If y(x) satisfies the differential eq...

If `y(x)` satisfies the differential equation `y^(prime)-ytanx=2xs e c x` and `y(0)=0` , then (a) `( b ) (c) y(( d ) (e) (f)pi/( g )4( h ) (i) (j))=( k )(( l ) (m)pi^(( n )2( o ))( p ))/( q )(( r )8sqrt(( s )2( t ))( u ))( v ) (w) (x)` (y) (b) `( z ) (aa) (bb) y^(( c c )prime( d d ))( e e )(( f f ) (gg) (hh)pi/( i i )4( j j ) (kk) (ll))=( m m )(( n n ) (oo)pi^(( p p )2( q q ))( r r ))/( s s )(( t t ) 18)( u u ) (vv) (ww)` (xx) (c) `( d ) (e) y(( f ) (g) (h)pi/( i )3( j ) (k) (l))=( m )(( n ) (o)pi^(( p )2( q ))( r ))/( s )9( t ) (u) (v)` (w) (d) `( x ) (y) (z) y^(( a a )prime( b b ))( c c )(( d d ) (ee) (ff)pi/( g g )3( h h ) (ii) (jj))=( k k )(( l l )4pi)/( m m )3( n n ) (oo)+( p p )(( q q )2( r r )pi^(( s s )2( t t ))( u u ))/( v v )(( w w )3sqrt(( x x )3( y y ))( z z ))( a a a ) (bbb) (ccc)` (ddd)

`y(pi/2)=pi^2/(8sqrt2), y'(pi/3)=(4pi)/3 + (2pi^2)/(3sqrt3)`

`y(pi/4)=pi^2/(4sqrt2), y'(pi/4)=pi^2/18`

`y(pi/3)=pi^2/9, y'(pi/3) = (4pi)/3+pi^2/(3sqrt3)`

`y(pi/3)=pi^2/(4sqrt2), y'(pi/3)=pi^2/18`

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An angle is double of its supplement. The measure of the angle is (a) ( b ) (c) (d) (e) 60^(( f )0( g ))( h )\ ( i ) (j) (b) ( k ) (l) (m) (n) 120^(( o )0( p ))( q ) (r) (s) (t) ( u ) (v) (w) (x) 40^(( y )0( z ))( a a ) (bb) (cc) (d) ( d d ) (ee) (ff) (gg) 80^(( h h )0( i i ))( j j ) (kk) (ll)

In Fig.93, if A O C is a straight line, then x= (a) ( b ) (c) (d) (e) 42^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 52^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 142^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 38^(( q )0( r ))( s ) (t) (u)

In Fig.88 P R is a straight line and /_P Q S :/_S Q R=7: 5. The measure of /_S Q R is (a) ( b ) (c) (d) (e) 60^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) 62 (m) (n) (o)1/( p )2( q ) (r)^(( s )0( t ))( u ) (v) (w) (c) ( d ) (e) 67 (f) (g) (h)1/( i )2( j ) (k)^(( l )0( m ))( n ) (o) (p) (d) ( q ) (r) (s) (t) 75^(( u )0( v ))( w ) (x) (y)

In Fig.97, If A B is parallel to CD, then the value of /_B P E is (a) ( b ) (c) (d) (e) 106^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 76^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 74^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 84^(( q )0( r ))( s ) (t) (u)

Two complementary angles are in the ratio 2: 3. The measure of the larger angle is (a) ( b ) (c) (d) (e) 60^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 54^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 66^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 48^(( q )0( r ))( s ) (t) (u)

Two supplementary angles are in the ratio 3: 2. The smaller angle measures (a) ( b ) (c) (d) (e) 108^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 81^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 72^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 68^(( q )0( r ))( s ) (t) (u)

The sum of an angle and half of its complementary angle is 75^0dot The measure of the angle is (a) ( b ) (c) (d) (e) 40^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 50^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 60^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 80^(( q )0( r ))( s ) (t) (u)

In Fig.103, P Q R S\ a n d\ /_P A B=60^0\ a n d\ /_A C S=100^0dot Then, /_B A C= (a) ( b ) (c) (d) (e) 40^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 60^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 80^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 50^(( q )0( r ))( s ) (t) (u)

In Fig.104, A B C D ,\ /_O A B=150^0\ a n d\ /_O C D=120^0dot Then, /_A O C= (a) ( b ) (c) (d) (e) 80^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 90^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 70^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 100^(( q )0( r ))( s ) (t) (u)

The sum of an angle and one third of its supplementary angle is 90^0dot The measure of the angle is (a) ( b ) (c) (d) (e) 135^(( f )0( g ))( h ) (i) (j) (b) ( k ) (l) (m) (n) 120^(( o )0( p ))( q ) (r) (s) (c) ( d ) (e) (f) (g) 60^(( h )0( i ))( j ) (k) (l) (d) ( m ) (n) (o) (p) 45^(( q )0( r ))( s ) (t) (u)

TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -COMPETITIVE THINKING

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