The solution of the equation log ((dy)/(...

The solution of the equation log `((dy)/(dx))=a x+b y` is (a) `( b ) (c) (d)(( e ) (f) e^(( g ) (h) b y (i))( j ))/( k ) b (l) (m)=( n )(( o ) (p) e^(( q ) (r) a x (s))( t ))/( u ) a (v) (w)+c (x)` (y) (b) `( z ) (aa) (bb)(( c c ) (dd) e^(( e e ) (ff)-b y (gg))( h h ))/( i i )(( j j )-b)( k k ) (ll)=( m m )(( n n ) (oo) e^(( p p ) (qq) a x (rr))( s s ))/( t t ) a (uu) (vv)+c (ww)` (xx) (c) `( d ) (e) (f)(( g ) (h) e^(( i ) (j)-b y (k))( l ))/( m ) a (n) (o)=( p )(( q ) (r) e^(( s ) (t) a x (u))( v ))/( w ) b (x) (y)+c (z)` (aa) (d) None of these

`(e^(by))/(b)=(e^(ax))/(a)+C`

`(e^(-by))/(-b)=(e^(ax))/(a)+C`

`(e^(-by))/(a)=(e^(ax))/(b)+C`

none of these

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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)

Tangent to a curve intercepts the y-axis at a point Pdot A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is (a) ( b ) (c) y (d)(( e ) dy)/( f )(( g ) dx)( h ) (i)-x (j) (k)(( l ) (m) (n)(( o ) dy)/( p )(( q ) dx)( r ) (s) (t))^(( u )2( v ))( w )=1( x ) (y) (b) ( z ) (aa) (bb)(( c c ) x (dd) d^(( e e )2( f f ))( g g ))/( h h )(( i i ) d (jj) x^(( k k )2( l l ))( m m ))( n n ) (oo)+( p p ) (qq)(( r r ) (ss) (tt)(( u u ) dy)/( v v )(( w w ) dx)( x x ) (yy) (zz))^(( a a a )2( b b b ))( c c c )=0( d d d ) (eee) (c) ( d ) (e) y (f)(( g ) dx)/( h )(( i ) dy)( j ) (k)+x=1( l ) (m) (d) None of these

The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a) ( b ) (c)1+( d ) x^(( e )2( f ))( g ) (h) y^(( i )2( j ))( k )=c x (l) (m) (b) ( n ) (o)1+( p ) x^(( q )2( r ))( s ) (t) y^(( u )2( v ))( w )=c y (x) (y) (c) ( d ) (e) y=0( f ) (g) (d) ( h ) (i) y=-( j )1/( k )(( l ) (m) x^(( n )2( o ))( p ))( q ) (r) (s) (t)

An angle is double of its supplement. The measure of the angle is (a) ( b ) (c) (d) (e) 60^(( f )0( g ))( h )\ ( i ) (j) (b) ( k ) (l) (m) (n) 120^(( o )0( p ))( q ) (r) (s) (t) ( u ) (v) (w) (x) 40^(( y )0( z ))( a a ) (bb) (cc) (d) ( d d ) (ee) (ff) (gg) 80^(( h h )0( i i ))( j j ) (kk) (ll)

The differential equation of all non-horizontal lines in a plane is (a) ( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q) (r) (s) (b) ( t ) (u) (v)(( w ) (x) d^(( y )2( z ))( a a ) x)/( b b )(( c c ) d (dd) y^(( e e )2( f f ))( g g ))( h h ) (ii)=0( j j ) (kk) (c) ( d ) (e) (f)(( g ) dy)/( h )(( i ) dx)( j ) (k)=0( l ) (m) (d) ( n ) (o) (p)(( q ) dx)/( r )(( s ) dy)( t ) (u)=0( v ) (w)

The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (a) ( b ) (c) (d) x^(( e )2( f ))( g ) y+( h )(( i ) (j) x^(( k )3( l ))( m ) (n) y^(( o )3( p ))( q ))/( r )3( s ) (t)=c (u) (v) (b) ( w ) (x) x (y) y^(( z )2( a a ))( b b )+( c c )(( d d ) (ee) x^(( f f )3( g g ))( h h ) (ii) y^(( j j )3( k k ))( l l ))/( m m )3( n n ) (oo)=c (pp) (qq) (c) ( d ) (e) (f) x^(( g )2( h ))( i ) y+( j )(( k ) (l) x^(( m )4( n ))( o ) (p) y^(( q )4( r ))( s ))/( t )4( u ) (v)=c (w) (x) (d) None of these

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )+2(( l ) (m) x-y (n))+21n (o)(( p )(( q ) (r) x-1( s ))(( t ) (u) y+1( v )))/( w ) c (x) (y)=0( z ) (aa) (bb) ( c c ) (dd) (ee) x^(( f f )2( g g ))( h h )+( i i ) y^(( j j )2( k k ))( l l )+2(( m m ) (nn) x-y (oo))+1n (pp)(( q q )(( r r ) (ss) x-1( t t ))(( u u ) (vv) y+1( w w )))/( x x ) c (yy) (zz)=0( a a a ) (bbb) (ccc) ( d d d ) (eee) (fff) x^(( g g g )2( h h h ))( i i i )+( j j j ) y^(( k k k )2( l l l ))( m m m )+2(( n n n ) (ooo) x-y (ppp))-21n (qqq)(( r r r )(( s s s ) (ttt) x-1( u u u ))(( v v v ) (www) y+1( x x x )))/( y y y ) c (zzz) (aaaa)=0( b b b b ) (cccc) (dddd) None of these

Solution of (dy)/(dx)+2x y=y is (a) ( b ) (c) y=c (d) e^( e ) (f) x-( g ) x^((( h )2( i ))( j ) (k))( l ) (m) (n) (b) ( o ) (p) y=c( q ) e^( r ) (s) (t) x^((( u )2( v ))( w )-x (x))( y ) (z) (aa) (c) ( d ) (e) y=c( f ) e^(( g ) x (h))( i ) (j) (k) (d) ( l ) (m) y=c (n) e^( o ) (p)-( q ) x^((( r )2( s ))( t ) (u))( v ) (w) (x)

In which of the following differential equation degree is not defined? (a) ( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q)+3( r ) (s)(( t ) (u) (v)(( w ) dy)/( x )(( y ) dx)( z ) (aa) (bb))^(( c c )2( d d ))( e e )=xlog( f f )(( g g ) (hh) d^(( i i )2( j j ))( k k ) y)/( l l )(( m m ) d (nn) x^(( o o )2( p p ))( q q ))( r r ) (ss) (tt) (uu) (vv) ( w w ) (xx) (yy)(( z z ) (aaa) d^(( b b b )2( c c c ))( d d d ) y)/( e e e )(( f f f ) d (ggg) x^(( h h h )2( i i i ))( j j j ))( k k k ) (lll)+( m m m ) (nnn)(( o o o ) (ppp) (qqq)(( r r r ) dy)/( s s s )(( t t t ) dx)( u u u ) (vvv) (www))^(( x x x )2( y y y ))( z z z )=xsin( a a a a )(( b b b b ) (cccc) d^(( d d d d )2( e e e e ))( f f f f ) y)/( g g g g )(( h h h h ) d (iiii) x^(( j j j j )2( k k k k ))( l l l l ))( m m m m ) (nnnn) (oooo) (pppp) (qqqq) ( r r r r ) (ssss) x=sin(( t t t t ) (uuuu) (vvvv)(( w w w w ) dy)/( x x x x )(( y y y y ) dx)( z z z z ) (aaaaa)-2y (bbbbb)),|x|<1( c c c c c ) (ddddd) (eeeee) ( f f f f f ) (ggggg) x-2y=log(( h h h h h ) (iiiii) (jjjjj)(( k k k k k ) dy)/( l l l l l )(( m m m m m ) dx)( n n n n n ) (ooooo) (ppppp))( q q q q q ) (rrrrr)

OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIAL EQUATIONS-Chapter Test

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