Simplify : `({(a^m)^(1/r)(a^q)^(1/n)}^(nr))/({root(q)(b^n)(root(m)(b))^r}^(mq))*{(a/b)^q}^(-r)`.

Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n) .

Simplify (i) ((x^(i))/(x^(m)))^((1)/(lm)).((x^(m))/(x^(n)))^((1)/(m)).((x^(n))/(x^(l)))^((1)/(nl)) (ii) ((x^(p))/(x^(q)))^((1)/(ml)).((x^(q))/(x^(r)))^((1)/(mn)).((x^(r))/(x^(p)))^(r+q)

(b) If (log a)/(q-r)=(log b)/(r-p)=(log c)/(p-q) , prove that a^(p)b^(q)c^(r)=1

The square of the perpendicular distance of apoint P(p,q,r) from a line through A(a,b,c) and whose direction cosine are l,m,n is (A) sum{(q-b)n-(r-c)m}^(2)(B)sum{(q+b)n-(r+c)m}^(2)(C)sum(q-b)n+(r-c)m}^(2)(D) none of these

If p+r=mq and (1)/(q)+(1)/(s)=(m)/(r ), then prove that : p:q=r:s .

If a=xy^(p-1),b=yz^(q-1),c=zx^(r-1) , then a^(q-r)b^(r-p)c^(p-q) is equal to

Let A=[(l,m,n),(p,q,r),(1,1,1)] and B=A^(2) . If (l-m)^(2)+(p-q)^(2)=9, (m-n)^(2)+(q-r)^(2)=16, (n-l)^(2)+(r-p)^(2)=25 , then the value of |det(B)-140| is_______

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

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