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Trigonometry

Principle of Mathematical Induction

Complex Numbers

Quadratic Equations

Permutations and Combinations

Binomial Theorem

Sequence and Series

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Limits and Derivatives

Statistics

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Conic Section

Introduction to ThreeDimensional Geometry

Mathematical Reasoning

Correlation Analysis

Index Numbers and Moving Averages
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 nN. 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
Find the number of terms in the expansion of [(x + y)^{3}(x  y)^{3}]^{2}.
Marks:1Answer:
[(x + y)^{3}(x  y)^{3}]^{2 }= [(x^{2}  y^{2})^{3}]^{2 }= (x^{2}  y^{2})^{6}
No. of terms in the expansion = n + 1 = 6 + 1 = 7

Q2
Find the coefficient of x^{2} in the expansion of (x + 1)^{6}.
Marks:1Answer:

Q3
Find the middle term in the expansion of
Marks:1Answer:

Q4
Write the general term for (x  a)^{n}.
Marks:1Answer:

Q5
State binomial theorem for (x + a)^{n}.
Marks:1Answer: