Straight Lines-Quiz-15

Straight Lines Quiz-15

Dear Readers,

The unit Straight Line holds sheer significance in the JEE Advanced and other engineering exams. It has a weightage of 6% pairing with Circles. With focused practice good marks can be fetched from this section. These questions are important in achieving your success in JEE and Other Engineering Exams..

Q1. If the equation of any two diagonals of a regular pentagon belongs to family of lines (1+2λ)y-(2+λ)x+1-λ=0 and their lengths are sin⁡〖36°〗, then locus of centre of circle circumscribing the given pentagon (the triangles formed by these diagonals with slides of pentagon have no side common) is

•  x²+y²-2x-2y+1+sin²⁡〖72°〗=0
•  x²+y²-2x-2y+cos²⁡〖72°〗=0
•  x²+y²-2x-2y+1+cos²⁡〖72°〗=0
•  x²+y²-2x-2y+sin^2⁡〖72°〗=0

Solution

Q2. If the equation of the pair of straight lines passing through the point (1, 1), one making an angle θ with the positive direction of x-axis and the other making the same angle with positive direction of y-axis, is x²-(a+2)xy+y²+a(x+y-1)=0,a≠-2, then the value of sin⁡2θ is

•  a-2
•  a+2
•  2/(a+2)
•  2/a

Solution

Q3. The incentre of the triangle with vertices (1,√3),(0,0) and (2, 0) is

•  (1,√3/2)
•  (2/3,1/√3)
•  (2/3,√3/2)
•  (1,1/√3)

Solution

Q4. If a pair of perpendicular straight lines drawn through the origin forms an isosceles triangle with the line 2x+3y=6, then area of the triangle so formed is

•  36/13
•  12/17
•  13/5
•  17/13

Solution

Q5. A line 'L' is drawn from P(4,3) to meet the lines L₁ and L₂ given by 3x+4y+5=0 and 3x+4y+15=0 at points A and B, respcetively. From 'A', a line perpendicular to L is drawn meeting the line L₂ at A₁. Similarly from point 'B', a line perpendicular to L is drawn meeting the line L₁ at B₁. Thus a parallelogram AA₁ BB₁ is formed. Then the equation of 'L' so that the area of the parallelogram AA₁ BB₁ is least is

•  x-7y+17=0
•  7x+y+31=0
•  x-7y-17=0
•  x+7y-31=0

Solution

Q6. The vertices of a triangle are (pq,1/_(pq),(qr,1/_(qr)) and (rq,1/_(rp)) where p,q,r are the roots of the equationy³-3y²+6y+1=0. the coordinates of its centriod are

•  (1, 2)
•  (2,-1)
•  (1,-1)
•  (2, 3)

Solution

Q7. P,Q,R and S are the points of intersection with the coordinate axes of the lines px+qy=pq and qx+py=pq, then (P,Q>0)

•  P,Q,R,S from a parallelogram
•  P,Q,R,S from a rhombus
•  P,Q,R,S are concyclic
•  None of these

Solution

Q8. If one of the lines of my²+(1-m² )xy-m²=0 is a bisector of the angle between the lines xy=0, then m is

•  3
•  2
•  -1/2
•  -1

Solution

Q9. The equation of straight line passing through (-a,0) and making the triangle with axes of area 'T' is

•  2Tx+a² y+2aT=0
•  2Tx-a²y+2aT=0
•  2Tx-a²y-2aT=0
•  None of these

Solution

Q10. Locus of a point is equidistant from the lines x + y-2√2=0 and x+y-√2=0 is

•  x+y-5√2=0
•  x+y-3√2=0
•  2x+2y-3√2=0
•  2x+2y-5√2=0

Solution