The graph of the function cos x cos (x +– cos 2 (x +is

A straight line passing through (0, – sin2with slope 2

A straight line passing through (0, 0)

A parabola with vertex (1, – sin21)

Lines L 1 : y – x = 0 and L 2 : 2x + y = 0 intersect the line L 3 : y + 2 = 0 at P and Q respectively. The bisector m, of the; acute angle between L 1 and L 2 intersects L 3 at R. Statement 1 : The ratio PR : RQ equals 2√2 : √5. Because Statement 2 : In any triangle, bisector of an angle divides the triangle into two similar triangle.

Statement 1 is true, statement 2 is false

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

Statement 1 is false, statement 2 is true

A → s, B → p,q, C → r, D → p,q,s

A → q, B → p, C → r, D → p,s

A → p, B → q, C → r, D → q,s

A → s, B → p,s, C → r, D → p,q

If the equation y 3 – 3x 2 y + m(x 3 – 3xy 2 ) = 0 represents the three lines passing through origin, then

Lines are equally inclined to each other

Two lines make equal angle with x-axis

All three lines make equal angle with x-axis

Let a and b be non-zero real numbers. Then, the equation (ax 2 + by 2 + c)(x 2 – 5y + 6y 2 ) = 0 represents

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

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

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

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

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 13

Maths-Straight Line and Pair of Straight Lines-52519.png

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Maths-Straight Line and Pair of Straight Lines-52525.png

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The distance between the parallel lines y = x + a, y = x + b is

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The equations of two equal sides of an isosceles triangle are 7x – y + 3 = 0 and x + y – 3 = 0 the third side passes through the point (1, –10). The equation of the third side is

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x – 3y – 31 = 0 but not 3x + y + 7 = 0
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3x + y + 7 = 0 but not x – 3y – 31 = 0
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3x + y + 7 = 0 or x – 3y – 31 = 0
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Neither 3x + y + 7 = 0 nor x – 3y – 31 = 0

The graph of the function cos x cos (x +– cos² (x +is

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A straight line passing through (0, – sin2with slope 2
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A straight line passing through (0, 0)
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A parabola with vertex (1, – sin21)
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Maths-Straight Line and Pair of Straight Lines-52539.png

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Maths-Straight Line and Pair of Straight Lines-52545.png

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Lines L₁ : y – x = 0 and L₂ : 2x + y = 0 intersect the line L₃ : y + 2 = 0 at P and Q respectively. The bisector m, of the; acute angle between L₁ and L₂ intersects L₃ at R.
Statement 1 : The ratio PR : RQ equals 2√2 : √5.
BecauseStatement 2 : In any triangle, bisector of an angle divides the triangle into two similar triangle.

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Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
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Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
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Statement 1 is true, statement 2 is false
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Statement 1 is false, statement 2 is true

Maths-Straight Line and Pair of Straight Lines-52552.png

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A → q, B → p, C → r, D → p,s
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A → s, B → p,q, C → r, D → p,q,s
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A → p, B → q, C → r, D → q,s
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A → s, B → p,s, C → r, D → p,q

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

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7x – 4y + 25 = 0,4x + 7y = 11 and 7x – 4y – 3 = 0
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7x + 4y + 25 = 0,7y + 4x – 11 = 0 and 7x – 4y – 3 = 0
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4x – 7y + 25 = 0,7x + 4y – 11= 0 and 4x – 7y – 3 = 0
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None of these

Maths-Straight Line and Pair of Straight Lines-52555.png

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A.P
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G.P
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H.P
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None of these

Maths-Straight Line and Pair of Straight Lines-52557.png

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Maths-Straight Line and Pair of Straight Lines-52563.png

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The point (4,undergoes the following three transformations successively
(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

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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

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3x2 – 3y2 + 8xy + 20x + 10y + 25 = 0
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3x2 – 3y2 + 8xy – 20x – 10y + 25 = 0
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3x2 – 3y2 + 8xy + 10x + 15y + 20 = 0
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3x2 – 3y2 – 8xy – 10x – 15y – 20 = 0

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

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

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Lines are equally inclined to each other
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Two lines make equal angle with x-axis
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All three lines make equal angle with x-axis
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None of these

Maths-Straight Line and Pair of Straight Lines-52580.png

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

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Four straight lines, when c = 0 and a, b are of the same sign
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Two straight lines and a circle, when a = b and c is of sign opposite to that of a
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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
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A circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

The product of perpendiculars drawn from the origin to the lines represented by the equation
ax² + 2hxy + by² + 2gx + 2fy + c = 0, will be

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The square of distance between the point of intersection of the lines represented by the equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 and origin, is

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None of these

Maths-Straight Line and Pair of Straight Lines-52596.png

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Maths-Straight Line and Pair of Straight Lines-52602.png

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The equation of pair of straight lines perpendicular to the pair ax² + 2hxy + by² = 0 is

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ax2 – 2hxy + by2 = 0
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bx2 + 2hxy + ay2 = 0
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ay2 – 2hxy + bx2 = 0
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ay2 – bx2 = 0

The equation of lines passing through the origin and parallel to the lines y = m₁x + c₁ and y = m₂x + c₂ is

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Maths-Straight Line and Pair of Straight Lines-52613.png

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Maths-Straight Line and Pair of Straight Lines-52618.png

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2
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0
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3
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1

The angle between the lines represented by the equation ax² + 2hxy + by² = 0 is given by

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Maths-Straight Line and Pair of Straight Lines-52624.png

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A line through the point A(2,which makes an angle of 30° with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15°. Then the equation of the straight line in the new position is

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The equations of the lines which pass through the origin and are inclined at an angle tan^–1 m to the line y = mx + c, are

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x = 0, 2mx + (m2 –y = 0
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y = 0, 2mx + (m2 –y = 0
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y = 0, 2mx + (1 – my = 0
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None of the above

Maths-Straight Line and Pair of Straight Lines-52636.png

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None of the above

Maths-Straight Line and Pair of Straight Lines-52641.png

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The equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3,is 7/5, are

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3x – 4y – 6 = 0 and 4x + 3y + 1 = 0
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3x – 4y + 6 = 0 and 4x – 3y – 1 = 0
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3x – 4y + 6 = 0 and 4x – 3y + 1 = 0
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None of the above

Maths-Straight Line and Pair of Straight Lines-52648.png

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The opposite angular points of a square are (3,and (1, –1). Then the co-ordinates of other two points are

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None of these

The base BC of a triangle ABC is bisected at the point (p, q) and the equations to the sides AB and AC arc respectively px + qy = 1 and px + py = 1. Then the equation to the median through A is

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None of the above

In an isosceles triangle ABC, the coordinates of the points B and C on the base BC are respectively (1,and (2, 1). If the equation of the line AB is y = 2x, then the equation of the line AC is

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A vertex of equilateral triangle is (2,and equation of opposite side is x + y = 2, then the equation of the one side from rest two, is

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y – 3 = 2(x – 2)
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y – 3 = (2 – √3)(x – 2)
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y – 3 = (√3 –(x – 2)
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None of the above

Maths-Straight Line and Pair of Straight Lines-52668.png

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If the line px – qy = r intersects the co-ordinate axes at (a,and (0,b), then value of a + b is equal to

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The slopes of the lines which make an angle 45^o with the line 3x – y = –5 are

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1, –1
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Equation of line through (α, β) which is the mid point of the line intercepted between the coordinate axes is

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The equations of the lines through (1,and making angle of 45^o with the line x + y = 0 are

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x – 1 = 0, x – y = 0
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x – y = 0, y – 1 = 0
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x + y – 2 = 0, y – 1 = 0
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x – 1 = 0, y – 1 = 0

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment L = 124.942 when C = 20 and L = 125.134 when C = 110.The expression of L in terms of C is

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JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 13 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 13 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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