4) (x-a) 4m (x a) l) h (h a la t by a -b)

If y=|[f(x), g(x), h(x)],[ l, m , n],[ a , b , c]| prove that (dy/dx)=|[f'(x), g'(x), h'(x)],[ l, m , n],[ a , b , c]|

If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)) is xAAx in R (b) {x , xi si r r a t ion a l1-x ,xi sr a t ion a l {x ,xi sr a t ion a l1-x ,xi si r r a t ion a l (d) none of these

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)

If x+y=pi/4a n dtanx+tany=1,t h e n(n in Z) (a) sinx=0a l w a y s (b)when x=npi+pi/4t h e ny=-npi (c)when x=npit h e ny=npi+(pi/4) (d)when x=npi+pi/4t h e ny=npi-(pi/4)

If x+y=pi/4a n dtanx+tany=1,t h e n(n in Z) (a) sinx=0a l w a y s (b)when x=npi+pi/4t h e ny=-npi (c)when x=npit h e ny=npi+(pi/4) (d)when x=npi+pi/4t h e ny=npi-(pi/4)

T h e v a l u eofint_0^oo(dx)/(1+x^4)i s (a) s a m ea st h a tofint_0^oo(x^2+1dx)/(1+x) (b) pi/(2sqrt(2)) (c) s a m ea st h a tofint_0^oo(x^2+1dx)/(1+x^4) (d) pi/(sqrt(2))

f is a continous function in [a, b] ; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x) for x in [a,b) , g(x) for x in (b,c] if f(b) =g(b) then (A) h(x) has a removable discontinuity at x = b. (B) h(x) may or may not be continuous in [a, c] (C) h(b-) = g(b+ ) and h(b+ ) = f(b- ) (D) h(b+ ) = g(b- ) and h(b- ) = f(b+ )

The figure shows the variation of photocurrent with anode potential for a photosensitve surface for three different radiations. Let l_a, l_b and l_c be the curves a, b and c, respectively (a) f_a = f_b and l_a != l_b (b) f_a = f_c and l_a = l_c (c ) f_a = f_b and l_a = l_b (d) f_b = f_c and l_b = l_c

The figure shows the variation of photocurrent with anode potential for a photosensitve surface for three different radiations. Let l_a, l_b and l_c be the curves a, b and c, respectively (a) f_a = f_b and l_a != l_b (b) f_a = f_c and l_a = l_c (c ) f_a = f_b and l_a = l_b (d) f_b = f_c and l_b = l_c

Find the volume in cubic metre (cu. m) of each of the cuboids whose dimensions are: l e n g t h\ =\ 12 m ,\ b r e a dt h=10 m ,\ h e igh t=4. 5 m l e n g t h\ =\ 4m ,\ b r e a dt h\ =\ 2. 5 m ,\ h e igh t\ =\ 50 c mdot l e n g t h\ =\ 10 m ,\ b r e a dt h\ =\ 25 d m ,\ h e igh t\ =\ 25 c mdot