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)

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 equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these

The number of triangles that the four lines y = x + 3, y = 2x + 3, y = 3x + 2, and y + x = 3 form is (a) 4 (b) 2 (c) 3 (d) 1

The distance between the point ( acosalpha,asinalpha) and ( acosbeta,asinbeta) is (a) ( b ) (c) acos( d )(( e )alpha-beta)/( f )2( g ) (h) (i) (j) (b) ( k ) (l)2acos( m )(( n )alpha-beta)/( o )2( p ) (q) (r) (s) (c) ( d ) (e)2as in (f)(( g )alpha-beta)/( h )2( i ) (j)( k ) (l) (d) ( m ) (n) asin( o )(( p )alpha-beta)/( q )2( r ) (s) (t) (u)

Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K >0 is (a) ( b ) (c) (d)(( e ) dy)/( f )(( g ) dt)( h ) (i)+K=0( j ) (k) (b) ( l ) (m) (n)(( o ) d r)/( p )(( q ) dt)( r ) (s)-K=0( t ) (u) (c) ( d ) (e) (f)(( g ) d r)/( h )(( i ) dt)( j ) (k)=K r (l) (m) (d) None of these

If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 sq. units, then, a) l,m,n are in G.P b) l,n,m are in G.P. c) lm=n d) ln=m

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

If the straight lines 2x+3y-1=0,x+2y-1=0 ,and a x+b y-1=0 form a triangle with the origin as orthocentre, then (a , b) is given by (a) (6,4) (b) (-3,3) (c) (-8,8) (d) (0,7)

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1 ,then x equals (a) 4 (b) 8 (c) 16 (d) 64