Multiple choice questions with answers / choose the correct answer with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems - Mathematics : Two Dimensional Analytical Geometry

**CHAPTER
: Two Dimensional Analytical Geometry**

**Choose
the correct or more suitable answer**

1. The equation of the locus of the
point whose distance from y-axis is half the distance from origin is

(1) x^{2} + 3y^{2} = 0

(2) x^{2} - 3y^{2}
= 0

(3) 3x^{2} + y^{2} = 0

**(4)
3x ^{2} **

*Solution*

2. Which of the following equation is
the locus of (at^{2}, 2at)

(3) x^{2} + y^{2} = a^{2}

**(4)
y ^{2} = 4ax**

*Solution*

3. Which of the following point lie on
the locus of 3x^{2} + 3y^{2} - 8x - 12y + 17 = 0

(1) (0, 0)

(2) (-2, 3)

**(3)
(1, 2) **

(4) (0,-1)

*Solution*

4. If the point (8,-5) lies on the
locus x^{2}/16 - y^{2}/25
= k, then the value of k is

(1) 0

(2) 1

(3) 2

**(4)
3**

*Solution*

5. Straight line joining the points (2,
3) and (-1, 4) passes
through the point (α,β) if

(1) α + 2β =7

(2) 3α + β =9

**(3)
α + 3β =11**

(4) 3α + β =11

*Solution*

6. The slope of the line which makes an
angle 45̊ with the line 3x -
y = -5 are

(1) 1, -1

**(2)
1/2, ****-****2 **

(3) 1,1/2

(4) 2, -1/2

*Solution*

7. Equation of the straight line that
forms an isosceles triangle with coordinate axes in the I-quadrant with
perimeter 4 + 2√2 is

(1) x + y + 2 = 0

**(2)
x + y ****-**** 2
= 0 **

(3) x + y - √2 = 0

(4) x + y + √2 = 0

*Solution*

8. The coordinates of the four vertices
of a quadrilateral are (-2,4),
(-1,2), (1,2) and
(2,4) taken in order.The equation of the line passing through the vertex (-1,2) and
dividing the quadrilateral in the equal areas is

(1) x+ 1 = 0

(2) x + y = 1

(3) x + y + 3 = 0

**(4)
x ****-**** y
+ 3 = 0**

*Solution*

9. The intercepts of the perpendicular
bisector of the line segment joining (1, 2) and (3,4) with

coordinate axes are

(1) 5, -5

**(2)
5, 5 **

(3) 5, 3

(4) 5, -4

*Solution*

10. The equation of the line with slope
2 and the length of the perpendicular from the origin equal to √5 is

(1) x + 2y = √5

(2) 2x + y = √5

**(3)
2x + y = 5 **

(4) x + 2y - 5 = 0

*Solution*

11. A line perpendicular to the line 5x - y = 0 forms a
triangle with the coordinate axes. If the area of the triangle is 5 sq. units,
then its equation is

**(1)
x+ 5y ± 5√2 = 0 **

(2) x- 5y ± 5√2 = 0

(3) 5x+y± 5√2 = 0

(4) 5x-y±5√2 = 0

*Solution*

12. Equation of the straight line
perpendicular to the linex-y+5
= 0, through the point of intersection the y-axis and the given line

(1) x - y - 5 = 0

**(2)
x + y ****-**** 5
= 0 **

(3) x + y + 5 = 0

(4) x + y + 10 = 0

*Solution*

13. If the equation of the base opposite
to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length
of a side is

(1) √ 3/2

(2) 6

**(3)
√6 **

(4) 3√2

*Solution*

14. The line (p + 2q)x + (p - 3q)y = p - q for different
values of p and q passes through the point

(1) (3/2, 5/2)

(2) (2/5, 2/5)

(3) (3/5, 3/5)

**(4)
(2/5, 3/5)**

*Solution*

15. The point on the line 2x - 3y = 5 is
equidistance from (1,2) and (3, 4) is

(1) (7, 3)

**(2)
(4, 1) **

(3) (1,-1)

(4) (-2, 3)

*Solution*

16. The image of the point (2, 3) in the
line y = -x is

**(1)
(****-****3,
****-****2)
**

(2) ( -3, 2 )

(3) ( -2, -3)

(4) ( 3, 2 )

*Solution*

17. The length of ┴ from the origin to the line x/3 – y/4 = 1, is

(1) 11/5

(2) 5/12

**(3)
12/5**

(4) -5/12

*Solution*

18. The y-intercept of the straight line
passing through (1,3) and perpendicular to 2x - 3y + 1 = 0 is

(1) 3/2

**(2)
9/2**

(3) 2/3

(4) 2/9

*Solution*

19. If the two straight lines x + (2k - 7)y + 3 = 0 and
3kx + 9y - 5 = 0 are
perpendicular then the

value of k is

**(1)
k = 3 **

(2) k = 1/3

(3) k = 2/3

(4) k = 3/2

*Solution*

20. If a vertex of a square is at the
origin and its one side lies along the line 4x + 3y - 20 = 0, then the
area of the square is

(1) 20 sq. units

**(2)
16 sq. units **

(3) 25 sq. units

(4) 4 sq.units

*Solution*

21. If the lines represented by the
equation 6x^{2} + 41xy -
7y^{2} = 0 make angles

and
with x- axis then tanα tanβ =

**(1)
****-****6/7**

(2) 6/7

(3) -7/6

(4) 7/6

*Solution*

22. The area of the triangle formed by
the lines x^{2} -
4y^{2} = 0 and x = a is

(1) 2a^{2}

(2) √3/2 a^{2}

**(3)
1/2 a ^{2} **

(4) 2/√3 a^{2}

^{}

*Solution*^{}

23. If one of the lines given by 6x^{2}
- xy + 4cy^{2}
= 0 is 3x + 4y = 0,, then c equals to

**(1)
****-****3 **

(2) -1

(3) 3

(4) 1

*Solution*

24. θ is acute angle between the lines x^{2}
- xy - 6y^{2}
= 0, then is

(1) 1

(2) -1/9

**(3)
5/9**

(4) 1/9

*Solution*

25. The equation of one the line
represented by the equation x^{2} + 2xy cotθ - y^{2} =
0 is

(1) x - y cot θ = 0

(2) x + y tan θ = 0

(3) x cos θ + y (sinθ + 1) = 0

**(4)
x sin θ + y (cosθ + 1) = 0**

*Solution*

Tags : Two Dimensional Analytical Geometry | Mathematics , 11th Mathematics : Chapter 6 : Two Dimensional Analytical Geometry

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11th Mathematics : Chapter 6 : Two Dimensional Analytical Geometry : Exercise 6.5: Choose the correct answer | Two Dimensional Analytical Geometry | Mathematics

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