11 maths impq 08 binomial theorem kvs
TRANSCRIPT
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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
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Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 6
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'?
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Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 7
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)
KVS, ZIET-BHUBANESHWAR