Straight Line and Pair of Straight Lines Test

Result

Straight Line and Pair of Straight Lines Test - 66

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Question 1
4 / -1

One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are (–3, 1) and (1, 1). Then the equations of other two sides are

A
7x – 4y + 25 = 0,4x + 7y = 11 and 7x – 4y – 3 = 0

B
7x + 4y + 25 = 0,7y + 4x – 11 = 0 and 7x – 4y – 3 = 0

C
4x – 7y + 25 = 0,7x + 4y – 11= 0 and 4x – 7y – 3 = 0

D
None of these

Solution
Question 2
4 / -1

A
A.P

B
G.P

C
H.P

D
None of these

Solution
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

A

B

C

D

Solution
Question 5
4 / -1

The point (4, 1) undergoes the following three transformations successively
(1) 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 anti clockwise direction.
The final position of the point is given by the co-ordinates

A

B

C

D

Solution
Question 6
4 / -1

Let PQR be a right-angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

A
3x² – 3y² + 8xy + 20x + 10y + 25 = 0

B
3x² – 3y² + 8xy – 20x – 10y + 25 = 0

C
3x² – 3y² + 8xy + 10x + 15y + 20 = 0

D
3x² – 3y² – 8xy – 10x – 15y – 20 = 0

Solution
Question 7
4 / -1

Mixed term xy is to be removed from the general equation ax² + by² + 2hxy + 2fy + 2gx + c = 0.One should rotate the axis through an angle θ given by tan 2θ equal to

A

B

C

D

Solution
Question 8
4 / -1

If the equation y³ – 3x²y + m(x³ – 3xy²) = 0 represents the three lines passing through origin, then

A
Lines are equally inclined to each other

B
Two lines make equal angle with x-axis

C
All three lines make equal angle with x-axis

D
None of these
Question 9
4 / -1

A

B

C

D

Solution
Question 10
4 / -1

Let a and b be non-zero real numbers. Then, the equation (ax² + by² + c)(x² – 5y + 6y²) = 0 represents

A
Four straight lines, when c = 0 and a, b are of the same sign

B
Two straight lines and a circle, when a = b and c is of sign opposite to that of a

C
Two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a

D
A circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

Solution