`I f(3a-b)xx(a+3b)=k axxbv a l u e o fk ?`

If a and b are vectors such that |a+b|=sqrt(29) and a xx(2i+3j+4k)=(2i+3j+4k)xx b, then a possivalue of (a+b)*(-7i+2j+3k) is

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

If a = 2i + 2j + k, a.b = 14, a xx b = 3i + j - 8k then b =

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 solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h )(( i ) (j) y^(( k )2( l ))( m ))/( n )2( o ) (p)+( q )1/( r )3( s ) (t) (u) (v)(( w ) (x) (y) x^(( z )2( a a ))( b b )+( c c ) y^(( d d )2( e e ))( f f ) (gg))^(( h h ) (ii) (jj)3/( k k )2( l l ) (mm) (nn))( o o )=c (pp) (qq) (rr) ( s s ) (tt) x+( u u )(( v v ) (ww) y^(( x x )3( y y ))( z z ))/( a a a )3( b b b ) (ccc)+( d d d )1/( e e e )2( f f f ) (ggg) (hhh) (iii)(( j j j ) (kkk) (lll) x^(( m m m )2( n n n ))( o o o )+( p p p ) y^(( q q q )2( r r r ))( s s s ) (ttt))^(( u u u ) (vvv) (www)1/( x x x )2( y y y ) (zzz) (aaaa))( b b b b )=c (cccc) (dddd) (eeee) ( f f f f ) (gggg) x-( h h h h )(( i i i i ) (jjjj) y^(( k k k k )2( l l l l ))( m m m m ))/( n n n n )2( o o o o ) (pppp)+( q q q q )1/( r r r r )3( s s s s ) (tttt) (uuuu) (vvvv)(( w w w w ) (xxxx) (yyyy) x^(( z z z z )2( a a a a a ))( b b b b b )+( c c c c c ) y^(( d d d d d )2( e e e e e ))( f f f f f ) (ggggg))^(( h h h h h ) (iiiii) (jjjjj)3/( k k k k k )2( l l l l l ) (mmmmm) (nnnnn))( o o o o o )=c (ppppp) (qqqqq)

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)

If a=1+2j-3k,b=2i+j-k and u is a vector satisfying a times u=a times b and a .u=0 then 2|u|^(2) is equal to

The solution of (y+x+5)dy=(y-x+1)dx is (a) ( b ) (c)log(( d ) (e) (f) (g)(( h ) (i) y+3( j ))^(( k )2( l ))( m )+( n ) (o)(( p ) (q) x+2( r ))^(( s )2( t ))( u ) (v))+( w ) (x)tan^(( y ) (z)-1( a a ))( b b ) (cc)(( d d ) y+3)/( e e )(( f f ) y+2)( g g ) (hh)+C (ii) (jj) (kk) ( l l ) (mm)log(( n n ) (oo) (pp) (qq)(( r r ) (ss) y+3( t t ))^(( u u )2( v v ))( w w )+( x x ) (yy)(( z z ) (aaa) x-2( b b b ))^(( c c c )2( d d d ))( e e e ) (fff))+( g g g ) (hhh)tan^(( i i i ) (jjj)-1( k k k ))( l l l ) (mmm)(( n n n ) y-3)/( o o o )(( p p p ) y-2)( q q q ) (rrr)+C (sss) (ttt) (uuu) ( v v v ) (www)log(( x x x ) (yyy) (zzz) (aaaa)(( b b b b ) (cccc) y+3( d d d d ))^(( e e e e )2( f f f f ))( g g g g )+( h h h h ) (iiii)(( j j j j ) (kkkk) x+2( l l l l ))^(( m m m m )2( n n n n ))( o o o o ) (pppp))+2( q q q q ) (rrrr)tan^(( s s s s ) (tttt)-1( u u u u ))( v v v v ) (wwww)(( x x x x ) y+3)/( y y y y )(( z z z z ) x+2)( a a a a a ) (bbbbb)+C (ccccc) (ddddd) (eeeee) ( f f f f f ) (ggggg)log(( h h h h h ) (iiiii) (jjjjj) (kkkkk)(( l l l l l ) (mmmmm) y+3( n n n n n ))^(( o o o o o )2( p p p p p ))( q q q q q )+( r r r r r ) (sssss)(( t t t t t ) (uuuuu) x+2( v v v v v ))^(( w w w w w )2( x x x x x ))( y y y y y ) (zzzzz))-2( a a a a a a ) (bbbbbb)tan^(( c c c c c c ) (dddddd)-1( e e e e e e ))( f f f f f f ) (gggggg)(( h h h h h h ) y+3)/( i i i i i i )(( j j j j j j ) x+2)( k k k k k k ) (llllll)+C (mmmmmm) (nnnnnn)