Refer to JEE Mathematics Straight Lines MCQs Set C provided below. JEE (Main) Full Syllabus Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Full Syllabus Mathematics with answers have been prepared as per the latest syllabus, JEE (Main) books and examination pattern suggested in Full Syllabus by JEE (Main), NCERT and KVS. Multiple Choice Questions for Straight Lines are an important part of exams for Full Syllabus Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise MCQs for JEE (Main) Full Syllabus Mathematics and also download more latest study material for all subjects
MCQ for Full Syllabus Mathematics Straight Lines
Full Syllabus Mathematics students should refer to the following multiple-choice questions with answers for Straight Lines in Full Syllabus. These MCQ questions with answers for Full Syllabus Mathematics will come in exams and help you to score good marks
Straight Lines MCQ Questions Full Syllabus Mathematics with Answers
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.
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JEE (Main) MCQs Mathematics Full Syllabus Straight Lines
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