In ` A B C ,ifa=10a n dbcotB+c cot C=2(r+R)` then the maximum area of ` A B C` will be (a) 50 (b) `sqrt(50) ` (c) 25 (d) 5

In triangle A B C , Medians A D and C E are drawn. If A D=5,/_D A C=pi/8,a n d/_A C E=pi/4 , then the area of the triangle A B C is equal to (25)/9 (b) (25)/3 (c) (25)/(18) (d) (10)/3

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a)1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of (a) 3 (b) 6 (c) 9 (d) none of these

Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D are mutually perpendicular. Let the area of triangles A B C ,A C Da n dA D B be 3, 4 and 5sq. units, respectively. Then the area of triangle B C D is 5sqrt(2) b. 5 c. (sqrt(5))/2 d. 5/2

If in A B C ,A C is double of A B , then the value of cot(A/2)cot((B-C)/2) is equal to 1/3 (b) -1/3 (c) 3 (d) 1/2

In a A B C ,ifA B=x , B C=x+1,/_C=pi/3 , then the least integer value of x is 6 (b) 7 (c) 8 (d) none of these

If a,b,c,in R^(+) , such that a+b+c=18 , then the maximum value of a^2,b^3,c^4 is equal to

If a^(2)+b^(2)+c^(2)=1 where, a,b, cin R , then the maximum value of (4a-3b)^(2) + (5b-4c)^(2)+(3c-5a)^(2) is

If A +B +C = 90 ^@ then ( cot A+ cot B + cot C) /(cot A cot B cot C ) =

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)