## MCQ Questions for Class 11 Maths Chapter 10 Straight Lines with Answers

Question 1.

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

Answer: (b) x – y = 0

Question 2.

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: (c) y – 2 = 3 × (x – 1)

Question 3.

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 theseAnswer

Answer: (b) θ is an obtuse angle

Hint:

Let θ be the angle of inclination of the given line with the positive direction of x-axis in the anticlockwise sense.

Then its slope is given by m = tan θ

Given, slope is positive

⇒ tan θ < 0

⇒ θ lies between 0 and 180 degree

⇒ θ is an obtuse angle

Question 4:

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 theseAnswer

Answer: (a) x + y = α + β

Hint:

Let the equation of the line be x/a + y/b = 1 which cuts off intercepts a and b with

the coordinate axes.

It is given that a = b, therefore the equation of the line is

x/a + y/a = 1

⇒ x + y = a …..1

But it is passes through (α, β)

So, α + β = a

Put this value in equation 1, we get

x + y = α + β

Question 5.

Two lines a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are coincedent if

(a) a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

(b) a_{1}/a_{2} ≠ b_{1}/b_{2} = c_{1}/c_{2}

(c) a_{1}/a_{2} ≠ b_{1}/b_{2} ≠ c_{1}/c_{2}

(d) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}Answer

Answer: (d) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Hint:

Two lines a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are coincedent if

a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Question 6:

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 = 0Answer

Answer: (c) 2x – y – 1 = 0

Hint:

Given, the point (2, 3) and slope of the line is 2

By, slope-intercept formula,

y – 3 = 2(x – 2)

⇒ y – 3 = 2x – 4

⇒ 2x – 4 – y + 3 = 0

⇒ 2x – y – 1 = 0

Question 7.

The slope of the line ax + by + c = 0 is

(a) a/b

(b) -a/b

(c) -c/b

(d) c/bAnswer

Answer: (b) -a/b

Hint:

Give, equation of line is ax + by + c = 0

⇒ by = -ax – c

⇒ y = (-a/b)x – c/b

It is in the form of y = mx + c

Now, slope m = -a/b

Question 8.

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 = myAnswer

Answer: (c) y = mx

Hint:

Equation of the line passing through (x_{1}, y_{1}) and slope m is

(y – y_{1}) = m(x – x_{1})

Now, required line is

(y – 0 ) = m(x – 0)

⇒ y = mx

Question 9.

The angle between the lines x – 2y = 4 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: (c) tan^{-1} (3/4)

Question 10.

Two lines a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are parallel if

(a) a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

(b) a_{1}/a_{2} ≠ b_{1}/b_{2} = c_{1}/c_{2}

(c) a_{1}/a_{2} ≠ b_{1}/b_{2} ≠ c_{1}/c_{2}

(d) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Answer: (a) a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

Question 11.

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

Answer: (b) x – y = 0

Question 12.

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: (b) (7, – 2)

Question 13.

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: (c) √3x + y = 14

Question 14.

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: (d) (-5, -3)

Question 15.

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: (c) x² + y² = c² – a²

Question 16.

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 = 0Answer

Answer: (c) 2x + y – 7 = 0

Question 17.

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: (c) Either the line is x-axis or it is parallel to the x-axis.

Question 18.

Two lines are perpendicular if the product of their slopes is

(a) 0

(b) 1

(c) -1

(d) None of these

Answer: (c) -1

Question 19.

y-intercept of the line 4x – 3y + 15 = 0 is

(a) -15/4

(b) 15/4

(c) -5

(d) 5

Answer: (d) 5

Question 20.

The equation of the locus of a point equidistant from the points 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: (b) 6x + 4y = 5