Straight Lines-Quiz-14

Straight Lines Quiz-14

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 foot of the perpendicular on the line 3x+y=λ drawn from the origin is C. If the line cuts the x-axis and y-axis at A and B, respectively, then BC:CA is

•  1:3
•  3:1
•  1:9
•  9:1

Solution

Q2. If it is possible to drawn a line which belongs to all the given family of lines y-2x+1+λ₁ (2y-x-1)=0,3y-x-6λ₂ (y-3x+6)=0,ax+y-2+λ₃ (6x+xy-a)=0, then

•  a=4
•  a=3
•  a=-2
•  a=2

Solution

Q3. The line x+y=p meets the x-and y-axes at A and B, respectively. A triangle APQ is inscribed in the triangle OAB,O being the origin, with right angle at Q.P and Q lie, respectively, on OB and AB. If the area of the area of the triangle APQ is 3/8th of the area of the triangle OAB, then AQ/BQ is equal to

•  2
•  2/3
•  1/3
•  3

Solution

Q4. In a triangle ABC, the bisectors of angles B and C lie along the lines x=y and y=0. if A is (1, 2), then the equation of line BC is

•  2x+y=1
•  3x-y=5
•  x-2y=3
•  x+3y=1

Solution

Q5. 

•  The vertices of a rectangle
•  Collinear
•  Trapezium
•  None of these

Solution

Q6. 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 integer is

•  2
•  0
•  4
•  1

Solution

Q7. The straight lines 4ax+3by+c=0, where a+b+c=0, are concurrent at the point

•  (4, 3)
•  (1/4, 1/3)
•  (1/2, 1/3)
•  None of these

Solution

Q8. A straight line passing through P(3,1) meets the coordinate axes at A and B. It is given that distance of this straight line from the origin 'O' is maximum. Area of triangle OAB is equal to

•  50/3 sq. units
•  25/3 sq. units
•  20/3 sq. units
•  100/3 sq. units

Solution

Q9. A rectangle ABCD has its side AB parallel to line y=x and vertices A,B and D lie on y=1,x=2 and x=-2, respectively. locus of vertex 'C' is

•  x=5
•  x-y=5
•  y=5
•  x+y=5

Solution

Q10. Line ax+by+p=0 makes angle π/4 with x cos⁡α+y sin⁡α=p,p∈R⁺. If these lines and the line x sin⁡α-y cos⁡α=0 are concurrent, then

•  a²+b²=1
•  a²+b²=2
•  2(a²+b² )=1
•  None of these

Solution