Page 56 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions
For a binomial (x + y) , the expansion is given by
n
n
(x + y) = C x + C x n – 1 y + C x n – 2 y + ....... + C x y = C (x) n – r y r
n
n
n
n
n
n
n
0
n
2
0 1 2 n r
r 0
Where C (x) n – r y is the general term i.e. (r + 1) term in the expansion.
n
th
r
r
Based on the above information, answer the following questions.
1. Find the binomial coefficient of 18 term in the bionomial (P + Q) 58
th
(a) 58 C (b) 58 C (c) 58 C (d) 58 C
17 18 0 9
2. In the binomial (x + y) , the 4 term is
6
th
(a) 25x y (b) 20x y (c) 25x y (d) None of these
3 3
3 3
4 2
3. In the binomial expansion of (x + y) , which term is equal to 35a b
4 3
7
(a) 3 (b) 4 (c) 7 (d) 5 th
th
rd
th
4. Find the coefficient of a in the expansion of (1 + 2a + a )
2 30
40
(a) 58 C (b) 30 C (c) 60 C (d) None of these
40 40 40
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Q. 1. Assertion (A) : C + C + C + ....... = 2 n – 1
n
n
n
0 2 4
Reason (R) : C + C + C + ....... = 2 n – 1
n
n
n
1
5
3
Q. 2. Assertion (A) : The r term from the end in the expansion of (x + a) is C x r – 1 n – r + 1
a
n
n
th
n – r + 1
Reason (R) : The r term from the end in the expansion of (x + a) is (n – r + 2) term.
th
n
th
Q. 3. Assertion (A) : In the binomial expansion of (a + b) , the r term is C (a) n – r b .
th
n
r
n
r
Reason (R) : If n is odd, then there are two middle terms.
Answers
Case-Study Based Questions: 1. (a) 2. (b) 3. (b) 4. (c)
Assertion-Reason Based Questions: 1. (a) 2. (a) 3. (d)
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