If `y=y(x)` and `(2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1,` then `y(pi/2)` equals (a) `( b ) (c) (d)1/( e )3( f ) (g) (h)` (i) (b) `( j ) (k) (l)2/( m )3( n ) (o) (p)` (q) (c) `( r ) (s)-( t )1/( u )3( v ) (w) (x)` (y) (d) 1

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

y(dy)/(dx)sinx=cosx(sinx-(y^(2))/(2)),y=1" when "x=(pi)/(2)

If y=cos^(-1)(cosx) ,then (dy)/(dx) at x= (5pi)/4 is equal to (a)1 (b)-1 (c)0 (d)4

If e^y(x+1)=1 , prove that (d^2y)/(dx^2)=((dy)/(dx))^2

If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/(dx) is. (a)1 (b) -1 (c) 0 (d) none of these

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1,t h e nxe q u a l s 4 (b) 8 (c) 16 (d) 64

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a) x/y (b) y/(x^2) (C) (x^2-y^2)/(x^2+y^2) (d) y/x

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a) cos(pi/4) (b) sin(pi/2) (c) sin(pi/6) (d) cos(pi/3)