If `p=a+bomega+comega^2`, `q=b+comega+aomega^2`, and `r=c+aomega+bomega^2`, where `a ,b ,c!=0` and `omega` is the complex cube root of unity, then (a) `p+q+r=a+b+c` (b) `p^2+q^2+r^2=a^2+b^2+c^2` (c) `p^2+q^2+r^2=-2(p q+q r+r p)` (d) none of these

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^2)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

Solve:- (p^2q^2r^4 - p^3q^5r^3 + p^5q^3r^2) div p^2q^2r^2

Solve:- (p^2q^2r^5 - p^3q^5r^3 + p^5 q^3r^3) div p^2q^2r^2

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

If omega is the imaginary cube root of unity and a+b+c=0 then show that (a+bomega+comega^2)^3+(a+bomega^2+comega)^3=27abc

prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc if a+b+c=0.

If omega is the imaginary cube root of 1 then prove that (a+bomega+comega^2)^3+(a+bomega^2+comega)^3 = (2a-b-c)(2b-a-c)(2c-a-b)

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is (a) x^2+y^2=b^2 (b) x^2+y^2=a^2 (c) x^2+y^2=a^2-b^2 (d) none of these

If alpha,beta are real and distinct roots of a x^2+b x-c=0 and p ,q are real and distinct roots of a x^2+b x-|c|=0,w h e r e(a >0), then (a) alpha,beta in (p ,q) (b). alpha,beta in [p ,q] (c). p ,q in (alpha,beta) (d). none of these