Straight Lines-Quiz-4

Straight Lines Quiz-4

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. A beam of light is sent along the linex-y=1, which after refraction from the x-axis enters the opposite side by running through 30° towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is

•  (x-1)^2+y^2=4
•  x+y=3
•  2x-y=0
•  None of these

Solution

Q2.A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has the equation

•  x²+5y²+4xy-1=0
•  x²+5y²+4xy+1=0
•  x²+5y²-4xy-1=0
•  4x²+5y²+4xy+1=0

Solution

Q3.  The number of integral values of m, for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also n integer is

•  2
•  0
•  4
•  1

Solution

Q4. If u=a₁ x+b₁ y+c₁=0,v=a₂ x+b₂ y+c₂=0 and a₁/a₂=b₁/b₂=c₁/c₂, then the curve u+kv=0 is

•  The same straight line u
•  Different straight line
•  Not a straight line
•  None of these

Solution

Q5.If x-2y+4=0 and 2x+y-5=0 are the sides of a isosceles triangle having are 10 sq. units the equation of third side is

•  3x-y=-9
•   3x-y+11=0
•  x-3y=19
•   3x-y+15=0

Solution

Q6. The locus of the point which moves such that its distance from the point (4, 5) is equal to its distance from the line 7x-3y-13=0 is

•  A straight line
•  A circle
• A parabola
•  An ellipse

Solution

Q7.If the vertices P and Q of a triangle PQR are given by (2, 5) and (4,-11), respectively, and the point R moves along the line N given by 9x+7y+4=0, then the locus of the centriod of the triangle PQR is a straight line parallel to

•  PQ
•  QR
•  RP
•  N

Solution

Q8.If x₁,x₂,x₃ as well as y₁,y₂,y₃ are in G.P. with same common ratio, then the points P(x₁,y₁ ),Q(x₂,y₂) and R(x₃,y₃)

•  Lie on a straight line
•  Lie on an ellipse
•  Lie on a circle
•  Are vertices of a triangle

Solution

Q9.The coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1, 0) and (2, 0), respectively. The equation of the diagonal CE is

•  √3 x+y=4
•  x+√3 y+4=0
•  x+√3 y=4
•  None of these

Solution

Q10. If sum of the distance of a point from two perpendicular lines in a plane is 1, then its locus is

•  A square
•  A circle
•  A straight line
• Two intersecting lines

Solution