Page 55 - Mathematics Class - XI

Viva-Voce

1. Write the coefficients of binomial expansion of (x + y) .
8
Ans. Coefficients are 1, 8, 28, 56, 70, 56, 28, 8, 1

2. State the binomial theorem for positive integral index.
Ans. If x and y are real numbers, then for all n ∈ N.
y + ... C
(x + y) = C x y + C x n – 1 1 n n – 2 2 n n – r r n x y + C x y
y + C x
y + ... C x
n
1 n – 1
n
n
0 n
n
n 0
0 1 2 r n – 1 n
n
i.e., (x + y) = ∑ n C r x nr− y r
n
r = 0
3. How many terms are in the binomial expansion of (x + y) ?
9
Ans. Since, any binomial expansion is raised to power 9, there will be 10 terms in the expansion.
4. What is Pascal’s triangle used for?
Ans. Pascal’s triangle can be used to determine the expanded pattern of coefficients.
5. “The number of terms in the expansion of (x + y) where n ∈ N is one less than the power n.” Is this
n
statement True or False?
Ans. Since, the number of terms in the given expression (x + y) is 1 more than n, i.e., n + 1.
n
Hence, the given statement is False.

MCQs

1. After the solution of (x + a) + (x – a) , then the total number of terms will be
100
100
a) 202 b) 51 c) 50 d) None of these
5
2. The value of 51 51 5 is

a) 252 b) 352 c) 452 d) 532

3. In the expansion of (1 – x – x + x ) , the coefficient of x is
3 6
7
2
a) –144 b) 132 c) 144 d) –132
4. In the expansion of (1 + x) and (1 + x) 2n – 1 , the coefficients of x are A and B, then A/B is equal to
2n
n
a) 1 b) 2 c) 1 d) 1
2 n
5. In the expansion of the function 1 + (1 + x) + (1 + x) + .......... + (1 + x) , the coefficient of x (0 < k < n) is
k
2
n
a) n + 1 C b) C c) C d) None of these
n
n
k + 1 k n – k – 1
9
9
6. In the expansion of 13 2 x 1 32 x , the number of non-zero terms is
a) 9 b) 0 c) 5 d) 10
Answers: 1. b) 51 2. b) 352 3. a) –144 4. b) 2 5. a) n + 1 c k + 1 6. c) 5

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