Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

(a)

7:2

(b)

3:4

(c)

2:7

(d)

5:3

If the points (0, 0), (a, 0) and (0, b) are collinear, then ____________

(a)

a = b

(b)

a + b

(c)

ab = 0

(d)

a ≠ b

If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

(a)

(6, -1)

(b)

(-6, 1)

(c)

(-2, 1)

(d)

(3, 5)

The area of triangle formed by the points (a, b+c), (b, c+a) and (c, a+b) is ____________

(a)

a+b+c

(b)

abc

(c)

(a+b+c)²

(d)

0

The four vertices of a quadrilateral are (1, 2), (5, -6), (7, -4) and (k, -2) taken in order. If the area of quadrilateral is zero then find the value of k.

(a)

4

(b)

-2

(c)

6

(d)

3

Find the slope and the y-intercept of the line \(3y-\sqrt { 3x } +1=0\) is ____________

(a)

\(\frac { 1 }{ \sqrt { 3 } } ,\frac { -1 }{ 3 } \)

(b)

\(-\frac { 1 }{ \sqrt { 3 } } ,\frac { -1 }{ 3 } \)

(c)

\(\sqrt { 3 } ,1\)

(d)

\(-\sqrt { 3 } ,3\)

Find the value of 'a' if the lines 7y = ax + 4 and 2y = 3 - x are parallel

(a)

\(\frac { 7 }{ 2 } \)

(b)

\(-\frac { 2 }{ 7 } \)

(c)

\(\frac { 2 }{ 7 } \)

(d)

\(-\frac { 7 }{ 2 } \)

A line passing through the point (2, 2) and the axes enclose an area ∝. The intercept on the axes made by the line are given by the roots of ____________

(a)

x²-2-∝x+∝ = 0

(b)

x²+2∝x+∝ = 0

(c)

x²-∝x+2∝ = 0

(d)

none of these

Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

(a)

3x+5y+15 = 0

(b)

3x+5y-20 = 0

(c)

2x+7y-20 = 0

(d)

4x+3y-15 = 0

In a right angle triangle, right angled at B, if the side BC is parallel to x axis, then the slope of AB is ___________

(a)

\(\sqrt { 3 } \)

(b)

\(\frac { 1 }{ \sqrt { 3 } } \)

(c)

1

(d)

not defined

The y-intercept of the line 3x - 4y + 8 = 0 is ___________

(a)

\(-\frac { 8 }{ 3 } \)

(b)

\(\frac { 8 }{ 3 } \)

(c)

2

(d)

\(\frac { 1 }{ 2 } \)

The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

(a)

(2, 7)

(b)

(2, 3)

(c)

(4, 17)

(d)

(-4, 23)

The angle of elevation of a cloud from a point h metres above a lake is b. The angle of depression of its reflection in the lake is 45^o. The height of location of the cloud from the lake is ___________

(a)

\(\frac { h(1+tan\beta ) }{ 1-tan\beta } \)

(b)

\(\frac { h(1-tan\beta ) }{ 1+tan\beta } \)

(c)

h tan(45^o- β)

(d)

None of these

The area of the triangle whose vertices are (2, - 3), (3, 2) and (- 2, 5) is ___________

(a)

11

(b)

12

(c)

14

(d)

13

AD is the median of triangle ABC with vertices A (- 3, 2), B (5, - 2) and C (1, 3) The area of triangle ABD is ___________

(a)

5

(b)

6

(c)

7

(d)

8