Straight Lines-Quiz-1

Straight Lines Quiz-1

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. OPQR is a square and M,N are the middle points of the sides PQ and QR, respectively, then the ratio of the areas of the square and the triangle OMN is

•  4:1
•  2:1
•  8:3
•  7:3

Solution

Q2.Vertices of a parallelogram ABCD are A(3,1),B(13,6),C(13,21) and D(3,16). If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is

•  11/12
•  11/8
•  25/8
•  13/8

Solution

Q3.  One diagonal of a square is along the line 8x-15y=0 and one of its vertex is (1, 2). Then the equations of the sides of the square passing through this vertex are

•  23x+7y=9,7x+23y=53
•  23x-7y+9=0,7x+23y+53=0
•  23x-7y-9=0,7x+23y-53=0
•  None of these

Solution

Q4. If a straight line through origin bisects the line passing through the given points(a cos⁡α,a sin⁡α) and (a cos⁡β,a sin⁡β), then the lines

•  Are perpendicular
•  Are parallel
•  Have an angle between them of π/4
•  None of these

Solution

Q5.If the lines represented by the equation 3y²-x²+2√3 x-3=0 are rotated about the point (√3,0) through an angle 15°, one clockwise direction and other in anti clockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

•  
•  
•  
•  

Solution

Q6. If the sum of the distances of a point from two perpendicular lines a plane is 1, then its locus is

•  Square
•  Circle
• Straight line
•  Two intersecting lines

Solution

Q7.The distance between the two lines represented by the equation 9x²-24xy+16y²-12x+16y-12=0 is

•  8/5
•  6/5
•  11/5
•  None of these

Solution

Q8.In ∆ ABC if orthocentre be (1, 2) and circumcentre be (0, 0) centroid of ∆ABC is

•  (1/2, 2/3)
•  (1/3, 2/3)
•  (2/3, 1)
•  None of these

Solution

Q9.Vertices of a triangle are (3, 4), (5 cos⁡θ,5 sin⁡θ) and (5 sin⁡θ,-5 cos⁡θ), where θ∈R. Locus of its orthocentre is

•  (x+y-1)²+(x-y-7)²=100
•  (x+y-7)²+(x-y-1)²=100
•  (x+y-7)²+(x+y-1)²=100
•  (x+y-7)²+(x-y+1)²=100

Solution

Q10. If the area of the rhombus enclosed by the lines lx±my±n=0 be 2 sq. units, then

•  l,m,n are in G.P.
•  l,n,m are in G.P.
•  im=n
• in=m

Solution