Straight Lines PYQs Set 5 (PDF)

Set 5 of 15 · Questions 121-150 of 442

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Straight Lines · Set 5 (Q121-150)
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121. $A rectangle is formed by the lines x = 0, y = 0, x = 3 and y = 4 . Let the line L be perpendicular to 3 x + y + 6 = 0 and divide the area of the rectangle into two equal parts. Then the distance of the point (\frac{1}{2}, - 5) from the line L is equal to:$ (1) $10$ (2) $25$ (3) $210$ (4) $310$ 122. $If A (2, 3) and B (3, - 2) are two fixed points and P (x, y) is a variable point satisfying the condition \| PA - PB \| = 2, then the locus of P is$ (1) $(x + y + 1)^{2} = 4 [(x - 3)^{2} + (y + 2)^{2}]$ (2) $(x - 5 y - 2)^{2} = 4 [(x - 2)^{2} + (y - 3)^{2}]$ (3) $(x - 5 y - 2)^{2} = 4 [(x - 3)^{2} + (y + 2)^{2}]$ (4) $(x + y + 1)^{2} = 4 [(x - 2)^{2} + (y - 3)^{2}]$ 123. $If the slope of one of the lines represented by a x^{2} + 2 hxy + b y^{2} = 0 is the square of the other then, (\frac{a + b}{h} + \frac{8 h ^{2}}{ab}) is equal to$ (1) $3$ (2) $2$ (3) $6$ (4) $4$ 124. $The equation of the pair of straight lines through the point (1, 1) and perpendicular to the pair of straight lines 3 x^{2} - 8 xy + 5 y^{2} = 0 is$ (1) $5 x^{2} + 8 xy + 3 y^{2} - 14 x - 18 y + 16 = 0$ (2) $5 x^{2} + 8 xy + 3 y^{2} - 18 x - 14 y + 16 = 0$ (3) $5 x^{2} - 8 xy + 3 y^{2} - 18 x - 14 y + 32 = 0$ (4) $5 x^{2} - 8 xy + 3 y^{2} - 14 x - 18 y + 32 = 0$ 125. $The image of the point (3, 5) in the line x - y + 1 = 0, lies on:$ (1) $(x - 2)^{2} + (y - 4)^{2} = 4$ (2) $(x - 4)^{2} + (y + 2)^{2} = 16$ (3) $(x - 4)^{2} + (y - 4)^{2} = 8$ (4) $(x - 2)^{2} + (y - 2)^{2} = 12$ 126. $The equation of the pair of straight lines perpendicular to the pair 2 x^{2} + 3 xy + 2 y^{2} + 10 x + 5 y = 0 and passing though the origin is$ (1) $2 x^{2} + 5 xy + 2 y^{2} = 0$ (2) $2 x^{2} - 3 xy + 2 y^{2} = 0$ (3) $2 x^{2} + 3 xy + y^{2} = 0$ (4) $2 x^{2} - 5 xy + 2 y^{2} = 0$ 127. $A (3, - 1), B (1, 3), C (2, 4) are vertices of ∆ ABC if D is centroid of ∆ ABC and P is point of intersection of lines x + 3 y - 1 = 0 and 3 x - y + 1 = 0 then which of the following points lies on line joining D and P$ (1) $(- 9, - 7)$ (2) $(- 9, - 6)$ (3) $(9, 6)$ (4) $(9, - 6)$ 128. $p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b respectively, then \frac{1}{a ^{2}} + \frac{1}{b ^{2}} equals$ (1) $p^{2}$ (2) $2 p^{2}$ (3) $\frac{1}{p ^{2}}$ (4) $\frac{1}{2 p ^{2}}$ 129. $The length of the segment of the straight line passing through (3, 3) and (7, 6) cut off by the coordinate axes is$ (1) $\frac{4}{5}$ (2) $\frac{5}{4}$ (3) $\frac{7}{4}$ (4) $\frac{4}{7}$ 130. $If A = (5, 3), B = (3, - 2) and a point P is such that the area of the traingle PAB is 9 , then the locus of P represents$ (1) $a circle$ (2) $a pair of coincident lines$ (3) $a pair of parallel lines$ (4) $a pair of perpendicular lines$ 131. $If p_{1} and p_{2} denote the lengths of perpendiculars from (2, 3) onto the lines given by 15 x^{2} + 31 xy + 14 y^{2} = 0, and if p_{1} > p_{2}, then p_{1}^{2} + \frac{1}{74} - p_{2}^{2} + \frac{1}{13} is equal to$ (1) $-2$ (2) $0$ (3) $2$ (4) $1$ 132. $The point of concurrence of all the chords of the curve 3 x^{2} - y^{2} - 2 x + 4 y = 0 which subtend a right angle at the origin is$ (1) $(1, 2)$ (2) $(1, - 2)$ (3) $(- 1, 2)$ (4) $(- 1, - 2)$ 133. $The absolute value of the tangent of the difference of the angles made by the lines 4 x^{2} - 24 xy + 11 y^{2} = 0 with the X -axis is$ (1) $\frac{4}{11}$ (2) $\frac{24}{11}$ (3) $\frac{4}{3}$ (4) $\frac{11}{24}$ 134. $If 2 x + 3 y + 4 = 0 is the perpendicular bisector of the line segment joining the points A (1, 2) and B (α, β), then the value of 13 α + 13 β equals$ (1) $- 81$ (2) $-99$ (3) $99$ (4) $81$ 135. $Which of the following equation does not represent a pair of lines?$ (1) $x^{2} - x = 0$ (2) $xy - x = 0$ (3) $y^{2} - x + 1 = 0$ (4) $xy + x + y + 1 = 0$ 136. $Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B . Then the distance of the point P (m, n) from the point Q (- 2, - 3) is$ (1) $10$ (2) $6$ (3) $4$ (4) $8$ 137. $If the line 3 x + 4 y + λ = 0 divides the distance between the lines 3 x + 4 y + 5 = 0 and 3 x + 4 y - 5 = 0 in the ratio of 3 : 7, then a value of λ is$ (1) $-2$ (2) $2$ (3) $0$ (4) $5$ 138. $The straight lines x + 3 y - 9 = 0, 4 x + 5 y - 1 = 0, px + qy + 10 = 0 are concurrent, if the line 5 x + 6 y + 10 = 0 passes through the point$ (1) $(q, - p)$ (2) $(q, p)$ (3) $(p, - q)$ (4) $(p, q)$ 139. $A line passing through P (2, 3) and making an angle of 30^{\circ} with the positive direction of x -axis meets x^{2} - 2 xy - y^{2} = 0 at A and B. Then the value of PA.PB is$ (1) $173 + 1$ (2) $17 (3 + 1)$ (3) $17 (3 - 1)$ (4) $173 - 1$ 140. $If a x^{2} + 6 xy - 2 y^{2} = 0 represents a pair of perpendicular lines and 9 x^{2} + 2 hxy + 4 y^{2} = 0 (h > 0) represents a pair of coincident lines then h =$ (1) $3 a$ (2) $2 a$ (3) $a$ (4) $4 a$ 141. $By rotating the axes through an angle of 30^{\circ} in the anti-clockwise direction about the origin, the equation 4 x^{2} + 12 xy + 9 y^{2} + 6 x + 9 y + 2 = 0 becomes a x^{2} + 2 hxy + b y^{2} + 2 gx + 2 fy + c = 0 then$ (1) $a = 21 - 63$ (2) $g / f = \frac{3 + 2 3}{3 3 - 2}$ (3) $b = 31 + 63$ (4) $c = 6$ 142. $If m is the slope of one of the lines represented by a x^{2} + 2 hxy + b y^{2} = 0, then (h + bm)^{2} =$ (1) $(a - b)^{2}$ (2) $(a + b)^{2}$ (3) $h^{2} - ab$ (4) $h^{2} + ab$ 143. $The joint equation of pair of straight lines passing through origin and having slopes (1 + 2) and (\frac{1}{1 + 2}) is$ (1) $x^{2} - 22 xy + y^{2} = 0$ (2) $x^{2} - 22 xy - y^{2} = 0$ (3) $x^{2} + 2 xy - y^{2} = 0$ (4) $x^{2} + 2 xy + y^{2} = 0$ 144. $If the line x - y + 1 = 0 cuts the lines 2 x + 2 y + 3 = 0 and 3 x + 3 y + 2 = 0 at the points A and B respectively, then AB =$ (1) $\frac{5}{6 2}$ (2) $\frac{1}{6 2}$ (3) $\frac{5}{3}$ (4) $\frac{5}{6 3}$ 145. $Equation of line passing through the point (1, 2) and perpendicular to the line y = 3 x - 1 is$ (1) $x - 3 y = 0$ (2) $x + 3 y = 0$ (3) $x + 3 y - 7 = 0$ (4) $x + 3 y + 7 = 0$ 146. $The distance between the points of concurrency of the two families of straight lines given by x + (5 λ + 1) y + 1 - 3 λ = 0 and (5 μ + 2) x - 3 y + 3 + 6 μ = 0 is$ (1) $4$ (2) $\frac{2 2}{5}$ (3) $\frac{2}{5}$ (4) $6$ 147. $The equation of the pair of lines through the point (2, 1) and perpendicular to the pair of lines 4 xy + 2 x + 6 y + 3 = 0 is$ (1) $xy - x - 2 y + 2 = 0$ (2) $xy + x - 2 y - 2 = 0$ (3) $xy + x + 2 y - 6 = 0$ (4) $xy - x + 2 y - 2 = 0$ 148. $If the slopes of the lines K x^{2} - 4 xy + y^{2} = 0 differ by 2 , then K =$ (1) $3$ (2) $4$ (3) $21/5$ (4) $4/5$ 149. $If the lines 3 x + y - 2 = 0, px + 2 y - 3 = 0 and 2 x - y - 3 = 0 are concurrent, then p =$ (1) $-5$ (2) $5$ (3) $3$ (4) $-3$ 150. $Suppose the pairs of straight lines x^{2} - 2 axy - y^{2} = 0 and x^{2} - 2 bxy - y^{2} = 0 are such that each pair bisects the angles between the other two. Then ab =$ (1) $1$ (2) $-1$ (3) $2$ (4) $\frac{1}{2}$