The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is

132.

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector.Then the maximum area (in sq. m) of the flower-bed, is

• 30

• 12.5

• 10

• 10

The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

•  6, –3, 2 

• 6/5, -3/5, 2/5

• 6/7, -3/7, 2/7

• 6/7, -3/7, 2/7

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

• 3x²/2

• x³/8

• x²/2

• x²/2

If (a, a2 ) falls inside the angle made by the lines y =x/2, x >0 and y = 3x, x > 0, then a belongs to

• (0,1/2)

• (3, ∞)

• (1/2, 3)

• (1/2, 3)

Let A(2,- 3) and B(- 2,1) be two angular points of AABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by

• 2x + 3y = 9

• 2x - 3y = 9

• 3x + 2y = 5

• 3x + 2y = 3

A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time t is given by s = t² + at - b + 17, where a and b are real numbers. If the particle comes to rest after 5 s at a distance of s = 25 units from the fixed point, then values of a and b are, respectively

• 10, - 33

• - 10, - 33

• - 8, 33

• - 10, 33

If a, band c are in AP, then the straight line ax + 2by + c = 0 will always pass through a fixed point whose coordinates are

• (1, - 1)

• (- 1, 1)

• (1, - 2)

• (- 2, 1)

The number of diagonals in a regular polygon of 100 sides is

• 4950

• 4850

• 4750

• 4650

Let p, q and r be the altitudes of a triangle with area S and perimeter 2 t. Then, the value of $\frac{1}{\mathrm{p}} + \frac{1}{\mathrm{q}} + \frac{1}{\mathrm{r}}$ is

• $\frac{\mathrm{S}}{\mathrm{t}}$

• $\frac{\mathrm{t}}{\mathrm{S}}$

• $\frac{\mathrm{S}}{2\mathrm{t}}$

• $\frac{2\mathrm{S}}{\mathrm{t}}$