Divide: `3y^5+6y^4+6y^3+7y^2+8y+9\ b y\ 3y^3+1` and verify that `d i v i d e d\ =\ d i v i s o r\ xx\ q uot i e n t\ +\ r e m a i n d e r`

If x^3+y^3+3a x y=0 , f i n d dy / dx

The empirical relation between mean, mode and median is (a) Mod e\ =\ 3\ M e d i a n\ -2\ M e a n (b) Mod e=2\ M e d i a n-3\ M e a n (c) M e d i a n=3\ Mod e-2\ M e a n (d) M e a n=3\ M e d i a n-2\ Mod e

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

E v a l u a t e\ (3. 2 x^6y^3)xx(2. 1 x^2y^2)w h e n\ x=1\ a n d\ y=0. 5

Add the following: (i) 3x\ a n d\ 7x (ii) -5x y\ a n d\ 9x y

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

The area bounded by the y=2-x^2a n d\ x+y=0 is (a) 7/2s qdotu n i t s b. 9/2\ s qdotu n i t s c. 9\ s qdotu n i t s d. none of these

The value of a flat worth Rs. 500000 is depreciating, at the rate of 10% p.a. In how many years will it' value be reduced to Rs. 364500? 3\ y e a r s b. 4\ y e a r s c. 5\ y e a r s d. 6\ y e a r s

Comprehension 1 Let x ,\ y ,\ z in R^+&\ D=|xx^3x^4-1y y^3y^4-1z z^3z^4-1| If x!=y!=z\ &\ x ,\ y ,\ z are in A.P. and D=o,\ t h e n\ 2x^2z+x^2z^2 is equal to a. 1 b. 2 c. 3\ d. none of these

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)