Straight Lines PYQs Set 8 (PDF)

Set 8 of 15 · Questions 211-240 of 442

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Straight Lines · Set 8 (Q211-240)
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211. $If the equations x = t^{2} + t + 1, y = t^{2} - t + 1 represents a curve C with parameter t, then the Cartesian equation of C is$ (1) $x^{2} - 2 xy + y^{2} - 2 x - 2 y + 4 = 0$ (2) $x^{2} + 2 xy + y^{2} - 2 x - 2 y + 4 = 0$ (3) $x^{2} - 2 xy + y^{2} + 2 x + 2 y + 4 = 0$ (4) $x^{2} - 2 xy - y^{2} + 2 x + 2 y + 4 = 0$ 212. $Let the angles made with the positive x -axis by two straight lines drawn from the point P (2, 3) and meeting the line x + y = 6 at a distance \frac{2}{3} from the point P be θ_{1} and θ_{2} . Then the value of (θ_{1} + θ_{2}) is:$ (1) $\frac{π}{3}$ (2) $\frac{π}{6}$ (3) $\frac{π}{2}$ (4) $\frac{π}{12}$ 213. $If the slope of one of the lines given by a x^{2} + 2 hxy + b y^{2} = 0 is two times the other, then$ (1) $8 h^{2} = 9 ab$ (2) $8 h^{2} = 9 a b^{2}$ (3) $8 h = 9 ab$ (4) $8 h = 9 a b^{2}$ 214. $If a x^{2} - 34 xy - 5 y^{2} + 2 x + 26 y - 5 = 0 represents a pair of straight lines, then the value of a is$ (1) $7$ (2) $5$ (3) $2$ (4) $13$ 215. $The equation of the line passing through the point of intersection of the lines 2 x + y - 4 = 0, x - 3 y + 5 = 0 and lying at a distance of 5 units from the origin, is$ (1) $x - 2 y - 5 = 0$ (2) $x + 2 y - 5 = 0$ (3) $x + 2 y + 5 = 0$ (4) $x - 2 y + 5 = 0$ 216. $The equation of the pair of lines joining the origin to the points of intersection of x^{2} + y^{2} = 9 and x + y = 3, is$ (1) $x^{2} + (3 - y)^{2} = 9$ (2) $(3 + y)^{2} + y^{2} = 9$ (3) $x^{2} - y^{2} = 9$ (4) $xy = 0$ 217. $The vertices of triangle are (6, 0), (0, 6) and (6, 6) . The distance between its circumcentre and centroid is$ (1) $1$ (2) $22$ (3) $2$ (4) $2$ 218. $The minimum area of the triangle formed by the variable line 3 cos θ \cdot x + 4 sin θ \cdot y = 12 and the co-ordinate axes is$ (1) $144$ (2) $25/2$ (3) $49/4$ (4) $12$ 219. $Find the equation of the line through the intersection of 3 x + 4 y - 7 = 0 and x = y - 2, and whose slope is 5 .$ (1) $35 x - 7 y + 18 = 0$ (2) $33 x - 7 y + 18 = 0$ (3) $35 x - 8 y + 18 = 0$ (4) $35 x - 7 y + 20 = 0$ 220. $The equation of the line parallel to the line 3 x - 4 y + 2 = 0 and passing through (- 2, 3) is$ (1) $3 x - 4 y + 18 = 0$ (2) $3 x - 4 y - 18 = 0$ (3) $3 x + 4 y + 18 = 0$ (4) $3 x + 4 y - 18 = 0$ 221. $A point on straight line, 3 x + 5 y = 15 which is equidistant from the coordinate axes will lie only in:$ (1) $4^{t h} quadrant$ (2) $1^{s t} quadrant$ (3) $1^{s t} and 2^{n d} quadrant$ (4) $1^{s t}, 2^{n d} and 4^{t h} quadrants$ 222. $The acute angle between lines 6 x^{2} + 11 xy - 10 y^{2} = 0 is$ (1) $tan^{- 1} (\frac{361}{2})$ (2) $tan^{- 1} (\frac{361}{4})$ (3) $tan^{- 1} (\frac{361}{2})$ (4) $tan^{- 1} (\frac{361}{4})$ 223. $If the lines x + 3 y - 9 = 0, 4 x + by - 2 = 0 and 2 x - y - 4 = 0 are concurrent, then the equation of the line passing through the point (b, 0) and concurrent with the given lines, is$ (1) $2 x + y + 10 = 0$ (2) $4 x - 7 y + 20 = 0$ (3) $x - y + 5 = 0$ (4) $x - 4 y + 5 = 0$ 224. $The angle between the pair of lines x^{2} + 2 xy - y^{2} = 0 is$ (1) $0$ (2) $π /3$ (3) $π /6$ (4) $π /2$ 225. $If a line L is common to the pairs of lines 6 x^{2} - xy - 12 y^{2} = 0 and 15 x^{2} + 14 xy - 8 y^{2} = 0, then the combined equation the other two lines is$ (1) $10 x^{2} - 19 xy + 6 y^{2} = 0$ (2) $5 x^{2} - 4 xy + 7 y^{2} = 0$ (3) $x^{2} - 9 xy + y^{2} = 0$ (4) $3 x^{2} + 6 xy + 11 y^{2} = 0$ 226. $If the slope of one of the lines represented by a x^{2} - 6 xy + y^{2} = 0 is the square of the other, then the value of a is$ (1) $-27 or 8$ (2) $-3 or 2$ (3) $-64 or 27$ (4) $-4 or 3$ 227. $The equation of the line through the point of intersection of the lines 3 x - 4 y + 1 = 0 and 5 x + y - 1 = 0 and making equal non-zero intercepts on the coordinate axes is$ (1) $2 x + 2 y = 3$ (2) $23 x + 23 y = 6$ (3) $23 x + 23 y = 11$ (4) $2 x + 2 y = 7$ 228. $The equation of a line, whose perpendicular distance from the origin is 5 units and the angle, which is perpendicular to the line from the origin makes, is 210^{\circ} with positive X -axis, is$ (1) $x 3 + y + 10 = 0$ (2) $x 3 + y - 10 = 0$ (3) $- x 3 + y + 10 = 0$ (4) $x 3 - y + 10 = 0$ 229. $Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x + 22 y = 4 . If the co-ordinates of the vertex A are (α, β), then the greatest integer less than or equal to \| α + 2 β \| is$ (1) $2$ (2) $5$ (3) $3$ (4) $4$ 230. $Suppose the pairs of straight lines 2 x^{2} + axy + 3 y^{2} = 0 and 2 x^{2} + bxy - 3 y^{2} = 0 are such that they have one common line with the other two remaining perpendicular. Then the values of a and b respectively are$ (1) $- 5, 1 1$ (2) $5, - 1$ (3) $5,1$ (4) $5, \frac{1}{5}$ 231. $If (α, β) is the image of the point (3, - 4) with respect to the line 4 x - y - 1 = 0, then the value of β - α is equal to$ (1) $\frac{- 31}{17}$ (2) $\frac{- 107}{17}$ (3) $\frac{31}{17}$ (4) $\frac{13}{71}$ 232. $The equation of the straight line passing through the point of intersection of 5 x - 6 y - 1, 3 x + 2 y + 5 = 0 and perpendicular to the line 3 x - 5 y + 11 = 0 is$ (1) $5 x + 3 y + 18 = 0$ (2) $- 5 x - 3 y + 18 = 0$ (3) $5 x + 3 y + 8 = 0$ (4) $5 x + 3 y - 8 = 0$ 233. $(x_{1}, y_{1}) is the point of concurrency of a family of lines. If the algebraic sum of the lengths of the perpendicular drawn to these lines from (2, 0), (0, 2) and (1, 1) is zero, then (x_{1}, y_{1}) =$ (1) $(1, 1)$ (2) $(0, 2)$ (3) $(- 1, 1)$ (4) $(1, 2)$ 234. $The combined equation of the straight lines of the form y = kx + 1 (where k is an integer) such that the point of intersection of each with the line 3 x + 4 y = 9 has an integer as its x -coordinate is$ (1) $(y + x + 1) (y + 2 x - 1) = 0$ (2) $(y + x - 1) (y + 2 x + 1) = 0$ (3) $(y + x + 1) (y + 2 x + 1) = 0$ (4) $(y + x - 1) (y + 2 x - 1) = 0$ 235. $The point on the line 4 x - y - 2 = 0 which is equidistant from the points (- 5, 6) and (3, 2) is$ (1) $(2, 6)$ (2) $(4, 14)$ (3) $(1, 2)$ (4) $(3, 10)$ 236. $The y -intercept of the line passing through A (6, 1) and perpendicular to the line x - 2 y = 4 is$ (1) $5$ (2) $13$ (3) $-2$ (4) $26$ 237. $A straight line passing through the point (1, 0) and not parallel to X -axis intersects the curve 2 x^{2} + 5 y^{2} - 7 x = 0 at two points A and B . The angle subtended by the line segment AB at the origin is$ (1) $30^{\circ}$ (2) $45^{\circ}$ (3) $60^{\circ}$ (4) $90^{\circ}$ 238. $The point (2, 3) is first reflected in the straight line y = x and then translated through a distance of 2 units along the positive direction X -axis. The coordinates of the transformed point are$ (1) $(5, 4)$ (2) $(2, 3)$ (3) $(5, 2)$ (4) $(4, 5)$ 239. $If the line 6 x - 7 y + 8 + λ (3 x - y + 5) = 0 is parallel to y -axis, then λ =$ (1) $-7$ (2) $-2$ (3) $7$ (4) $2$ 240. $If a line passing through (2, 2) is perpendicular to the line 3 x + y = 3, its x -intercept is given by$ (1) $\frac{4}{3}$ (2) $- \frac{4}{3}$ (3) $-4$ (4) $4$