Page 42 - Math SL HB Sem 1

BNO\,II.\L THEORE\{

8. Erpand ( I -x -*2 i, ascending por,r'ers of x until the rerm in x l.
6
1
9. Evaluate the following using binomial rheorem:

a) ( 99 )a (b) ( 103 )4

x
10.. Use the expansion ( 2 - )j to find the value oi ( r.98 )j correct to 5 decimal praces,
11. Expand ( 2 + r ) a in ascending powers ofr. Usine this expansion. find
a)(2t)a b)(1.9)4

:
x
12. By substituting x 0.05 in the binomial expansion 1+- 6 , find the vatue of ( i.01) 6
)
corect to 4 decimal places.

13 In the expansion of( 1 + ax )r0, &e coefficients ofx3 and xa are the same. Find the

r,..1'r,: Ol- a.
14 The expansion of( 1 +px )10 in ascending powers ofx is given by

I +2y + !1 ,' ', . . . Find the value of p and n.
8
1 5. Let m and n be positive integers with m< n. If in ttre expansion of ( I + 2x ),, . the

-l
coefficient of xm i times the coefficient of x'-1. show that m and n satisfies
2
4r-'7m+4-0

Hence, fir-rd the value of m and n thal satisfies the above equation
ANSWERS

L (a)40320 (b) 120960 (c) 50a0 (d) 7i4
(e) 56 (f) l00l (g) lsaa

(n t)(n -2) ' n+1
2. (a) l0 (b) 816 (c) (d (n+2xn+i )n (e) (n-2[n-l) (f)
)
.'(n4)| n+3
-
6. (a) 792rt2 (b) -96opuo-ro (c) 2lO (d) 3la928xi (e) 5a-rbayr
7.216x+243xi
8. I 6x+2lx?-50xj
9. (a) 960i9601 (b) 1125s0881
10. r 8.89568
I 1. (a) 19.4481 (b) I3.0321
t2. I.06t5
t3 4/1
14. n=l6. p: i/8