Add: (i)`p\ (p-q), q(q-r)` and`\ r\ (r-p)` (ii)`2x\ (z-x-y)\ ` and`\ 2y\ (z-y-x)`

(a) Add: p(p-q), q(q-r) and r(r-p) (l) add: 2x(z-x-y) and 2y(z-y-x) (w) Subtract: 3l(l-4m+5n) from 4l(10n-3m+2l) (ii) (d) Subtract: 3a(a+b+c)-2b(a-b+c) from 4c(-a+b+c)

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these

The lines 1) (p-q)x+(q-r)y+(r-p)=0,2)(q-r)x+(r-p)y+(p-q)=0,3)(r-p)x+(p-q)y+(q-r)=0

If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

Factorize each of the following expressions: (1) q r-p r+q s-p s (2) p^2q-p r^2-p q+r^2 (3) 1+x+x y+x^2y (4) a x+a y-b x-b y

STATEMENT-1 : If log (x + z) + log (x -2y +z) = 2 log (x -z) then x,y,z are in H.P. STATEMENT-2 : If p , q , r in AP and (a -x)/(px) = (a-y)/(qy) = (a-z)/(rz) , then x, y, z are in A.P. STATEMENT-3 : If (a + b)/(1 - ab), b, (b + c)/(1 - bc) are in A .P. then a, (1)/(b) , c are in H.P.

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

(a) If r^(2) = pq , show that p : q is the duplicate ratio of (p + r) : (q + r) . (b) If (p - x) : (q - x) be the duplicate ratio of p : q then show that : (1)/(p) + (1)/(q) = (1)/(r) .

If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?