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If (1+x)^n=sum(r=0)^n .^nCr x^r then sum...

If `(1+x)^n=sum_(r=0)^n .^nC_r x^r` then `sum_(r=m)^n .^rC_m` is equal to

A

`.^(n+1)C_m`

B

`.^(n+1)C_(m+1)`

C

`.^(n+2)C_(m+1)`

D

none of these

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The correct Answer is:
B
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
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  2. The greatest coefficient iin the expansion of (x+y+z+t)^(15) is

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  3. If (1+x)^n=sum(r=0)^n .^nCr x^r then sum(r=m)^n .^rCm is equal to

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  4. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  5. Give the integers rgt1 , ngt2 and c0-efficients of (3r)^th and (r+2)^(...

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  6. If n in I^+ the value of sum(k=1)^n k^3 (^nCk)/(^nC(k-1))^2

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  7. In a triangle ABC the value of sum(r=0)^(50) ^(50)Cr a^rb^(50-r) cos(R...

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  8. The value of "^30C0.^30C10+^30C1.^30C11+^30C2.^30C(12)+……+^30C(20) . ^...

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  9. The number of distinct terms in the expansion of (x^3+1+(1/x^3)): xinK...

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  10. The number of integral of integral terms in the expansion of (17^(1/3)...

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  11. The expression (x+sqrt(x^3-1))^7+(x-sqrt(x^3-1))^7 is a polynomial of ...

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  12. The coefficient of x^(50) in (1+x)^(41)(1-x+x^2)^(40)is

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  13. The coefficient of x^n in the expansion (2x+3)^n-(2x+3)^(n-1)(5-2x)+(2...

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  14. The coefficient of x^(65) in the expansion of (1+x)^(131)(x^2-x+1)^(30...

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  15. Remainder when 5^(40) is divided by 11.

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  16. If (1+x-2x^2)^6=1+a1x+a2x^2+……+a(12)x^12 then

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  17. Number of values of r satisfying the equation ,^69C(3r-1) -^(69)C(r^2)...

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  18. In the expansion of (x+(a/x^2))^n, (ane0) if term independent of x doe...

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  19. If f(n)=sum(r=1)^n[r(n ^(n-1)C(r-1)-r^C(r-1))+(2r+1)^nCr]

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  20. The value of ,^nC0 + ^(n+1)C1 +^(n+2)C2+……+^(n+k)Ck is equal to

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