The number of common tangent to the circles x²+y²-4x-6y-12=0 and x²+y²+6x+18y+26 = 0 is

• 1

• 2

• 3

• 3

The angle between the lines whose direction cosines satisfy the equations l +m+n=0 and l² = m²+n² is

• π/3

• π/4

• π/6

• π/6

If PS is the median of the triangle with vertices P(2,1), Q(6,-1) and R (7,3), then equation of the line passing through (1,-1) and parallel to PS is

• 4x-7y - 11 =0

• 2x+9y+7=0

• 4x+7y+3 = 0

• 4x+7y+3 = 0

Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax +2ay +c= 0 and 5bx +2by +d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

• 2bc-3ad =0 

• 2bc+3ad =0

• 2ad-3bc =0

• 2ad-3bc =0

5.

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