Straight Lines PYQs Set 7 (PDF)

Set 7 of 15 · Questions 181-210 of 442

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Straight Lines · Set 7 (Q181-210)
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181. $Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:$ (1) $9$ (2) $18$ (3) $36$ (4) $32$ 182. $\frac{x ^{2}}{a} + \frac{xy}{h} + \frac{y ^{2}}{b} = 0 (a \neq = 0, h \neq = 0, b \neq = 0) represents two coincident if$ (1) $h^{2} = ab$ (2) $4 h^{2} = ab$ (3) $h^{2} = 4 ab$ (4) $h^{2} = 2 ab$ 183. $Given two points Q (3, 4) and R (1, 2) . What is the point P (x, y) on the line 2 x - y - 1 = 0 for which PQ + PR = QR holds$ (1) $(- 3, - 7)$ (2) $(- 2, - 5)$ (3) $(2, 3)$ (4) $(4, 7)$ 184. $If the line 2 x - y - 4 = 0 divides the line segment joining the points (2, - 1) and (1, - 4) at the point (a, b) in the ratio m : n then 4 (a - b (\frac{m}{n})^{2}) =$ (1) $-5$ (2) $14$ (3) $11$ (4) $10$ 185. $If pairs of straight lines x^{2} - 2 pxy - y^{2} = 0 and x^{2} - 2 qxy - y^{2} = 0 be such that each pair bisects the angle between the other pair, then$ (1) $pq = 1$ (2) $pq = 2$ (3) $pq = - 2$ (4) $pq = - 1$ 186. $If the slope of one of the lines represented by 5 x^{2} + \frac{40}{3} xy + k y^{2} = 0 is 3 , then the angle between the pair of lines is$ (1) $0$ (2) $\frac{π}{4}$ (3) $\frac{π}{3}$ (4) $\frac{π}{2}$ 187. $If a point (α, β) of 3 x + y = 0 and (3, 4) lie on the opposite sides of 3 x - 4 y - 8 = 0 then which of the following is correct?$ (1) $15 α - 8 > 0$ (2) $α \in (- \infty, \infty)$ (3) $15 α - 8 = 0$ (4) $α = 0$ 188. $Let P be the point of intersection of the lines L_{1} = x - y - 7 = 0 and L_{2} \equiv x + y - 5 = 0. A (x_{1}, y_{1}) and B (x_{2}, y_{2}) are points on the lines L_{1} = 0 and L_{2} = 0 respectively such that PA = 32; PB = 2, x_{1}, y_{1} \geq 0, x_{2}, y_{2} \geq 0, then the angle made by the line segment AB at the origin is$ (1) $\frac{π}{4}$ (2) $\frac{π}{2}$ (3) $cos^{- 1} (\frac{3}{4})$ (4) $cos^{- 1} (\frac{9}{85})$ 189. $If P (2, 2), Q (- 2, 4) and R (3, 4) are the vertices of △ PQR then the equation of the median through vertex R is$ (1) $x + 3 y + 9 = 0$ (2) $x - 3 y + 9 = 0$ (3) $x - 3 y - 9 = 0$ (4) $x + 3 y - 9 = 0$ 190. $The equation of bisector of the angle between the lines represented by 3 x^{2} - 5 xy + 4 y^{2} = 0 is$ (1) $9 x^{2} + 6 y^{2} - 2 x = 0$ (2) $5 (x^{2} - y^{2}) = 2 xy$ (3) $3 x^{2} + 2 xy - y^{2} = 0$ (4) $5 x^{2} + xy + 4 y^{2} = 0$ 191. $Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant ?$ (1) $third$ (2) $second$ (3) $first$ (4) $fourth$ 192. $If lines represented by (1 + sin^{2} θ) x^{2} + 2 hxy + 2 sin θ y^{2} = 0, θ \in [0, 2 π] are perpendicular to each other then θ =$ (1) $\frac{π}{2}$ (2) $π$ (3) $\frac{3 π}{2}$ (4) $\frac{π}{6}$ 193. $If the coordinates of a point P changes to (2, - 6) when the coordinate axes are rotatẹd through an angle of 135^{\circ}, then the coordinates of P in the original system are$ (1) $(- 2, 6)$ (2) $(- 6, 2)$ (3) $(22, 42)$ (4) $(2, - 2)$ 194. $Let M be the foot of the perpendicular drawn from the point (5, - 7) to the line 3 x - 5 y + 1 = 0 . Then the perpendicular distance from M to the line 2 x + 5 y - 3 = 0 is$ (1) $\frac{1}{2 29}$ (2) $\frac{9}{2 29}$ (3) $\frac{13}{2 29}$ (4) $\frac{3}{2 29}$ 195. $If one of the lines of my2 + (1 - m2) xy - mx2 = 0 is a bisector of the angle between the lines xy = 0, then m is$ (1) $- \frac{1}{2}$ (2) $- 2$ (3) $\pm 1$ (4) $2$ 196. $Suppose a point P moves so that BP^{2} - AP^{2} = 121, where A and B are (2, 5) and (5, 11) respectively. Then the locus of P is a straight line, whose slope is$ (1) $½$ (2) $-2$ (3) $- 1/2$ (4) $2$ 197. $A straight line passes through the points (5, 0) and (0, 3) . The length of perpendicular from the point (4, 4) on the line is$ (1) $\frac{15}{34}$ (2) $\frac{17}{2}$ (3) $\frac{17}{2}$ (4) $\frac{17}{2}$ 198. $If P_{1}, P_{2}, P_{3}, \dots, P_{n} are n points on the line y = x all lying in the first quadrant, such that (O P_{n}) = n (O P_{n - 1}) (O is origin), O P_{1} = 1 and P_{n} = (25202, 25202), then n =$ (1) $5$ (2) $6$ (3) $7$ (4) $8$ 199. $If each line of a pair of lines passing through origin is at a perpendicular distance of 4 units from the point (3, 4), then the equation of the pair of lines is$ (1) $7 x^{2} + 24 xy = 0$ (2) $7 y^{2} + 24 xy = 0$ (3) $7 y^{2} - 24 xy = 0$ (4) $7 x^{2} - 24 xy = 0$ 200. $A point P (x, y) is such that its distance from (- 1, 0) and (0, 2) are in a ratio of 2 : 1 . Then the locus of P is$ (1) $(x - 1)^{2} + (y - 4)^{2} = 10$ (2) $(x + 2)^{2} + (y + 2)^{2} = 10$ (3) $(x - 1)^{2} + (y - 4)^{2} = 100$ (4) $(x + 2)^{2} + (y + 2)^{2} = 100$ 201. $The equation x^{2} - y^{2} + ax + b = 0 represents a pair of lines for the ordered pair (a, b) =$ (1) $(2, 6)$ (2) $(3, 4)$ (3) $(4, 8)$ (4) $(6, 9)$ 202. $If the perpendicular distance between the point (1, 1) to the line 3 x + 4 y + c = 0 is 7 , then the possible values of c are$ (1) $- 35, 42$ (2) $35,28$ (3) $42, - 28$ (4) $28, - 42$ 203. $If the pair of straight lines 6 x^{2} - 5 xy + y^{2} = 0 makes angles α and β with the X -axis, then tan (α - β) =$ (1) $2$ (2) $\frac{1}{7}$ (3) $3$ (4) $7$ 204. $If the angle between the pair of lines x^{2} + 22 xy + k y^{2} = 0, k > 0 is 45^{\circ}, then the area (in square units) of the triangle formed by the pair of bisectors of angles between the given lines and the line x + 2 y + 1 = 0 is$ (1) $\frac{1}{3}$ (2) $1$ (3) $\frac{2}{3}$ (4) $2$ 205. $If 2 x^{2} - 10 xy + 2 λ y^{2} + 5 x - 16 y - 3 = 0 represents a pair of straight lines, then point of intersection of those lines is$ (1) $(2, - 3)$ (2) $(5, - 16)$ (3) $(- 10, \frac{- 7}{2})$ (4) $(- 10, \frac{- 3}{2})$ 206. $If f (x, y) = 0 is the combined equation of the lines joining the origin to the points where the line 4 x - 6 y - 2 = 0 meets the curve 3 x^{2} - 4 xy + 5 y^{2} - 2 x + y - 6 = 0, then \frac{f ( 1 , - 1 )}{f ( - 1 , - 1 )} =$ (1) $153$ (2) $-153$ (3) $1$ (4) $-1$ 207. $Let a point A lie between the parallel lines L_{1} and L_{2} such that its distances from L_{1} and L_{2} are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines L_{1} and L_{2}, respectively, is :$ (1) $156$ (2) $213$ (3) $122$ (4) $27$ 208. $If A (1, - 1, 2), B (5, 7, - 6), C (3, 4, - 10) and D (- 1, - 4, - 2) are the vertices of a quadrilateral ABCD, then its area is :$ (1) $487$ (2) $1229$ (3) $247$ (4) $2429$ 209. $If the distance from a variable point P to a fixed-point A (a, 0) is equal to the perpendicular distance from P to the line x + y = 0 then the equation of the locus of P is$ (1) $x^{2} + y^{2} - 2 xy - 4 ax = 0$ (2) $x^{2} + y^{2} - 2 xy - 4 ax + 2 a^{2} = 0$ (3) $x^{2} - 4 ay + y^{2} = 0$ (4) $(x - a)^{2} + y^{2} = 4 axy$ 210. $The equation of one of the straight lines which passes through the point (1, 3) and makes an angles tan^{- 1} (2) with the straight line, y + 1 = 32 x is$ (1) $42 x + 5 y - (15 + 42) = 0$ (2) $52 x + 4 y - (15 + 42) = 0$ (3) $42 x + 5 y - 42 = 0$ (4) $42 x - 5 y - (5 + 42) = 0$