JEE Mathematics Straight Lines MCQs Set C

Question: The equation of the straight line joining the origin to the point of intersection of y – x + 7 = 0 and y + 2x – 2 = 0 is

• a) 4x + 3y = 0
• b) 3x – 4y = 0
• c) 3x + 4y = 0
• d) 4x – 3y = 0

Answer: 4x + 3y = 0

Question: The distance of point (– 2, 3) from the line x – y = 5 is

• a) 5√2
• b) 2√5
• c) 3√5
• d) 4√5

Answer: 5√2

Question: A straight line makes an angle of 135° with x-axis and cuts y-axis at a distance of – 5 from the origin. The equation of the line is

• a) x + y + 5 = 0
• b) x + y + 3 = 0
• c) 2x + y + 5 = 0
• d) x + 2y + 3 = 0

Answer: x + y + 5 = 0

Question: If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, Then value of b is equal to

• a) 6
• b) 1
• c) 3
• d) 0

Answer: 6

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b then

• a) 1/p²=1/a² + 1/b²
• b) 1/p²=1/a² - 1/b²
• c) p² = a² + b²
• d) p² = a² - b²

Answer: 1/p²=1/a² + 1/b²

Question: The equation to the line bisecting the join of(3, – 4) and (5, 2) and having its intercepts on the X-axis and the Y-axis is in the ratio 2 : 1, is

• a) x + 2y = 2
• b) x + y – 3 = 0
• c) 2x – y = 9
• d) 2x + y = 7

Answer: x + 2y = 2

Question: Which of the following lines is farthest from the origin?

• a) x + y – 2 = 0
• b) 2x – y + 3 = 0
• c) x – y + 1 = 0
• d) x + 2y – 2 = 0

Answer: x + y – 2 = 0

Question: A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its Y – intercept is

• a) 4/3
• b) 4/3
• c) 1/3
• d) None of these

Answer: 4/3

Question: The equation of the locus of a point whose abscissa and ordinate are always equal is

• a) y – x = 0
• b) y + x – 1= 0
• c) y – x + 1 = 0
• d) y + x = 0

Answer: y – x = 0

Question: One of the equations of the lines passing through the point (3, – 2) and inclined at 60° to the line √3x+y = 1, is

• a) y + 2 = 0
• b) x + 2 = 0
• c) x – y =√ 3
• d) x + y = 0

Answer: y + 2 = 0

Question: The lines a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0 are perpendicular to each other if

• a) a₁a₂ + b₁b₂ = 0
• b) a₁b₁ – b₁a₂ = 0
• c) a₁b₁ + a₂b₂ = 0
• d) None of these

Answer: a₁a₂ + b₁b₂ = 0

Question: Three lines 3x – y = 2, 5x + ay = 3 and 2x + y = 3 are concurrent, then a is equal to

• a) – 2
• b) 2
• c) 3
• d) – 1

Answer: – 2

Question: The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point

• a) (2, 2)
• b) (4, 4)
• c) (1, 1)
• d) (3, 3)

Answer: (2, 2)

Question: The equation of straight line through the intersection of the lines x – 2y = 1 and x + 3y = 2 and parallel to 3x + 4y = 0 is

• a) 3x + 4y – 5 = 0
• b) 3x + 4y + 5 = 0
• c) 3x + 4y – 10 = 0
• d) 3x + 4y + 6 = 0

Answer: 3x + 4y – 5 = 0

More Questions..........................

Question: The length of the perpendicular from the origin to a line is 7 and line makes an angle of 150° with the positive direction of y-axis, then the equation of the line is

• a) √3x + y = 14
• b) –x + 3y = 2
• c) √3x - y = 10 √2
• d) 4x + 5y = 7

Answer: √3x + y = 14

Question: A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is

• a) 4x + 3y = 24
• b) x + y = 7
• c) 3x – 4y + 7 = 0
• d) 3x + 4y = 25

Answer: 4x + 3y = 24

Question: The lines p(p² +1)x – y + q = 0 and (p2 + 1)2x + (p² + ¹)y + 2q = 0 are perpendicular to a common line for

• a) exactly one value of p
• b) more than two values of p
• c) exactly two values of p
• d) all value of p

Answer: exactly one value of p

Question: If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is

• a) 5/4
• b) √10/4
• c) √13/4
• d) None of these

Answer: 5/4

Question: The distance of point (– 2, 3) from the line x – y = 5 is

• a) √5/2
• b) √3/5
• c) √2/5
• d) √5/3

Answer: √5/2

Question: The equation of a line through the point of intersection of the lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and whose distance from the origin is √5 is

• a) 2x + y – 5 =0
• b) x + 2y – 7 = 0
• c) x – 3y + 6 = 0
• d) x – 3y + 6 = 0

Answer: 2x + y – 5 =0

Question: If the lines x = 2a + m, y =1 and y = mx + 2 are concurrent, then minimum positive value of a is

(1) a ≤ -1        (2) a ≥ 1
(3) -1 ≤ a ≤ 1 (4) a > 0

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question:

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: Constant term of the equation of a straight line passing through the point of intersection of x – y + 1 = 0 and 3x + y – 5 = 0 and perpendicular to one of them is (1) 8 (2) 5 (3) 7 (4) –1

• a) 2 and 4 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 2 and 4 are correct

Question:

Statement-1: The equation of the straight line which passes through the point (2, –3) and the point of the intersection of the lines x + y + 4 = 0 and 3x – y – 8 = 0 is 2x – y – 7 =                  

Statement-2: : Product of slopes of two perpendicular straight lines is -1.

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question:

Statement-1: If a, b, c are in A.P. then every line of the form of ax + by + c = 0 where a, b, c are arbitrary constants pass through the point (1, –2)                 

Statement-2: Every line of the form of ax + by + c = 0 where a, b, c are arbitrary constants pass through a fixed point if their exist a linear relation between a, b & c.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:  Consider a line L : ax + by + c = 0 where ab > 0 and ac > 0.

Statement-1 : The line L cannot pass through first quadrant.

Statement-2 : Slope and x-intercept of the line are negative

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) x² + y² = a²
• b)

  

• c) x² + y² = 2a²
• d) None of these

Answer: x² + y² = a²

Question: The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for

• a) two values of a
• b) for one value of a
• c) three values of a
• d) None of these

Answer: two values of a

Question: If the sum of the slopes of the lines given by x² – 2cxy – 7y² = 0 is four times their product, then the value of c =

• a) 2
• b) –2
• c) –1
• d) 1

Answer: 2

Question: If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0, then c equals

• a) –3
• b) 3
• c) –1
• d) 1

Answer: –3

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The condition that the pair of straight lines joining the origin to the intersections of the line y = mx + c and the circle x² + y² = a² may be at right angles is

• a) 2c² = a² (1 + m²)
• b) 2a² = c² (1 – m²)
• c) a² = c² (1 + m²)
• d) None of these

Answer: 2c² = a² (1 + m²)

Question: If the pair of straight lines x² - 2 pxy - y² = 0 and x² - 2qxy - y² = 0 be such that each pair bisects the angle between the other pair, then

• a) pq = –1
• b) p = –q
• c) p = q
• d) pq = 1.

Answer: pq = –1

Question: The bisector of the acute angle formed between the lines 4x – 3y + 7 = 0 and 3x – 4y + 14 = 0 has the equation

• a) x – y + 3 = 0
• b) x + y +3 = 0
• c) x – y – 3 = 0
• d) 3x + y – 7 = 0

Answer: x – y + 3 = 0

Question:

• a) 8
• b) 4
• c) 6
• d) 2

Answer: 8

Question: The gradient of one of the lines x² + hxy + 2y² = 0 is twice that of the other, then h is equal to

• a) ± 3
• b) ± 2
• c) ± 1
• d) None of these

Answer: ± 3

Question: If ax² – y² + 4x – y = 0 represents a pair of lines, then a is equal to

• a) 16
• b) – 4
• c) – 16
• d) 4

Answer: 16

Question: The angle between the pair of straight lines.

• a) None of these
• b)

  

• c)

  

• d)

  

Answer: None of these

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

• a) bx² – 2hxy + ay² = 0
• b) ay² + 2hxy + bx² = 0
• c) ax² – 2hxy + by² = 0
• d) bx² + 2hxy + ay² = 0

Answer: bx² – 2hxy + ay² = 0

Question:  If equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, – 1) then the length of its side is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: If slope of one of the lines ax² + 2hxy + by² = 0 is twice that of the other, then

• a) 8h² = 9 ab
• b) h² = ab
• c) h = a + b
• d) 9h² = 8ab

Answer: 8h² = 9 ab

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

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

• a) m₁m₂x₂ – (m₁ + m₂)xy + y₂ = 0
• b) m₁m₂x₂ + (m₁ + m₂)xy + y₂ = 0
• c) Both
• d) None of these

Answer: m₁m₂x₂ – (m₁ + m₂)xy + y₂ = 0

Question: A point moves so that square of its distance from the point (3, – 2) is numerically equal to its distance from the line 5x – 12y = 13. The equation of the locus of the point is

• a) 13x² + 13y² – 83x + 64y + 182 = 0
• b) x² + y² – 11x + 16y + 26 = 0
• c) x² + y² – 11x + 16y = 0
• d) None of these

Answer: 13x² + 13y² – 83x + 64y + 182 = 0

Question: The joint equation of the straight lines x + y = 1 and x – y = 4 is

• a) (x + y – 1) (x – y – 4) = 0
• b) (x + y + 1) (x – y + 4) = 0
• c) x² – y² = 4
• d) None of these

Answer: (x + y – 1) (x – y – 4) = 0

Question: If the point (2, –3) lies on kx² – 3y² + 2x + y – 2 = 0, then k is equal to

• a) 7
• b) 16
• c) 12
• d) /7

Answer: 7

Question:

(1) 3                                 (2) 5
(3) lies between 1 and 4     (4) 6

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question:

(1) [0, 4] (2) [–2, 2]
(3) (2, 5) (4) (3, 6)

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: The lines L₁ and L₂ are denoted by 3x² + 10xy + 8y² + 14x + 22y + 15 = 0 intersect at the point P and have gradient m₁ and m₂ respectively. The acute angle between them is q. Which of the following relations hold good –

(1) m₁ m₂ = 3/8
(2) acute angle between L₁ and L₂ is sin^–1(-2/5√5)
(3) sum of the abscissa and ordinate of the point P is –1
(4) m₁ + m₂ = 5/4

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

Equation of side BC is –

• a) 7x + 3y + 4 = 0
• b) 7x – 3y – 4 = 0
• c) 7x + 3y – 4 = 0
• d) 7x – 3y + 4 = 0

Answer: 7x + 3y + 4 = 0

Question:

Coordinates of vertex B are –

• a)

  

• b)

  

• c)

  

• d) (1, 1)

Answer:

Question:

Equation of side AB is –

• a) 3x + 7y = 24
• b) 3x + 7y + 24 = 0
• c) 13x + 7y + 8 = 0
• d) 13x – 7y + 8 = 0

Answer: 3x + 7y = 24

Question:

Statement-1 : Let the lines 2x + 3y + 19 = 0 and 9x + 6y – 17 = 0 cut the x-axis in A, B and y axis in C, D. Then points A, B, C, D are concyclic.

Statement-2 : Since OA . OB = OC . OD where O is origin therefore A, B, C, D points are concyclic.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement-1 is False, Statement-2 is True.
• d) Statement-1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement-1 is True, Statement-2 is False.
• b) Statement-1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is False.

Question: Consider the family of straight lines

Statement-1 : All the lines of the given family pass through the point (3, –2).
Statement-2 : All the lines of the given family pass through a fixed point. 

• a) Statement-1 is False, Statement-2 is True.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• c) Statement-1 is True, Statement-2 is False.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Answer: Statement-1 is False, Statement-2 is True.