131.

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

• 
• 
• 
• 

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

• $\frac{\mathrm{S}}{\mathrm{t}}$

• $\frac{\mathrm{t}}{\mathrm{S}}$

• $\frac{\mathrm{S}}{2\mathrm{t}}$

• $\frac{2\mathrm{S}}{\mathrm{t}}$