## Straight Lines Quiz-6

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 intercept made on the line y=mx by lines y=2 and y=6 is less than 5, then the range of values of m is
•  (-∞,-4/3)∪(4/3,+∞)
•  (-4/3,4/3)
•  (-3/4,4/3)
•  None of these
Solution
Q2. If each of the points (x1,4),(-2,y1 ) lies on the line joining the points (2,-1),(5,-3) then the point P(x1,y1 ) lies on the line
•  6(x+y)-25=0
•  2x+6y+1=0
•  2x+3y-6=0
•  6(x+y)+25=0
Solution
Q3. P is a point on the line y+2x=1 and, Q and R are two points on the line 3y+6x=6 such that triangle PQR is an equilateral triangle. The length of the side of the triangle is
•  2/√5
•  3/√5
•  4/√5
•  None of these
Solution

Q4. The equation to the straight line passing through the point (a cos3⁡Î¸, a sin3⁡Î¸) and perpendicular to the line x sec⁡Î¸+y cosec Î¸=a is
•  x cos⁡Î¸- y sin⁡Î¸=a cos⁡2Î¸
•  x cos⁡Î¸+ y sin⁡Î¸=a cos⁡2Î¸
•  x sin⁡Î¸+ y cos⁡Î¸=a cos⁡2Î¸
•  None of these
Solution
Q5. A rectangular billiard table has vertices at P(0,0),Q(0,7),R(10,7) and S(10,0). a small billiard ball starts at M(3,4) and moves in a straight line to the top of the table, bounces to the right side of the table, then comes to rest at N(7,1). The y-coordinate of the point where it hits the right side, is
•  3.7
•  3.8
•  3.9
•  4
Solution
Q6. The equation of the straight line which passes through the point (-4,3) such that the portion of the line between the axes is divided internally by the point in the ratio 5:3 is
•  9x-20y+96=0
•  9x+20y=24
•  20x+9y+53=0
•  None of these
Solution

Q7.
•  Equal in area
•  Similar
•  Congruent
•  None of these
Solution

Q8. The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is
•  x+y+5=0
•  x-y+1=0
•  x-y=5
•  None of these
Solution
Q9. If one side of rhombus has end points (4, 5) and (1, 1) then the maximum area of the rhombus is
•  50 sq. units
•  25 sq. units
•  30 sq. units
•  20 sq. units
Solution
Q10. Consider points A(3,4) and B(7,13). If P be a point on the line y=x such that PA+PB is minimum, then coordinates of P are
•  (12/7, 12/7)
•  (13/7, 13/7)
•  (31/7, 31/7)
•  (0, 0)
Solution

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