Straight Lines-Quiz-12

Straight Lines Quiz-12

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. 

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Solution

Q2. A is a point on either of two y+√3 |x|=2 at a distance of 4√3 units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are

•  (2/√3,2)
•  (0, 0)
•  (2√3,2)
•  (0, 4)

Solution

Q3. The condition on a and b, such that the portion of the line ax+by-1=0, intercepted between the lines ax+y=0 and x+by=0, subtends a right angle at the origin is

•  a=b
•  a+b=0
•  a=2b
•  2a=b

Solution

Q4. m,n are integers with 0<n<m. A is the point (m ,n) on the Cartesian plane. B is the reflection of A in the line y=x. C is the reflection of B in the y-axis, D is the reflection of C in the x-axis and E is the reflection of D in the y-axis. The area of the pentagon ABCDE is

•  2m(m+n)
•  m(m+3n)
•  m(2m+3n)
•  2m(m+3n)

Solution

Q5. The equation a^2 x^2+2h(a+b)xy+b^2 y^2=0 and ax^2+2hxy+by^2=0 reprsent

•  Two pairs of perpendicular straight lines
•  Two pairs of parallel straight lines
•  Two pairs of straight lines which are equally inclined to each other
•  None of these

Solution

Q6. The combined equation of the lines l_1,l_2 is 2x^2+6xy+y^2=0 and that of the lines m_1 ,m_2is 4x^2+18xy+y^2=0. If the angle between l_1 and m_2 be α, then the angle between l_2 and m_1 will be

•  π/2-α
•  2α
•  π/4+α
•  α

Solution

Q7. Let O be the origin. If A(1,0) and B(0,1) and P(x,y) are points such that xy>0 and x+y<1, then

•  P lies either inside the triangle OAB or in the mid quadrant
•  P cannot lie inside the triangle OAB
•  P lies inside the triangle OAB
•  P lies in the first quadrant only

Solution

Q8. The line x+3y-2=0 bisects the angle between a pair of straight line s of which one has equation x-7y+5=0. the equation of the other line is

•  3x+3y-1=0
•  x-3y+2=0
•  5x+5y-3=0
•  None of these

Solution

Q9. Let ABC be a triangle. Let A be the point (1, 2), y=x be the perpendicular bisector of AB and x-2y+1=0 be the angle bisector of ∠C. If equation of BC is given by ax+by-5=0, then the value of a+b is

•  1
•  2
•  3
•  4

Solution

Q10. The equation x-y=4 and x^2+4xy+y^2=0 represent the sides of

•  An equilateral triangle
•  A right angled triangle
•  An isosceles triangle
•  None of these

Solution