Binomial Theorem

A binomial expression has two terms, which are connected by the operators ‘+’ or ‘–’. The total number of terms in the expansion of (a + b)n, for any positive integral n is (n + 1), i.e., one more than the index. In each term of the expansion of (a + b)n, for any positive integral n, the sum of the indices of a and b is same and equal to n. For any positive integer n, the binomial theorem is given by (a + b)n = nc0anb0 + nc1an – 1b1 + nc2an – 2b2 + … + ncna0bn, where nN. In the expansion of (a + b)n , nc0, nc1, nc2, ncn are called the binomial coefficients. The general term in the expansion of (a + b)n is given by (r + 1)th term, i.e., Tr + 1 = ncran – rbr, where 0 ≤ r ≤ n. In case of an even index, the number of the middle terms in the expansion of (a + b)n is one and is given by [(n/2) + 1]th term. In case of an odd index, the number of the middle terms in the expansion of (a + b)n is two which are given by [(n + 1)/2]th term and [(n + 1)/2 + 1]th term.

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  • Q1

    5th term in the expansion of (x - y)6 is

    Marks:1
    Answer:

    15 x2 y4.

    Explanation:

    The general term in the expansion of (x - y)6 is given by

        Tr+1 = 6Cr(x)6-r.(-y)r

     T4+1 = (-1)4.6C4.x6-4y4

               =15 x2 y4

     

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  • Q2

    The position of middle term in the expansion of (1 + x)20 is

    Marks:1
    Answer:

    11th term.

    Explanation:

    Total number of terms = 20+1 =21

    Middle term = (21+1)/2 = 11th term

     

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  • Q3

    The position of middle term in the expansion of (1 + x)20 is

    Marks:1
    Answer:

    11th term.

    Explanation:

    Total number of terms = 20+1 =21

    Middle term = (21+1)/2 = 11th term

     

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  • Q4

    5th term in the expansion of (x - y)6 is

    Marks:1
    Answer:

    15 x2 y4.

    Explanation:

    The general term in the expansion of (x - y)6 is given by

    Tr+1 = 6Cr(x)6-r.(-y)r

    T4+1 = (-1)4.6C4.x6-4y4

    =15 x2 y4

     

    View Answer
  • Q5

    Marks:1
    Answer:

    r + 1.

    Explanation:

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