The expansion (a+x)^(n) = .^(n)c(0)a^(n)...

The expansion `(a+x)^(n) = .^(n)c_(0)a^(n) + ^(n)c_(1)a^(n-1)x +` ………… +` .^(n)c_(n)x^(n)` is valid when n is

An integer

A rational number

An irrational number

A natural number

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When n is any postive integer,the expansion (x+a)^(n) = .^(n)c_(0)x^(n) + .^(n)c_(1)x^(n-1)a + ……. + .^(n)c_(n)a^(n) is valid only when

The value of ""(n)C_(1). X(1 - x )^(n-1) + 2 . ""^(n)C_(2) x^(2) (1 - x)^(n-2) + 3. ""^(n)C_(3) x^(3) (1 - x)^(n-3) + ….+ n ""^(n)C_(n) x^(n) , n in N is

The value of .^(n)C_(0).^(n)C_(n)+.^(n)C_(1).^(n)C_(n-1)+...+.^(n)C_(n).^(n)C_(0) is

The middle term in the expansion of ((2x)/(3)-(3)/(2x^(2)))^(2n) is ^(2n)C_(n) b.(-1)^(n)2nC_(n)x^(-n) c.^(2n)C_(n)x^(-n)d .none of these

sum_(n=1)^(oo) (""^(n)C_(0) + ""^(n)C_(1) + .......""^(n)C_(n))/(n!) is equal to

if (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a++.^(n)C_(2)a^(2)+ . . .+.^(n)C_(n)a^(n) , then prove that (.^(n)C_(1))/(.^(n)C_(0))+(2(.^(n)C_(2)))/(.^(n)C_(1))+(3(.^(n)C_(3)))/(.^(n)C_(2))+. . . +(n(.^(n)C_(n)))/(.^(n)C_(n-1))= Sum of first n natural numbers.

If (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a+.^(n)C_(2)a^(2)+ . . +.^(n)C_(n)a^(n) , then prove that .^(n)C_(1)+2.^(n)C_(2)+3.^(n)3C_(3)+ . . .+n.^(n)C_(n)=n.2^(n-1) .

""^(n)C_(r)+^(n)C_(r+1)=^(n+1)C_(x) ,then x=?

The value of (n+2).^(n)C_(0).2^(n+1)-(n+1).^(n)C_(1).2^(n)+(n).^(n)C_(2).2^(n-1)-….." to " (n+1) terms is equal to

AAKASH INSTITUTE-BINOMIAL THEOREM-Assignment (section-A)

A binomial is
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The expansion (a+x)^(n) = .^(n)c(0)a^(n) + ^(n)c(1)a^(n-1)x + ………… + ....
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If the coefficient of rth term and (r+1)^(th) term in the expansion of...
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When n is any postive integer,the expansion (x+a)^(n) = .^(n)c(0)x^(n)...
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If n is a positive integer, then the number of terms in the expansion ...
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The term independent of x in the expansion of (2x+1/(3x))^(6) is
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The 6th term of expansion of (x-1/x)^(10) is
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The number of the terms which are not similar in the expansion of (L+M...
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The exponent of x occuring in the 7th term of the expansion of ((ax)/2...
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The term containing a^(3)b^(4) in the expansion of (a-2b)^(7) is
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The term independent of x in the expansion of (x-3/x^(2))^(18) is
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In the expansion of (x^(3)-2/x^(2))^(12), fifth term from the end is
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If m and n are positive integers, then prove that the coefficients of ...
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The number of terms in expansion of {(a+4b)^(3)(a-4b)^(3)}^(2) is
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If r^(th) term in the expansion of (x^(2)+1/x)^(12) is independent of ...
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The non zero terms in the expansion of (1+3sqrt(2)a)^(9)+(1-3sqrt(2)a)...
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In the expansion of (2+1/(3x))^(n), the cofficient of x^(-7) and x^(-...
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In in the expansion of (1+px)^(q), q belongs to N, the coefficients of...
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The expansion of (x^(alpha)+1/x^(beta))^(n) has constant term, if
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The number of rational terms in the expansion of ((25)^(1/3) + 1/(25)^...
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