Let `S(n)` denote the number of ordered pairs `(x ,y)` satisfying `1//x+1//y=1//nw h e r en >1a n dx ,y ,n in Ndot` (i) Find the value of `( i i ) (iii) S(( i v )6( v ))dot( v i )` (vii) (viii) Show that if `( i x ) n (x)` (xi) is prime, then `( x i i ) (xiii) S(( x i v ) n (xv))=3( x v i )` (xvii) always.

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n,AA ,n in N , then find S(10) .

Let S(n) denotes the number of ordered pairs (x,y) satisfying 1/x+1/y=1/n, " where " n gt 1 " and " x,y,n in N . " " (i) Find the value of S(6). " " (ii) Show that, if n is prime, then S(n)=3, always.

Let (S) denotes the number of ordered pairs (x,y) satisfying (1)/(x)+(1)/(y)=(1)/(n),x,y,n in N . Q. sum_(r=1)^(10)S(r) equals

Given points P(2,3),Q(4,-2),a n dR(alpha,0) (i) Find the value of ( i i )alpha( i i i ) (iv) if ( v ) (vi) P R+r Q (vii) (viii) is minimum (ix) Find the value of ( x )alpha( x i ) (xii) if ( x i i i ) (xiv)|( x v ) P R-R Q|( x v i ) (xvii) is maximum

Convert the following Cartesian coordinates to the corresponding polar coordinates using positive r and negative rdot (i) ( i i ) (iii)(( i v ) (v)-1,1( v i ))( v i i ) (viii) (ii) ( i x ) (x)(( x i ) (xii)2,-3( x i i i ))( x i v ) (xv)

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i