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

If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2 , then k is equal to

Prove that: |-a^2 ab ac ba -b^2 bc ac bc c^2| =4a^2b^2c^2 .

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,and C=a^2c +'a c^2-b^2' c-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 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, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

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

If a^2+b^2+c^2-a b-b c-c a=0,\ p rov e\ t h a t\ a=b=c

Of f(x)=p x^2+q x+r is a quadratic expression such that [a^2 a1 b^2 b1 c^2 c1][f(0) f(1) f(-1)]=[2a+1 2b+1 2c+1] for three unequal numbers a ,b ,c then (a) p=3/2 (b) q=-1/2 (c) r=1 (d) p+q+r=2

If a,b,c in R - {0} and a^(2) = bc and a + b +c = abc then the least possible value of a^(2) is