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Match List - I with List-II...

Match List - I with List-II

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`[(1)to(P,R)],[(2)to(P,Q,R,S)],[(3)to(P,Q)],[(4)to(Q,R,S)]`
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. In reference to the expansion (1+x)^n=sum(r=0)^nCrx^r, n in N, match t...

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  2. Match List - I with List-II

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  3. Match List - I with List-II

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  4. If 6^83+8^83 is divided by 49, then the sum of the digits of remainder...

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  5. Given (1-2x+5x^2-10x^3)(1+x)^n=1+a1x+a2x^2+.... and that a1^2=2a2, the...

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  6. The digit in the units place of the decimal representation of 7^1000 i...

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  7. The remainder, if 1+2+2^2+2^3+....+2^1999 in divided by 5 is

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  8. The sum of possible values of x for which the fifth term in the expans...

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  9. Find the coefficient of x^24 in (x^2+(3a)/x)^15

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  10. If in the expansion of (1+x)^43 the coefficient of (2r+1)^(th) term in...

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  11. The coefficient of the middle term of the expansion of (1-2x+x^2)^n is

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  12. Find the coefficient of x^4 in the expansion of (1+x-2x^2)^7

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  13. If the coefficients of four consecutive terms in the expansion of (1+x...

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  14. If (1+x)^n=sum(r=0)^nCrx^r prove that (2^2C0)/(1 . 2)+(2^3C1)/(2 . 3)+...

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  15. If p+q=1, then show that sum(r=0)^nr^2^nCrp^rq^(n-r)=npq+n^2p^2

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  16. Prove that C1+C5+C9+....=1/2(2^(n-1)+2^(n//2)sin((npi)/4))

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  17. Prove that C1+C4+C7+....=1/3[2^n-2cos((n+1)/3pi)]

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  18. Prove that (2nC0)^2-(2nC1)^2+(2nC2)^2+.....+(2nC2n)^2=(-1)^n2nCn

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  19. The coefficient of x^9 in the expansion of (1+x)(1+x^2)(1+x^3)....(1+x...

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  20. The sum of coefficient of integral powers of x in the binomial expansi...

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