Straight Line and Pair of Straight Lines Test

Result

Straight Line and Pair of Straight Lines Test - 52

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Weekly Quiz Competition

Question 1
4 / -1

The equation 2x² + 4xy – py² + 4x + qy + 1 = 0 will represent two mutually perpendicular straight lines, if

A
p = 1 and q = 2 or 6

B
p = 2 and q = 0 or 6

C
p = 2 and q = 0 or 8

D
p = –2 and q = – 2 or 8

Solution
Question 2
4 / -1

If the equation Ax² + 2Bxy + Cy² + Dx + Ey + F = 0 represents a pair of straight lines, then B² – AC

A
< 0

B
= 0

C
> 0

D
None of these

Solution
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

If the slope of one of the lines represented by the equation ax² + 2hxy + by² = 0 be λ times that of the other, then

A
4λh = ab(1 + λ)

B
λh = ab(1 + λ)²

C
4λh² = ab(1 + λ)²

D
None of these

Solution
Question 5
4 / -1

A

B

C

D
None of these

Solution
Question 6
4 / -1

A

B

C

D

Solution
Question 7
4 / -1

The equations of the lines represented by the equation ax² + (a + b)xy + by² + x + y = 0 are

A
ax + by + 1 = 0, x + y = 0

B
ax + by – 1 = 0, x + y = 0

C
ax + by + 1 = 0, x – y = 0

D
None of these

Solution
Question 8
4 / -1

If two sides of a triangle are represented by x² – 7xy + 6y² = 0 and the centroid is (1,0), then the equation of third side is

A
2x + 7y + 3 = 0

B
2x – 7y + 3 = 0

C
2x + 7y – 3 = 0

D
2x – 7y – 3 = 0

Solution
Question 9
4 / -1

The equation of one of the lines represented by the equation x² + 2xy cot θ – y² = 0, is

A
x – y cot θ = 0

B
x + y tan θ = 0

C
x sin θ + y (cos θ + 1) = 0

D
x cos θ + y (sin θ + 1) = 0

Solution
Question 10
4 / -1

The equation of one of the lines represented by the equation pq(x² – y²) + (p² – q²)xy = 0, is

A
px + qy = 0

B
px – qy = 0

C
p²x + q²y = 0

D
q²x – p²y = 0