Straight Line and Pair of Straight Lines Test

Result

Straight Line and Pair of Straight Lines Test - 54

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Weekly Quiz Competition

Question 1
4 / -1

If the lines represented by the equation 2x² – 3xy + y² = 0 make angles α and β with x-axis, then cot² α + cot² β

A
0

B

C

D

Solution
Question 2
4 / -1

Angle between the lines joining the origin to the points of intersection of the curves 2x² + 3y² + 10x = 0 and 3x² + 5y² + 16x = 0 is

A

B

C
90^o

D
None of these

Solution
Question 3
4 / -1

The lines (lx + my)² – 3(mx – ly)² = 0 and lx + my + n = 0 form

A
An isosceles triangle

B
A right-angled triangle

C
An equilateral triangle

D
None of these

Solution
Question 4
4 / -1

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is

A
30^o

B
45^o

C
60^o

D

Solution
Question 5
4 / -1

The angle between the lines represented by the equation (x² + y²) sin θ + 2xy = 0 is

A
θ

B

C

D

Solution
Question 6
4 / -1

The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve 3x² + 4xy – 4x + 1 = 0 include an angle

A

B

C

D

Solution
Question 7
4 / -1

A
3

B
4

C
5

D
6

Solution
Question 8
4 / -1

If two of the three lines represented by the equation ax³ + bx²y + cxy² + dy³ = 0 are perpendicular, then

A
a² + d² = 2ac

B
a² + d² = 2bd

C
a² + ac + bd + d² = 0

D
a² + d² = 4bc

Solution
Question 9
4 / -1

The acute angle formed between the lines joining the origin to the points of intersection of the curves x² + y² – 2x –1 = 0 and x + y = 1, is

A

B
tan^–12

C

D
60^o

Solution
Question 10
4 / -1

If the angle 2θ is acute, then the acute angle between x² (cos θ – sin θ) + 2xy cos θ + y² (cos θ + sin θ) = 0 is

A
2θ

B

C
θ

D

Solution