(a) Add: `p(p-q), q(q-r) and r(r-p)` (l) add: `2x(z-x-y) and 2y(z-y-x)` (w) Subtract: `3l(l-4m+5n) from 4l(10n-3m+2l)` (ii) (d) Subtract: `3a(a+b+c)-2b(a-b+c) from 4c(-a+b+c)`
(a) Add: `p(p-q), q(q-r) and r(r-p)` (l) add: `2x(z-x-y) and 2y(z-y-x)` (w) Subtract: `3l(l-4m+5n) from 4l(10n-3m+2l)` (ii) (d) Subtract: `3a(a+b+c)-2b(a-b+c) from 4c(-a+b+c)`
Text Solution
AI Generated Solution
Let's solve the given problems step by step.
### Part (a): Add \( p(p - q), q(q - r), \) and \( r(r - p) \)
1. **Expand each expression:**
- \( p(p - q) = p^2 - pq \)
- \( q(q - r) = q^2 - qr \)
- \( r(r - p) = r^2 - rp \)
...
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
Subtract: 3l\ (l-4m+5n) from 4l(10 n-3m+2l)
Add: (i) p\ (p-q), q(q-r) and \ r\ (r-p) (ii) 2x\ (z-x-y)\ and \ 2y\ (z-y-x)
Solution of (dy)/(dx)+2x y=y is (a) ( b ) (c) y=c (d) e^( e ) (f) x-( g ) x^((( h )2( i ))( j ) (k))( l ) (m) (n) (b) ( o ) (p) y=c( q ) e^( r ) (s) (t) x^((( u )2( v ))( w )-x (x))( y ) (z) (aa) (c) ( d ) (e) y=c( f ) e^(( g ) x (h))( i ) (j) (k) (d) ( l ) (m) y=c (n) e^( o ) (p)-( q ) x^((( r )2( s ))( t ) (u))( v ) (w) (x)
The equation of a curve passing through (1,0) for which the product of the abscissa of a point P and the intercept made by a normal at P on the x-axis equal twice the square of the radius vector of the point P is (a) ( b ) (c) (d) x^(( e )2( f ))( g )+( h ) y^(( i )2( j ))( k )=( l ) x^(( m )4( n ))( o ) (p) (q) (b) ( r ) (s) (t) x^(( u )2( v ))( w )+( x ) y^(( y )2( z ))( a a )=2( b b ) x^(( c c )4( d d ))( e e ) (ff) (gg) (c) ( d ) (e) (f) x^(( g )2( h ))( i )+( j ) y^(( k )2( l ))( m )=4( n ) x^(( o )4( p ))( q ) (r) (s) (d) None of these
If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1
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)
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 (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)
If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1
NCERT ENGLISH-ALGEBRAIC EXPRESSIONS AND IDENTITIES-EXERCISE 9.3
- Find the product. (i) (a^2) xx (2a^22) xx (4a^26) (ii) (2/3 xy) xx ...
Text Solution
|
- Complete the table.
Text Solution
|
- Carry out the multiplication of the expressions in each of the followi...
Text Solution
|
- (a) Add: p(p-q), q(q-r) and r(r-p) (l) add: 2x(z-x-y) and 2y(z-y-x...
Text Solution
|
- (a) Simpify 3 xx (4x-5)+3 and find its values for (i) x=3 (ii) x=1/2....
Text Solution
|