^{2} - 1}$ . If the curve passes through the point $(1, 1)$ , then $e \cdot y (e)$ is equal to
1. A. $\frac{1 - t a n ( 1 )}{1 + t a n ( 1 )}$
2. B. $tan (1)$
3. C.1
4. D. $\frac{1 + t a n ( 1 )}{1 - t a n ( 1 )}$
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Answer: D