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

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

If x(t) is a solution of ((1+t)dy)/(dx)-t y=1 and y(0)=-1 then y(1) is (a) ( b ) (c)-( d )1/( e )2( f ) (g) (h) (i) (b) ( j ) (k) e+( l )1/( m )2( n ) (o) (p) (q) (c) ( d ) (e) e-( f )1/( g )2( h ) (i) (j) (k) (d) ( l ) (m) (n)1/( o )2( p ) (q) (r) (s)

If ((2+cosx)/(3+y))(dy)/(dx)+sinx=0 and y(0)=1 , then y((pi)/(3)) is equal to

If ((2+cosx)/(3+y))(dy)/(dx)+sinx=0 and y(0)=1 , then y((pi)/(3)) is equal to

The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 when y_1(0)=1 and y(0) is (a) ( b ) (c) (d)(( e )-sin3x)/( f )9( g ) (h)+( i ) e^(( j ) x (k))( l )+( m )(( n ) (o) x^(( p )4( q ))( r ))/( s )(( t ) 12)( u ) (v)+( w )1/( x )3( y ) (z) x-1( a a ) (bb) (cc) ( d d ) (ee) (ff)(( g g )-sin3x)/( h h )9( i i ) (jj)+( k k ) e^(( l l ) x (mm))( n n )+( o o )(( p p ) (qq) x^(( r r )4( s s ))( t t ))/( u u )(( v v ) 12)( w w ) (xx)+( y y )1/( z z )3( a a a ) (bbb) x (ccc) (ddd) (eee) ( f f f ) (ggg) (hhh)(( i i i )-cos3x)/( j j j )3( k k k ) (lll)+( m m m ) e^(( n n n ) x (ooo))( p p p )+( q q q )(( r r r ) (sss) x^(( t t t )4( u u u ))( v v v ))/( w w w )(( x x x ) 12)( y y y ) (zzz)+( a a a a )1/( b b b b )3( c c c c ) (dddd) x+1( e e e e ) (ffff) (d) None of these

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)

The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^2-2x^3y^3) is (a) ( b ) (c) (d)(( e ) (f) y^(( g )2( h ))( i ))/( j ) x (k) (l)-( m ) x^(( n )3( o ))( p ) (q) y^(( r )2( s ))( t )=c (u) (v) (w) ( x ) (y) (z)(( a a ) (bb) x^(( c c )2( d d ))( e e ))/( f f )(( g g ) (hh) y^(( i i )2( j j ))( k k ))( l l ) (mm)+( n n ) x^(( o o )3( p p ))( q q ) (rr) y^(( s s )3( t t ))( u u )=c (vv) (ww) (xx) ( y y ) (zz) (aaa)(( b b b ) (ccc) x^(( d d d )2( e e e ))( f f f ))/( g g g ) y (hhh) (iii)+( j j j ) x^(( k k k )3( l l l ))( m m m ) (nnn) y^(( o o o )2( p p p ))( q q q )=c (rrr) (sss) (d) ( t t t ) (uuu) (vvv)(( w w w ) (xxx) x^(( y y y )2( z z z ))( a a a a ))/( b b b b )(( c c c c )3y)( d d d d ) (eeee)-2( f f f f ) x^(( g g g g )3( h h h h ))( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m )=c (nnnn) (oooo)

A curve passing through (2,3) and satisfying the differential equation int_0^x ty(t)dt=x^2y(x),(x >0) is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=13 (l) (m) (b) ( n ) (o) (p) y^(( q )2( r ))( s )=( t )9/( u )2( v ) (w) x (x) (y) (c) ( d ) (e) (f)(( g ) (h) x^(( i )2( j ))( k ))/( l )8( m ) (n)+( o )(( p ) (q) y^(( r )2( s ))( t ))/( u )(( v ) 18)( w ) (x)=1( y ) (z) (d) ( a a ) (bb) x y=6( c c ) (dd)