NCERT Solutions for class 11 Maths | Chapter 10 - Straight Lines

Questions
1 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
2 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)

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3 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
4 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

Answer:Square
5 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

Answer:a = 0, b ≠ 0
6 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
7 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)
8 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
9 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)
10 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
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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