Straight Lines-Quiz-10

Straight Lines Quiz-10

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. Equation of a line which is parallel to the line common to the pair of lines given by 6x²-xy-12y²=0 and 15x²+14xy-8y²=0 and at a distnace 7 from it is

•  3x-4y=-35
•  5x-2y=7
•  3x+4y=35
•  2x-3y=7

Solution

Q2. The equation of the line segment AB is y=x. If A and B lie on the same side of te line mirror 2x-y=1, the the image of AB has the equation

•  x+y=2
•  8x+y=9
•  7x-y=6
•  None of these

Solution

Q3. A light ray emerging from the point source placed at P(2,3) is reflected at a point 'Q' on the y-axis and then passes through the point R(5,10). Coordinates of 'Q' are

•  (0, 3)
•  (0, 2)
•  (0, 5)
•  None of these

Solution

Q4. If the origin is shifted to be point (ab/(a-b,0) without rotation, then the equation (a-b)(x²+y² )-2abx=0 becomes

•  (a-b)(x²+y² )-(a+b)xy+abx=a²
•  (a+b)(x²+y² )=2ab
•  (x²+y² )=(a²+b²)
•  (a-b)² (x²+y² )=a² b²

Solution

Q5. The number of triangles that the four lines y=x+3,y=2x+3,y=3x+2 and y+x=3 form is

•  4
•  2
•  3
•  1

Solution

Q6. The point (4, 1) undergoes the following three transformation successively
i. Reflection about the line y=x
ii. Translation through a distance 2 units along the positive direction of x-axis
iii. Rotation through an angle π/4 about the origin in the counterclockwise direction
Then the final position of the point is given by the coordinates

•  (1/√2,7/√2)
•  (-√2,7√2)
•  (-1/√2,7/√2)
•  (√2,7√2)

Solution

Q7. Line L has intercepts a and b on the coordinates axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q. Then,

•  
•  
•  
•  

Solution

Q8. In the ABC, the coordinates of B are (0, 0), AB=2,∠ABC=π/3 and the middle point of BC has the coordinates (2, 0. The centriod of the triangle is

•  (1/2,√3/2)
•  (5/3,1/√3)
•  (4+√3/3,1/3)
•  None of these

Solution

Q9. A triangle ABC with vertices A(-1,0),B(-2,3/4) and C(-3,-7/6) has its orthocentre H. Then the orthocentre of triangle BCH will be

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

Solution

Q10. If the ends of the base of an isosceles triangle are at (2, 0) and (0, 1) and the equation of one side is x=2, then the orthocentre of the triangle is

•  (3/2, 3/2)
•  (5/4, 1)
•  (3/4, 1)
•  (4/3, 7/12)

Solution