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If x prop (y+z) , y prop (z+x) and z pr...

If x `prop (y+z) , y prop (z+x) and z prop(x+y)` and if k, l and m are the variation constants of them respectively , then prove that `(k)/(k+1) +(l)/(l+1) +(m)/(m+1) =1`.

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CALCUTTA BOOK HOUSE-VARIATION-EXERCISE
  1. If (x+y) prop z when y is constant and (z+x) prop y when z is cons...

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

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

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  5. A large sphere is made by melting two gold - spheres of raii r and r r...

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  6. 2 men can cultivate 6 acres of land in 4 days . By using theory of var...

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  7. 15 men can cultivate 18 bighas of land in 5 days. By using theory of v...

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  8. If 5 men can cultivate 10 acres of land in 9 days,then by usnig theory...

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  9. In a fort there was reserved enough food of 2400 soldires for 39 days...

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  10. If 5 men working 6 hours a day can complete a work in 20 days , in how...

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  11. The length of a pendulum varies inversely as the square of the number ...

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  12. If x prop yz^2, y prop ab^2 and zprop b/a , then find how x varies wit...

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  13. if in the variation x =ky and y=k'z, a,b,c and a' ,b',c' be two sets o...

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  14. If ax^2+2hxy+by^2 prop z^2 and (lx+my) prop z where a,b,h,l,m are co...

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  15. If (u^2+v^2) prop (x^2 +y^2 ) and uv prop xy then show that (u+v) pro...

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  16. The area of circle varies directly as its radius . If the radius be 2 ...

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  17. The volume of a pyramid varies jointly as the height and the area of...

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  18. The volume of a right circualr cylinder varies as the square of the r...

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  19. The distance through which a heavy body falls from rest varies as the ...

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  20. If a stone falls s ft in t seconds from rest s propt^2 . If it is obs...

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