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Show that the coefficients of x^(m) and ...

Show that the coefficients of `x^(m)` and `x^(n)` are equal to the expansion of `(1+x)^(m+n)`.

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If the coefficient of x^(r)andx^(r+1) are equal in the expansion of (1+x)^(2n+1) , then find the value of r .

prove that the coefficient of the (r +1)th term in the expansion of (1+x)^(n) is equal to the sum of the coefficients of the rth and (r+1)th terms in the expansion of (1+x)^(n-1)

Show that the sum of the coefficients of the odd terms in the expansion of (1+x)^(2n)" is "2^(2n-1)

Show that the sum of the coefficient of first (r+1) terms in the expansions of (1-x)^(-n) is ((n+1)(n+2)...(n+r))/(r!)

If r gt 1, n gt2 are positive integers and the coefficients of (r+2) th and 3rd terms in the expansion of (1+x)^(2n) are equal, then n is equal to-

Show that the coefficient of the middle term in the expansion of (1+x)^(40) is equal to the sum of the coefficients of the two middle terms of (1+x)^(39) .

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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 find the value of n.

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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE (Very short answer Type Questions )
  1. Simplify : (2+sqrt(3))^(6) + (2-sqrt(3))^(6)

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  2. Simplify : (x+y)^(4) - 4y(x+y)^(3) + 6y^(2)(x+y)^(2)-4y^(3)(x+y)+y^(...

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  3. Simplify : (a-3)^(3) + 6(a-3)^(2)+12(a-3)+8

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  4. Simplify : (x+sqrt(x^(2)-1))^(7) + (x-sqrt(x^(2)-1))^(7)

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  5. Expand (3x-5/(x^3))^(8) up to the term independent of x.

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  6. Determine: 10th term in the expansion of (3a+2/a)^(12)

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  7. Determine: 4th term in the expansion of (a/b-b/a)^(10)

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  8. Determine: nth term in the expansion of (x+1/x)^(2n)

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  9. Determine: the general term in the expansion of (a-1/(3a))^(m)

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  10. 5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

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  11. Determine: (r+1)th term from the end in the expansion of (1-3x)^(n)...

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  12. Show that the coefficients of x^(m) and x^(n) are equal to the expansi...

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  13. Prove that the coefficents of x^(n) in the expansion of (1+x)^(2n) is ...

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  14. Prove that in the expansion of (1+x)^(57), the coefficents of x^(14) a...

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  15. Find the middle term (or terms) in the following expansions: (i) (x+...

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  16. Find the middle term (or terms) in the following expansions: (ii) ((...

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  17. Find the middle term (or terms) in the following expansions: (iii) (...

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  18. Find the middle term (or terms) in the following expansions: (iv) (2...

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  19. Using binomial therom find the value: (999)^(3)

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  20. Using binomial therom find the value: (101)^(4)

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