These Straight Lines Class 11 NCERT Question And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Straight Lines Class 11 NCERT Question And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.
Straight Lines Class 11 NCERT Question And Answers
1. Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are coincedent if
(A) a1/a2 = b1/b2 ≠ c1/c2
(B) a1/a2 ≠ b1/b2 = c1/c2
(C) a1/a2 ≠ b1/b2 ≠ c1/c2
(D) a1/a2 = b1/b2 = c1/c2
Answer: a1/a2 = b1/b2 = c1/c2
2. In a ΔABC, if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is
(A) (1, 4)
(B) (7, – 2)
(C) none of these
(D) (4, 1)
Answer: (7, – 2)
3. 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
Answer: -1
4. 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
Answer: (3/2, –2)
5. The locus of the mid-point of the portion intercepted between the axes by the line x cos a + y sin a = p, where p is a constant is
(A) x2 + y2 = 4p2
(B) 1/x2+1/y2=4/p2
(C) x² + y² = 4/p2
(D) 1/x2+1/y2=2/p2
Answer: 1/x2+1/y2=4/p2
6. Points on the line x + y = 4 that lie at a unit distance from the line 4x+ 3y–10=0 are
(A) (3, 1) and (–7, 11)
(B) (–3, 7) and (2, 2)
(C) (–3, 7) and (–7, 11)
(D) none of these.
Answer: (3, 1) and (–7, 11)
7. If one vertex of an equilateral triangle is at (1, –2) and the base is x + y + 2 = 0, then the length of each side is
(A) √3/2
(B) √2/3
(C) 2/3
(D) 3/2
Answer: √2/3
8. 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
Answer: b – c
9. 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
Answer: Concurrent at (1, 1)
10. If the angle between the two straight lines represented by 2x2+ 5xy+ 3y2+7y+4= 0 is tan–1 m then m equals to
(A) 1/5
(B) 1
(C) 7/5
(D) 7
Answer: 1/5
11. The equation of the line through (3, 4) and parallel to the line y =3x +5 is
(A) 3x – y – 5 =0
(B) 3x + y – 5 = 0
(C) 3x + y + 5 = 0
(D) 3x – y + 5 = 0
Answer: 3x – y – 5 =0
12. The incentre of the triangle formed by the lines y = |x| and y = 1 is
(A) (0, 2 – √2)
(B) (2 –√2, 0)
(C) (2 +√2, 0)
(D) (0, 2 +√2 )
Answer: (0, 2 – √2)
13. The quation of the line joining the points (– 1, 3) and (4, – 2) is
(A) x + y – 1 =0
(B) x + y +1 =0
(C) x + y +2 =0
(D) x + y – 2 =0
Answer: x + y – 2 =0
14. The area of the quadrilateral formed by y = 1 – x, y = 2 – x and the coordinate axes is
(A) 1
(B) 2
(C) 3/2
(D) None of these
Answer: 3/2
15. The quadratic equation whose roots are the x and y intercepts of the line passing through (1, 1) and making a triangle of area A with axes is
(A) x2 + Ax + 2A = 0
(B) x2 – 2Ax +2A = 0
(C) x2 – Ax + 2A = 0
(D) None of these
Answer: x2 – 2Ax +2A = 0
16. Locus of the point of intersection of lines x cosa+ y sin α = a and x sin α – y cos α =a is
(A) x2 + y2 =a2
(B) x2 + y2 = 2a2
(C) x2 + y2 + 2x + 2y = a2
(D) None of these
Answer: x2 + y2 = 2a2
17. The equation of the line through (3, 4) and parallel to the line y =3x +5 is
(A) 3x – y – 5 =0
(B) 3x + y – 5 = 0
(C) 3x + y + 5 = 0
(D) 3x – y + 5 = 0
Answer: 3x – y – 5 =0
18. The quation of the line joining the points (– 1, 3) and (4, – 2) is
(A) x + y – 1 =0
(B) x + y +1 =0
(C) x + y +2 =0
(D) x + y – 2 =0
Answer: x + y – 2 =0
19. The equation of straight line which passes through the point (1, 2) and makes an angle cos–1(-1/3)with the x– axis is
(A) (a)
(B) (b)
(C) (c)
(D) (d)
Answer: (a)
20. The member of the family of lines ( p +q)x + (2p +q)y = p + 2q, where p≠0, q≠0, pass through the point
(A) (3, – 1)
(B) (– 3 ,1)
(C) (1, 1)
(D) None of these
Answer: (3, – 1)
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