If `bc+qr=ca+rp=ab+pq=-1` and `(abc,pqr!=0)` then `|[ap,a,p],[bq,b,q],[cr,c,r]|` is (A) 1 (B) 2 (C) 0 (D) 3

if bc+ qr= ca+rp = ab+ pq =-1 then prove that |{:(ap,,a,,p),(bq,,b,,q),(cr,,c,,r):}|=0

If bc +qr=ca+rp=ab+pq=-1 , show that |{:(ap,bp,cr),(a,b,c),(p,q,r):}|=0

If bc +qr=ca+rp=ab+pq=-1, show that |{:(ap,bp,cr),(a,b,c),(p,q,r):}|=0

Statement 1: If b c+q r=c a+r p=a b+p q=-1, then |ap a p bq b q cr c r|=0(a b c ,p q r!=0)dot Statement 2: if system of equations a_1x+b_1y+c_1=0,a_2x+b_2y+c_2=0,a_3x+b_3y+c_3=0 has non -trivial solutions |a_1b_1c_1 a_2b_2c_2 a_3b_3c_3|=0

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

Prove that |[1,p,p^2-qr],[1,q,q^2-rp],[1,r,r^2-pq]|= 0

If a(p+q)^2+2bpq+c=0 and q(p+r)^2+2bpr+c=0 then (A) qr=p^2 + c/a (B) qr=p^2 - c/a (C) q+r = 2(a+b)/a (D) q+r= -2(a+b)/(a)

If every pair from among the equations x^(2)+px+qr=0,x^(2)+qx+rp=0 and x^(2)+rx+pq=0 has a common root then the product of three common root is (A) pqr (B) 2 pqr (C) (p^(2)q^(2)r^(2)) (D)one of these