If `|0a b^2a c^2a^2b0b c^2a^2cc b^2 0|=2a^pb^q c^r ,t h e np+q+r+10` is equal to 27 (b) 18 (c) 19 (d) 8

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, a n dC=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

In a triangle ABC if a^4+b^4+c^4=2c^2(a^2+b^2) , then angle C is equal to (A) 60^0 (B) 120^0 (C) 45^0 (D) 135^0

In a triangle A B C , if a : b : c=3:7:8,t h e n R : r is equal to a. 2:7 b. 7:2 c. 3:7 d. 7:3

If a^2+b^2+c^2+a b+b c+c alt=0AAa ,b ,c in R , then value of the determinant |(a+b+2)^2a^2+b^2 1 1(b+c+2)^2b^2+c^2c^2+a^2 1(c+a+2)^2|e q u a l s 65 (b) a^2+b^2+c^2+31 4(a^2+b^2+c^2 (d) 0

If p/a+q/b+r/c=1 and a/p+b/q+c/r=0 where a , b , c , p , q , r are non-zero real numbers, then (p^2)/(a^2)+(q^2)/(b^2)+(r^2)/(c^2) is equal to (a) 0 (b) 1 (c) 3 (d) 9

If a+b+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are:

In a A B C ,\ D ,\ E ,\ F are the mi-points of sides B C ,\ C A\ a n d\ A B respectively. If a r( A B C)=16 c m^2, then a r\ (t r a p e z i u m\ F B C E)= 4\ c m^2 (b) 8\ c m^2 (c) 12 c m^2 (d) 10 c m^2

If 2 is a root of the equation x^2+b x+12=0 and the equation x^2+b x+q=0 has equal roots, then q= (a) 8 (b) -8 (c) 16 (d) -16

Value of the expression (b-c)/(r_1)+(c-a)/(r_2)+(a-b)/(r_3) is equal to 1 (b) 2 (c) 3 (d) 0