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

Questions
1 If two vertices of a triangle are (3, -2) and (-2, 3) and its orthocenter is (-6, 1) then its third vertex is
A (5, 3)
B (-5, 3)
C (5, -3)
D (-5, -3)

Answer:(-5, -3)
2 The angle between the lines x – 2y = y and y – 2x = 5 is
A tan-1 (1/4)
B tan-1 (3/5)
C tan-1 (5/4)
D tan-1 (2/3)

Answer:tan-1 (5/4)

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3 The equation of straight line passing through the point (1, 2) and parallel to the line y = 3x + 1 is
A y + 2 = x + 1
B y + 2 = 3 × (x + 1)
C y – 2 = 3 × (x – 1)
D y – 2 = x – 1

Answer:y – 2 = 3 × (x – 1)
4 The locus of a point, whose abscissa and ordinate are always equal is
A x + y + 1 = 0
B x – y = 0
C x + y = 1
D none of these.

Answer:x – y = 0
5 The equation of the line passing through the point (2, 3) with slope 2 is
A 2x + y – 1 = 0
B 2x – y + 1 = 0
C 2x – y – 1 = 0
D 2x + y + 1 = 0

Answer:2x – y – 1 = 0
6 What can be said regarding if a line if its slope is zero
A θ is an acute angle
B θ is an obtuse angle
C Either the line is x-axis or it is parallel to the x-axis.
D None of these

Answer:Either the line is x-axis or it is parallel to the x-axis.
7 The equation of the line which cuts off equal and positive intercepts from the axes and passes through the point (α, β) is
A x + y = α + β
B x + y = α
C x + y = β
D None of these

Answer:x + y = α + β
8 The sum of squares of the distances of a moving point from two fixed points (a, 0) and (-a, 0) is equal to 2c² then the equation of its locus is
A x² – y² = c² – a²
B x² – y² = c² + a²
C x² + y² = c² – a²
D x² + y² = c² + a²

Answer:x² + y² = c² – a²
9 The locus of a point, whose abscissa and ordinate are always equal is
A x + y + 1 = 0
B x – y = 0
C x + y = 1
D none of these.

Answer:x – y = 0
10 Two lines are perpendicular if the product of their slopes is
A 0
B 1
C -1
D None of these

Answer:-1
11 Equation of the line passing through (0, 0) and slope m is
A y = mx + c
B x = my + c
C y = mx
D x = my

Answer:y = mx
12 The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is
A 6x – 4y = 5
B 6x + 4y = 5
C 6x + 4y = 7
D 6x – 4y = 7

Answer:6x + 4y = 5
13 The equation of the line through the points (1, 5) and (2, 3) is
A 2x – y – 7 = 0
B 2x + y + 7 = 0
C 2x + y – 7 = 0
D x + 2y – 7 = 0

Answer:2x + y – 7 = 0
14 y-intercept of the line 4x – 3y + 15 = 0 is
A -15/4
B 15/4
C -5
D 5

Answer:5
15 Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are parallel if
A n/(n+1)
B 1/(n+1)
C 1/n
D None of these

Answer:a1/a2 = b1/b2 ≠ c1/c2
16 The slope of the line ax + by + c = 0 is
A a/b
B -a/b
C -c/b
D c/b

Answer:-a/b
17 The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150 degrees with the positive direction of the y-axis. Then the equation of line is
A x + y = 14
B √3y + x = 14
C √3x + y = 14
D None of these

Answer:√3x + y = 14
18 What can be said regarding if a line if its slope is negative
A θ is an acute angle
B θ is an obtuse angle
C Either the line is x-axis or it is parallel to the x-axis.
D None of these

Answer:θ is an obtuse angle
19 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
20 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)

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