Straight Lines-Quiz-7

Straight Lines Quiz-7

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 number of straight lines equidistant from three non-collinear points in the plane of the points is equal to

•  0
•  1
•  2
•  3

Solution

Q2. The point A(2,1) is translated parallel to the line x-y=3 by a distance 4 units. if the new position A^' is in third quadrant, then the coordinates of A^' are

•  (2+2√2,1+2√2)
•  (-2+√2,-1-2√2)
•  (2-2√2,1-2√2)
•  None of these

Solution

Q3. The number of possible straight lines, passing through (2, 3) and forming a triangle with coordinate axes, whose area is 12 sq. units, is

•  One
•  Two
•  Three
•  Four

Solution

Q4. If the straight lines x+y-2=0,2x-y+1=0 and ax+by-c=0 are concurrent, then the family of lines 2ax+3by+c=0 (a,b,c are nonzero) is concurrent at

•  (2, 3)
•  (1/2,1/3)
•  (-1/6,-5/9)
•  (2/3,-7/5)

Solution

Q5. The straight lines x+2y-9=0,3x+5y-5=0 and ax+by-1=0 are concurrent, if the straight line 35x-22y+1=0 passes through the point

•  (a,b)
•  (b,a)
•  (-a,-b)
•  None of these

Solution

Q6. Given A(0,0) and B(x,y) with x∈(0,1) and y>0. Let the slope of the line AB equal to m₁. Point C lies on the line x=1 such that the slope of BC equal to m₂ where 0 <m₂ <m₁. If the area of the triangle ABC can be expressed as (m₁-m₂ )f(x), then the largest possible value of x is

•  1
•  1/2
•  1/4
•  1/8

Solution

Q7. If the pairs of lines x²+2xy+ay²=0 and ax²+2xy+y²=0 have exactly one line in common, then the joint equation of the other two lines is given by

•  3x²+8xy-3y²=0
•  3x²+10xy+3y²=0
•  y²+2xy-3x²=0
•  x²+2xy-3y²=0

Solution

Q8. If two vertices of a triangle are (-2,3) and (5,-1), orthocentre lies at the origin and centroid on the line x+y=7, then the third vertex lies at

•  (7, 4)
•  (8, 14)
•  (12, 21)
•  None of these

Solution

Q9. Points A and B are in the first quadrant; point 'O' is the origin. If the slope of OA is 1, slope of OB is 7 and OA=OB, then the slope of AB is

•  -1/5
•  -1/4
•  -1/3
•  -1/2

Solution

Q10. The image of P(a,b) in the line y=-x is Q and the image of Q in the y=x is R. Then the midpoint of PR is

•  (a+b,b+a)
•  ((a+b)/2,(b+2)/2)
•  (a-b,b-a)
•  (0, 0)

Solution