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Let m be the smallest positive integer s...

Let m be the smallest positive integer such that the coefficient of `x^2` in the expansion of `(1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50` is `(3n + 1) .^51C_3` for some positive integer n. Then the value of n is

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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the coefficient of pth, (p+1)thand (p+2)th terms in the expansion ...

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  2. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

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  3. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+ ,a n da1=a2=10...

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  4. In the binomial expansion of (a - b)^(n) , n ge 5 , the sum of the ...

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  5. The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...

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  6. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

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  7. The remainder left out when 8^(2n)""(62)^(2n+1) is divided by 9 is (1)...

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  8. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

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  9. So, statement-1 is also true. Stetement-2 is a correct expanation fo...

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  10. The coefficient of x^(7) in the expansion of (1-x-x^(2) + x^(3))^(6) i...

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  11. If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is ...

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  12. In the expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^10 ...

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  13. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

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  14. If the coefficients of x^(3) and x^(4) in the expansion of (1 + ax + b...

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  15. Coefficient of x^(11) in the expansion of (1+x^2)(1+x^3)^7(1+x^4)^(12)...

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  16. The sum of coefficients in integral powers of x in the binominal expan...

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  17. The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...

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  18. If the number of terms in the expansion of (1-2/x+4/(x^2))^n , x!=0, i...

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  19. Let m be the smallest positive integer such that the coefficient of x^...

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  20. The value of (.^(21)C(1) - .^(10)C(1)) + (.^(21)C(2) - .^(10)C(2)) + (...

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