Which of the following is correct order of size of `M^(3+)` ions of `Ce(58),Sm(62),Dy(66)" and "Yb(70)?`
(A) `Ce>Sm>Dy>Yb`
(B) `Yb>Dy>Sm>Ce`
(C) `Ce>Dy>Sm>Yb`
(D)`Ce>Dy=Sm>Yb`

Which of the following statements is not true for Ce^(3+) and Yb^(3+) ?

Which of the following lanthanoid ions is diamagnetic? (Atomic number of Ce=58,Sm=62,Eu=63,Yb=70 ]

Which is the correct order of ionic sizes ? (Atomic no . : Ce = 58 , Sn = 50 , Yb = 70 and Lu)

Which of the followig lanthanoid ions are coloured (a). Lu^(+3) (b). Pm^(+3) (c). Sm^(+3) (d). Eu^(+3)

The correct order of ionic radii of Ce, La, Pm and Yb in +3 oxidation state is

Which of the following equation(s) is/are linear? (a) dy/dx+y/x=lnx(b) y(dy/dx)+4x=0(c)(2x+y^3)(dy/dx)=3y (d)N.O.T.

In which of the following differential equation degree is not defined? (a) ( b ) (c) (d)(( e ) (f) d^(( g )2( h ))( i ) y)/( j )(( k ) d (l) x^(( m )2( n ))( o ))( p ) (q)+3( r ) (s)(( t ) (u) (v)(( w ) dy)/( x )(( y ) dx)( z ) (aa) (bb))^(( c c )2( d d ))( e e )=xlog( f f )(( g g ) (hh) d^(( i i )2( j j ))( k k ) y)/( l l )(( m m ) d (nn) x^(( o o )2( p p ))( q q ))( r r ) (ss) (tt) (uu) (vv) ( w w ) (xx) (yy)(( z z ) (aaa) d^(( b b b )2( c c c ))( d d d ) y)/( e e e )(( f f f ) d (ggg) x^(( h h h )2( i i i ))( j j j ))( k k k ) (lll)+( m m m ) (nnn)(( o o o ) (ppp) (qqq)(( r r r ) dy)/( s s s )(( t t t ) dx)( u u u ) (vvv) (www))^(( x x x )2( y y y ))( z z z )=xsin( a a a a )(( b b b b ) (cccc) d^(( d d d d )2( e e e e ))( f f f f ) y)/( g g g g )(( h h h h ) d (iiii) x^(( j j j j )2( k k k k ))( l l l l ))( m m m m ) (nnnn) (oooo) (pppp) (qqqq) ( r r r r ) (ssss) x=sin(( t t t t ) (uuuu) (vvvv)(( w w w w ) dy)/( x x x x )(( y y y y ) dx)( z z z z ) (aaaaa)-2y (bbbbb)),|x|<1( c c c c c ) (ddddd) (eeeee) ( f f f f f ) (ggggg) x-2y=log(( h h h h h ) (iiiii) (jjjjj)(( k k k k k ) dy)/( l l l l l )(( m m m m m ) dx)( n n n n n ) (ooooo) (ppppp))( q q q q q ) (rrrrr)

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

Which of the following is a homogeneous differential equation? (A) (4x + 6y + 5) dy - (3y + 2x + 4) dx = 0 (B) (x y)dx-(x^3+y^3)dy=0 (C) (x^3+2y^2)dx+2x ydy=0 (D) y^2dx+(x^2+x y-y^2)dy=0

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) ( b ) (c) P=y+x (d) (e) (b) ( f ) (g) P=y-x (h) (i) (c) ( d ) (e) P+Q=1-x+y+y +( f ) (g)(( h ) (i) y^(( j )prime( k ))( l ) ( m ))^(( n )2( o ))( p ) (q) (r) (s) ( t ) (u) P-Q=x+y-y -( v ) (w)(( x ) (y) y^(( z )prime( a a ))( b b ) ( c c ))^(( d d )2( e e ))( f f ) (gg) (hh)