`(x+i y)^(1/3)=a+i bt h e n p r o v e t h a tx/a+y/b=4(a^2-b^2)`

Column I, Column II y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a nb e , p. 1 y=(x^2-3x-2)/(2x-3),x in R ,t h e ny c a nb e , q. 4 y=(2x^2-2x+4)/(x^2-4x+3),x in R ,t h e ny c a nb e , r. -3 x^2-(a-3)x+2<0,AA,x in (-2,3),t h a nac a nb e , s. -10

If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove that: 1+a b+a^2b^2+oo=(x y)/(x+y-1)

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot The value of (a+b)//3 equals ______.

If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot The value of (a+b)//3 equals ______.

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these

If the complex numbers xa n dy satisfy x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot The value of (a+b)//3 equals ______.