## Straight Lines Quiz-16

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. The area of a parallelogram formed by the lines ax±bx±c=0 is
•  c2/(ab)
•  2c2/(ab)
•  c2/2ab
•  None of these
Solution
Q2. Line L ha sintercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q then,
•  a2+b2=p2+q2
•  1/a2+1/b2=1/p2+1/q2
•  a2+p2=b2+q2
•  1/a2+1/p2=1/b2+1/q2
Solution
Q3. The lines y=m1x,y=m2x and y=m3x make equal intercepts on the line x+y=1, then
•  2(1+m1 )(1+m3 )=(1+m2 )(2+m1+m3)
•  (1+m1 )(1+m3 )=(1+m2 )(1+m1+m3)
•  (1+m1 )(1+m2 )=(1+m3 )(2+m1+m3)
•  2(1+m1 )(1+m2 )=(1+m2 )(1+m1+m3)
Solution

Q4. The condition that one of the straight line given by the equation ax^2+2hxy+by^2=0 may coincide with one of those given by the equation a' x2+2h'xy+b'y2=0 is
•  (ab'-a' b)2=4(ha'-h' a)(bh'-b' h')
•  (ab'-a' b)2=(ha'-h' a)(bh'-b' h')
•  (ha'-h' a)2=4(ab'-a' b)(bh'-b' h')
•  (bh'-b' h)2=4(ab'-a' b)(ha'-h' a)
Solution
Q5. If the point (x1+t(x2-x1 ),y1+t(y2-y1 )) divides the join of (x1,y1) and (x2,y2) internally, then
•  t<0
•  0<t<1
•  t>1
•  t=1
Solution
Q6. The straight lines represented by (y-mx)2=a2 (1+m) and (y-nx)2=a2 (1+n2) form a
•  Rectangle
•  Rhombus
•  Trapezium
•  None of these
Solution

Q7. If the vertices of a triangle are (√5,0),(√3,√2) and (2, 1), then the orthocentre of the triangle is
•  (√5,0)
•  (0, 0)
•  (√5+√3+2,√2+1)
•  None of these
Solution

Q8. If A(1,p2 ),B(0,1) and C(p,0) are the coordinates of three points, then the value of p for which the area of the triangle ABC is minimum is
•  1/√3
•  -1/√3
•  1/√2
•  None of these
Solution
Q9. If the straight lines 2x+3y-1=0,x+2y-1=0 and ax+by-1=0 form a triangle with origin as orthocentre, then (a,b) is given by
•  (6, 4)
•  (-3,3)
•  (-8,8)
•  (0, 7)
Solution
Q10. A square of side a lies above the x-axis and has vertex at the origin. The side passing through the origin makes an angle Î±(0<Î±<Ï€/4) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is
•  y(cos⁡Î±+sin⁡Î± )+x(sin⁡Î±-cos⁡Î± )=a
•  y(cos⁡Î±+sin⁡Î± )+x(sin⁡Î±+cos⁡Î± )=a
•  y(cos⁡Î±+sin⁡Î± )+x(cos⁡Î±-sin⁡Î± )=a
•  y(cos⁡Î±-sin⁡Î± )-x(sin⁡Î±-cos⁡Î± )=a
Solution

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