JEE Mathematics Straight Lines MCQs Set 03

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: A

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: A

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: A

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: A

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: A

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: A

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: A

Question. A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its Y – intercept is
(a) 4/3
(c) 1/3
(d) None of these

Answer: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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

Answer: A

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: A

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: A

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: A

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: A

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: A

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: 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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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: A