11 maths impq 08 binomial theorem kvs

8/10/2019 11 Maths Impq 08 Binomial Theorem Kvs

1/3

Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 5

CHAPTER-8

BINOMIAL THEOREM)

Points to be remembered:-

1. If 'n' is a natural no., 'x' & 'a' are any two nos. then (x+a)n=

nC0x

n+

nC1

x(n-1)

a+nC2 x

(n-2)a

2+.......+

nCrx

(n-r)a

r+.........+

nCna

n.

2. General term: T(r+1)=nCrx

(n-r)a

r

3. Middile terms:

(a) If 'n' is even,there is only one middle term.

Required middle term=T((n/2)+1)

(b) If 'n' is odd, there are two middle terms.

Required middle terms are= T((n+1)/2)and T((n+3)/2)

4. (r+1)th term from end in the expansion of (x+a)(r+1beginning in the

expansion of (x+a)^n.

SHORT ANSWER TYPE QUESTIONS(1 MARK EACH)

1. Find the 3rd term in the expansion of (2x+3/x2)7

2. Write the general term in the expansion of (3x2-1/5x)

8

3. Write the values of6C0+

6C1+

6C2+......

6C6

4. Find the term void of 'x' in the expansion of (x/a +a/x)12

5. Find the no. of terms in the expansion of (1+x)12

+ (1-x)12

6. Find 'n' if the coefficient of 3rd term from the end in the expansion of

(1+x)nis 45

KVS, ZIET-BHUBANESHWAR


2/3


7. Find teh no. of non-zero terms in gthe expansion of (1+3

8. Find the coefficients of xm

and xnin the expansion of (1+x)

(m+n)

9. If p+q=1, then find the value value of

10. If the coefficient of (r+4)th

& (2r+1)th

terms in the expansion of (1+x)18

are equal, find 'r'

11. Find the middle term in the expansion of (x+ 1/x)6

12. Write the 1st two terms in the expansion of (1+0.01)10000

13. Using binomial theorem , evaluate (11)

4

14. Find the term containing x

3in the expansion of (x-2y)

7

15. Find the integral parts of

LONG ANSWER TYPE QUESTIONS (4 MARKS EACH)

1.

Simplify (x+y)6

+ (x-y)6

and hence evaluate

( 2 +3)6+ (23)

6

2. Using binomial theorem prove that 3(2n+2)

-8n-9 is divisible by 64 for all

n belongs to N.

3. Find 'a' ,'b' & 'n' if the 1st three terms in the expansion of (a+b)n are

729,7290 & 30375

4. If 6th

, 7th

, 8th

& 9th

terms in the expansion of (x+y)nare a,b,c & d then

prove that (b2-ac)/(c

2-bd) =4a/3c

5. Find the coefficient of 'x' in the expansion of (1-2x^3+3x^5)(1+1/x)^8?

6. If the term free from 'x' in the expansion of ( 12x)10

is

405, find 'k'?



3/3


7. If 'n' is an even positive integer,show that the middle term in the

expansion of (x+1/x)nis equal to

nCn/2

8. Prove that the coefficient of xnin the expansion of (1+x)

2nis twice the

coefficient of xnin the expansion of (1+x)(2n-1)

9. If the coefficient of (r-1)th, rth and (r+1)th terms in the expansion of

(1+x)nare in the ration 1:3:5 ,find both 'n' & 'r'?

10. If a1,a2,a3& a4are the coefficients of any 4 consecutive terms in the

expansion of (1+x)n, prove that

(a1/(a1+a2)) +(a3/(a3+a4)) = 2a2/(a2+a3)


11 maths impq 08 binomial theorem kvs

Documents