The base of prism is equilateral triangle. The distance from the centre of one base to one of the vertices of the other base is `ldot` Then altitude of the prism for which the volume is greatest is `l/2` (b) `l/(sqrt(3))` (c) `l/3` (d) `l/4`

The base of prism. Is triangular in shape with sides 3cm , 4cm , and 5cm , Find the volume of the prism if its height is 10 cm .

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is (fig) 4:2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

The angle of incidence for an equilateral prism of refractive index sqrt(3) so that the ray is parallel to the base inside the prism is

For an angle of incidence theta on an equilateral prism of refractive index sqrt(3) , the ray refracted is parallel to the base inside the prism. The value of theta is

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is (a) 500 (b) 450 (c) 230 (d) 465

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio a)2:4:5 (b) 1:2:3 (c) 1:2:4 (d) 2:4:3

The distance between the circumcenter and the orthocentre of the triangle whose vertices are (0,0),(6,8), and (-4,3) is Ldot Then the value of 2/(sqrt(5))L is_________

The vertex of a parabola is the point (a , b) and the latus rectum is of length ldot If the axis of the parabola is parallel to the y-axis and the parabola is concave upward, then its equation is (a) (x+a)^2=l/2(2y-2b) (b) (x-a)^2=l/2(2y-2b) (c) (x+a)^2=l/4(2y-2b) (d) (x-a)^2=l/8(2y-2b)

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is 500 (b) 450 (c) 230 (d) 565

A right triangle has perimeter of length 7 and hypotenuse of length 3. If theta is the larger non-right angle in the triangle, then the value of costhetae q u a ldot (sqrt(6)-sqrt(2))/4 (b) (4+sqrt(2))/6 (4-sqrt(2))/3 (d) (4-sqrt(2))/6