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Prove that ""^(m+n)C(r) = ""^(m)C(r) ...

Prove that
`""^(m+n)C_(r) = ""^(m)C_(r) + ""^(m)C_(r-1) + ""^(n)C_(1) + ""^(m)C_(r-2) ""^(n)C_(2) +…+ ""^(n)C_(r)`
If ` r ltm, r lt n ` and m,n,r and positive integers .

A

`(""^(n)C_(r))^(2)`

B

`""^(m+n)C_(r)`

C

`""^(m+n)C_(r) + ""^(m)C_(r) + ""^(n)C_(r)`

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. If (1+x)^(n) = C(0) + C(1) xm + C(2)x^(2) + "……" + C(n)x^(n), then ...

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  2. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

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  3. Prove that ""^(m+n)C(r) = ""^(m)C(r) + ""^(m)C(r-1) + ""^(n)C(1) +...

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  4. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

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  5. The term independent of x in the expansion of (x-1/x)^(4) (x+1/x)^(3) ...

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  6. if the coefficients of x^(5)" and "x^(15) in the expansion of (x^(2)+(...

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  7. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  8. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  9. about to only mathematics

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  10. The coefficient of x^(n) in the expansion of (1)/((1-x)(3 -x)), is

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  11. The coefficient of x^(n) in the expansion of ((1+x)^(2))/((1 - x)^(3))...

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  12. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

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  13. The coefficient of x^(6) in the expansion of (1 + x + x^(2))^(-3) is

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  14. The coefficient of x^n in the expansion of (1 + x+x^2+...........)^-...

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  15. If the binomial expansion of (a +b x)^-2 is 1/4-3x+......., then (a, ...

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  16. If C(r) = ""^(n)C(r) and (C(0) + C(1)) (C(1) + C(2)) … (C(n-1) + C(n))...

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  17. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

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  18. If p is nearly equal to q and n gt 1 , such that ((n+1) p+(n-1)q)/(...

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  19. If y=3 x + 6 x^(2) + 10 x^(3) +… then x =

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  20. If y = (1)/(3) + (1*3)/(3 *6) + (1 * 3*5)/(3*6*9) +… then the value ...

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