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State true or false. The product of K co...

State true or false. The product of K consecutive natural numbers is divisible by K!.

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MBD PUBLICATION-Elements of Mathematics-QUESTION BANK
  1. State true or false. There is a term independent of both x and y in th...

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  2. State true or false. The highest power in the expansion of x^40(x^2+1/...

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  3. State true or false. The product of K consecutive natural numbers is d...

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  4. Answer the following: If 6th term in the expansion of (x+*)^n is equal...

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  5. Find the number of terms in the expansion of (1+x)^n(1-x)^n.

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  6. Find the value of "^nC(r-1)//"^nCr

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  7. How many terms in the expansion of (3/a+a/3)^10 have positive powers o...

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  8. Find the middle term in the expansion of the (a/b+b/a)^6.

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  9. Find the middle term in the expansion of the (x+1/x)^9

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  10. Find the middle term in the expansion of the (x^(3/2)-y^(3/2))^8

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  11. Find the 6th term in the expansion of (x^2+a^4/y^2)^10.

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  12. Find the fifth term in the expansion of (6x-a^3/x)^10

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  13. Find the coefficient of 1/y^10 in the expansion of (y^3+a^7/y^5)^10

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  14. In the expansion of (y^3+a^7/y^5)^10, Does there exist a term indepen...

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  15. Find the coefficient of x^4 in the expansion of (1+3x+10x^2)(x+1/x)^10

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  16. Find the term independent of x in the above expansion. (1+3x+10x^2)(x+...

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  17. Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) a...

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  18. An expression of the form (a+b+c+d+ .... ) consisting of sum of many d...

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  19. State and prove a multinomial Theorem.

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  20. Prove that "^(2n)C0 + ^(2n)C2 + .... + ^(2n)C(2n) = 2^(2n-1)

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