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)

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 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)

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 sin beta is the G.M between sin alpha and cos alpha , then cos 2 beta is

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 line joining A(bcosalphabsinalpha) and B(acosbeta,asinbeta) is produced to the point M(x ,y) so that A M and B M are in the ratio b : adot Then prove that x+ytan(alpha+beta/2)=0.

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .

If theta is eliminated from the equations x=a"cos"(theta-alpha) and y=bcos(theta-beta), then (x^2/a^2)+(y^2/b^2)-(2xy)/(ab)cos(alpha-beta) is equal to (a) sec^2(alpha-beta) (b) cos e c^2(alpha-beta) (c) cos^2(-beta) (d) sin^2(alpha-beta)

Let (sin(theta-alpha))/("sin"(theta-beta))=a/b a n d(cos(theta-alpha))/("cos"(theta-beta))=c /d t h e n(a c+b d)/(a d+b c)= (a) cos(alpha-beta) (b) sin(alpha-beta) (c) sin(alpha+beta) (d) none of these