AP POLYCET MATHEMATICS Multiple Choice Questions (MCQs)

AP POLYCET Mathematics - Binomial Theorem: Multiple Choice Questions

121. What is the general term in the expansion of (a + b)^n?

     1. (a) n! / [(n - r)! * r!] * a^(n-r) * b^r
     2. (b) n * a^(n-r) * b^r
     3. (c) a^n + b^r
     4. (d) a^r * b^(n-r)

     Answer: a

122. In the binomial expansion of (1 + x)^n, the sum of coefficients is:

     1. (a) n + 1
     2. (b) 2^n
     3. (c) n^2
     4. (d) n!

     Answer: b

123. The coefficient of x^3 in the expansion of (1 + x)^6 is:

     1. (a) 15
     2. (b) 10
     3. (c) 20
     4. (d) 6

     Answer: a

124. The total number of terms in the expansion of (a + b)^n is:

     1. (a) n
     2. (b) n + 1
     3. (c) 2n + 1
     4. (d) n - 1

     Answer: b

125. The middle term in the expansion of (x + y)^{10} is:

     1. (a) 5th term
     2. (b) 6th term
     3. (c) 7th term
     4. (d) 8th term

     Answer: b

126. If the binomial expansion of (1 + x)^n contains 11 terms, the value of n is:

     1. (a) 10
     2. (b) 11
     3. (c) 12
     4. (d) 9

     Answer: a

127. The binomial theorem is valid only for:

     1. (a) Positive integers
     2. (b) Negative integers
     3. (c) Rational numbers
     4. (d) All real numbers

     Answer: a

128. The sum of the binomial coefficients in the expansion of (x + y)^7 is:

     1. (a) 14
     2. (b) 7
     3. (c) 128
     4. (d) 64

     Answer: c

129. The term independent of x in the expansion of (x + 1/x)^6 is:

     1. (a) 15
     2. (b) 20
     3. (c) 6
     4. (d) 10

     Answer: d

130. The coefficient of x^4 in the expansion of (1 - x)^8 is:

     1. (a) -70
     2. (b) 70
     3. (c) -35
     4. (d) 35

     Answer: a

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