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If x prop y then x^(n) prop...

If x `prop ` y then x^(n) `prop`

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`x propy rArr x =ky` ( k =non zero variation constant )
`rArr (x)^(n) =(ky)^(n) ` (taking n-th power )
`rArr x^(n) =k^(n).y^(n). `
`rArrn^(n)=my^(n)` (when m =`k^(n) ne0=`variation constant )
`rArr x^(n)prop y^(n)` (`because` m =non -zero variation constant ).
`therefore x^(n) propy^(n) .`
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CALCUTTA BOOK HOUSE-VARIATION-EXERCISE
  1. If x prop y then x^(n) prop

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  2. If a prop1/b, then

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  3. If a prop b, then

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  4. If x prop y andy =20 when x=10. if y=10 then the value of x will be

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  5. If x propsqrt(y) and y=16 when x =3 . If y =64 ,then the positive valu...

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  6. If x^3 prop sqrt(y) and y =16 when x=4 then y=1 when x=2 .

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  7. If x varies inversely with y, then the value of (x+y) will be least wh...

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  8. If ax +b/y prop cx+d/y (where a ,b ,c ,d are constants ),then xy=

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  9. If (A^2+B^2 ) prop (A^2-B^2)then show that A prop

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  10. If x^2 prop a^2 then a prop

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  11. If x prop (1)/sqrt(a) , then a prop

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  12. If x^2 prop yz ,y^2 prop zx and z^2 prop xy, then find the product of...

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  13. y prop x^2 and y=9 when x =9 . If y =4 then find the value of x .

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  14. Given that A =B +C , where B prop x^2 and C prop x^3 . If x =1 , the...

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  15. If a prop b^2 and (1+b) prop sqrt© and if a=1 , then c=9 and b=5 , t...

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  16. If A varies directly with B and C both , then show that A varies direc...

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  17. If a/b prop (a+b) and b/a prop (a-b) , then show that a^2 -b^2 = const...

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  18. If (x+y) prop z when y is constant and (z+x) prop y when z is cons...

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  19. If x,y,z are variables , but (y+z-x) is a constant and if (x+y-z) prop...

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  20. If x prop (y+z) , y prop (z+x) and z prop(x+y) and if k, l and m are ...

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  21. A variable is the sum of two such quantities one of which varies dire...

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