Refer to JEE Mathematics Straight Lines MCQs Set A provided below available for download in Pdf. The MCQ Questions for Full Syllabus Mathematics with answers are aligned as per the latest syllabus and exam pattern suggested 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 improve your understanding and 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.
Straight Lines MCQ Questions Full Syllabus Mathematics with Answers
15. If a, c, b are in G.P then the line ax + by + c= 0
(A) has a fixed direction
(B) always passes through a fixed point
(C) forms a triangle with axes whose area is constant
(D) none of these
16. If a ray travelling along the line x = 1 gets reflected from the line x + y = 1, then the equation the line along which the reflected ray travels is
(A) y = 0 (B) x –y = 1
(C) x = 0 (D) none of these
17. The equations of the lines representing the sides of a triangle are 3x – 4y =0, x+y =0 and 2x –3y =7. The line 3x +2y =0 always passes through the
(A) incentre (B) centroid
(C) circumcentre (D) orthocentre
18. If the lines x = a + m, y = -2 and y = mx are concurrent, the least value of |a| is
(A) 0 (B) √2
(C) 2√2 (D) None of these
19. Equation of a line passing through the intersection of the lines 2x +y =3 and x + y = 1 and perpendicular to the line y = 2x +k is
(A) x - 2y =0 (B) x+ 2y =0
(C) y – x =0 (D) y +x = 0
20. If the sum of the reciprocals of the intercepts made by a line on the coordinate axes is 1/5, then the line always passes through
(A) ( 5, -5) (B) ( -5, 5)
(C) (-5, -5) (D) ( 5, 5)
21. If 4a2 + 9b2 – c2 + 12ab = 0, a, b, c ε R+, then the family of straight lines ax + by + c = 0 is concurrent at
(A) (2, 3) (B) (– 2, – 3)
(C) 2, – 3) (D) (– 3, 2)
22. Point P (2, 4) is translated parallel to the line y – x – 1 = 0, through a distance 3 √2 so that its ordinate is decreased and it reaches at Q. If R is the mirror image of Q in the line y – x – 1 = 0, its coordinate are
(A) (– 1, 1) (B) (0, 0)
(C) (6, 6) (D) none of these
23. If the line y = √3 x cuts the curve x3 + y2 + 3x2 + 9 = 0 at the points A, B, C, then OA.OB.OC ( O being origin) equals
(A) 36 (B) 72
(C) 108 (D) none of these
24. Let O be the origin, and let A(1, 0), B(0, 1) be two points. If P(x, y) is a point such that xy > 0 and x + y < 1, then
(A) P lies either inside the ΔOAB or in the third quadrant
(B) P cannot be inside the ΔOAB
(C) P lies inside the ΔOAB
(D) none of these
25. Let ABC be a triangle with equation of sides AB, BC, CA respectively x – 2 =0, y – 5 = 0 and 5x + 2y – 10 = 0, then the orthocentre of triangle lies on the line
(A) x – y = 0 (B) 3x + y =1
(C) 4x + y = 13 (D) x – 2y =1
26. The foot of the perpendicular on the line 3x + y = λ drawn from the origin is C if the line cuts the x–axis and y–axis at A and B respectively then BC : CA is
(A) 1: 3 (B) 3 : 1
(C) 1: 9 (D) 9 : 1
28. In what ratio does the point (3, –2) divide the line segment joining the points (1, 4) and (–3, 16)?
(A) 1 : 3 (externally) (B) 3 : 1 (externally) (C) 1 : 3 (internally) (D) 3 : 1 (internally)
29. For what value of x will the points (x, –1), (2, 1) and (4, 5) lie on a line?
(A) 1 (B) 0 (C) 2 (D) none of these
30. The angle between straight lines x2 –y2 –2y –1 = 0 is
(A) 90° (B) 60° (C) 75° (D) 36°
31. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
(A) 7/2 (B) 7/10 (C) 4 (D) none of these
32. Find the length of the perpendicular from origin to the straight line 3x –y + 2 = 0
(A) 2 (B) –2/ √10 (C) 2/ √10 (D) none of these
33. If the sum of the slopes of the lines given by 4x2 + 2kxy –7y2 = 0 is equal to the product of the slopes then k =
(A) –4 (B) 4 (C) –2 (D) 2
34. Find the value of k, so that the equation –2x2 + xy + y2 –5x + y + k = 0 may represent a pairof straight lines
53. The straight lines of the family x(a+b) + y (a-b) = 2a (a and b being parameters) are
(A) not concurrent (B) Concurrent at (1, -1)
(C) Concurrent at (1, 1) (D) None of these
54. If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
(A) square (B) a circle
(C) straight line (D) two intersecting lines
55. If the line y = mx meets the lines x + 2y – 1= 0 and 2x – y + 3 = 0 at the same point, then m is equal to
(A) 1 (B) -1
(C) 2 (D) -2
56. The area inclosed by 3|x| + 4|y| ≤ 12 is
(A) 6 squar units (B) 12 sq. units
(C) 24 square units (D) 36 square units
57. If a, b, c are in A.P. then line 2ax + 3by + 3c = 0 always passes through fixed point
(A) (2, –2) (B) (3/2, 2)
(C) (3/2, –2) (D) none of these
58. Equation (3a – 2b)x2 + (c –2a)y2 + 2hxy = 0 represents pair of straight lines which are perpendicular to each other then (a – b) is equal to
(A) b + c (B) b – c
(C) c – b (D) 2c
59. ax + by + c = 0 represents a line parallel to x–axis if
(A) a = 0, b = 0 (B) a = 0, b≠0
(C) a≠0, b = 0 (D) c = 0
60. If the angle between the two straight lines represented by 2x2+ 5xy+ 3y2+7y+4= 0 is tan–1m then m equals to
(A) 1/5 (B) 1
(C) 7/5 (D) 7
61. The diagonals of a parallelogram PQRS are along the straight lines ax + 2by = 50 and 4bx – 2ay =100. Then PQRS must be a
(A) rhombus (B) rectangle
(C) square (D) none of these
62. The area enclosed by |x| + |y| = 1 is
(A) 1 (B) 2
(C) 3 (D) 4
68. The distance of the line 2x –3y = 4 from the point (1, 1) in the direction of the line x + y = 1 is …………………………………………….
69. If the point (2, a) lies between the lines x + y = 1 and 2(x + y) = 5, then a lies between ……………………….. and …………………………………..
70. If mn = 1, then the lines mx + y = 1 and y – nx = 2 will be ………………………………………
71. If the point (2a –3, a2 –1) is on the same side of the line x + y –4 = 0 as that of the origin,then the set of values of a is ……………………………
72. The set of lines ax + by + c = 0 where 3a + 2b + 4c = 0 is concurrent at the point ………………………………………………..
73. If the image of the point (–2, 1) by a line mirror be (2, –1) then the equation of the line mirror is ……………………………………..…………
13. Equation of the bisector of angle B of the triangle ABC is y = x. If A is (2, 6) and B is (1, 1); equation of side BC is
(A) 2x + y – 3 = 0 (B) x – 5y + 4 = 0
(C) x – 6y + 5 = 0 (D) none of these
14. Vertex opposite to the side x + y – 2 = 0 of the equilateral triangle, with centroid at the origin; is
(A) (– 1, 1) (B) (2, 2)
(C) (– 2, – 2) (D) none of these
19. The number of lines that can be drawn from the point (2, 3), so that its distance from (-1, 6) is equal to 6, is
(A) 1 (B) 2
(C) 0 (D) infinite
20. If ΔOAB is an equilateral triangle (O is the origin and A is a point on the x-axis), then centroid of the triangle will be
(A) always rational (B) rational if B is rational
(C) rational if A is rational (D) never rational
(a point P(x, y) is said to be rational if both x and y are rational)
21. Equation of a straight line passing through the point (4, 5) and equally inclined to the lines
3x = 4y + 7 and 5y = 12x + 6 is
(A) 9x –7y = 1 (B) 9x + 7y = 71
(C) 7x – 9y = 73 (D) 7x – 9y + 17 = 0
22. Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, then the third vertex is
(A) (-4, 7) (B) (-4, -7) (C) (4, -7) (D) (4, 7)
23. Drawn from the origin are two mutually perpendicular lines forming an isosceles triangle with the straight line 2x + y = a. Then the area of this triangle is ………………………….
24. Two particles start form the same point (2, –1), one moving 2 units along the line x + y = 1 and the other 5 units along the line x –2y = 4. If the particles move towards increasing y, then their new positions are ……………….., ……………………………
ANSWERS
19. If 3 a + 4 b + 2 c = 0, then the point of concurrent of the family of lines a x + b y + c = 0 and (1, 2) are
(A) on the same sides of the line 4 x - y + 1 = 0
(B) on the opposite side of the line 4 x - y + 1 = 0
(C) are at equal distances from the origin.
(D) None of these
20. If a, b, c are three consecutive integers, then the family of lines a x + b y + c = 0 are concurrent at the point,
(A) (1, 2) (B) (-2, 1)
(C) (1, -2) (D) None of these
ANSWERS
LEVEL −III
1. C
2. A
3. A
4. C
5. B
6. D
7. D
8. A
9. A
10. B
11. D
12. B
13. D
14. C
15. A
16. A
17. D
18. B
19. A
20. C
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MCQs for Straight Lines Mathematics Full Syllabus
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