In Fig.113, if`\ A C D F\ a n d\ A B C E ,` then (a) `( b ) (c) x=145 ,\ y=223 (d)` (e) (b) `( f ) (g) x=223 ,\ y=145 (h)` (i) (c) `( d ) (e) x=135 ,\ y=223 (f)` (g) (d) `( h ) (i) x=233 ,\ y=135 (j)` (k)

In Fig.107, If A O B\ a n d\ C O D are straight lines, then (a) ( b ) (c) x=29 ,\ y=100 (d) (e) (b) ( f ) (g) x=100 ,\ y=29 (h) (i) (c) ( d ) (e) x=29 ,\ y=110 (f) (g) (d) ( h ) (i) x=39 ,\ y=110 (j) (k)

In Fig.113, if \ A C || D F\ a n d\ A B || C E , then (a) x=145 ,\ y=223 (b) x=223 ,\ y=145 (c) x=135 ,\ y=223 (d) x=233 ,\ y=135

In Fig.101, A B C D\ a n d\ E F is a transversal. The value of y-x is (a) 30 (b) 35 (c) 95 (d) 25

In Fig.101, A B C D\ a n d\ E F is a transversal. The value of y-x is (a) 30 (b) 35 (c) 95 (d) 25

In Figure, If A B || C D ,\ C D || E F\ a n d\ y : z=3:7, find x .

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)

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)

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

The circumcenter of the triangle formed by the line y=x ,y=2x , and y=3x+4 is (a) ( b ) (c)(( d ) (e)6,8( f ))( g ) (h) (b) ( i ) (j)(( k ) (l)6,8( m ))( n ) (o) (c) ( d ) (e)(( f ) (g)3,4( h ))( i ) (j) (d) ( k ) (l)(( m ) (n)-3,-4( o ))( p ) (q)

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)