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If the coefficients of second, third and fourth terms in the expansion of `(1 + x)^(2n)` are in A.P., show that `2n^(2) - 9n + 7=0`.

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ICSE-BINOMIAL THEOREM-EXERCISE 13 (a)
  1. Write out the expansions of the following: (3x-y)^(4)

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  2. Write out the expansions of the following: (3+2x^(2) )^(4)

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  3. Write out the expansions of the following: (c ) (x- (y)/(2) )^(4)

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  4. Write out the expansion of the following: (2x + (y)/(2) )^(5)

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  5. Write out the expansions of the following: (e ) (1+2x)^(7)

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  6. Write out the expansions of the following: (f) ((2)/(x) - (x)/(2) )^...

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  7. Using binomial theorem, expand [ ( x+y)^(5) + (x-y)^(5) ] and hence fi...

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  8. Expand (2+ x)^(5) - (2- x)^(5) in ascending powers of x and simplify y...

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  9. Evaluate the following: (i) (2 + sqrt(5) )^(5) + (2 - sqrt(5) )^(5) ...

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  10. If the first three terms in the expansion of (1 + ax)^(n) in ascending...

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  11. Find the first three terms in the expansion of [ 2+ x ( 3+ 4x)]^(5) in...

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  12. Expand (1+ 2 x + 3x^(2) )^(n) in a series of ascending powers of x up ...

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  13. Write down the expansion by the binomial theorem of (3x - (y)/(2) )^(4...

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  14. Using binomial theorem, evaluate : (999)^(3).

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  15. Write down in terms of x and n, the term containing x^3 in the expans...

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  16. (i) Obtain the binomial expansion of (2- sqrt(3) )^(6) in the form a+b...

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  17. Find the coefficient of x^5 in the expansion of (1 + 2x)^6 (1-x)^7.

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  18. If the coefficients of second, third and fourth terms in the expansion...

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  19. Let n be a positive integer. If the coefficients of 2nd, 3rd, 4th term...

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  20. In the binomial expansion of ( root(3) (4) + sqrt(2) )^5 find the term...

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