Page 42 - Math SL HB Sem 1

BNO\II.\L THEORE\4

8 Expand ( I - x - x2 ; 6 in ascendins por.r'ers of x until the rerm in x 3.
9 Evaluate the following using binomial rheorem:
a) (99)a (b) ( i03 )4

10. Use the expansion ( 2 x ro find the value of ( 1.98 ;: correct to 5 decimal places
- )j
tl Expand(2+x)a in ascending pow'ers ofx. Using this expansion- find
a) (2.1)a b) ( l.ef

x\
12. By substituting x = 0.05 in the binomial expansion I +:l , find the value of ( 1.01) 6
).)

correct to 4 decimal places.

13 In the expansion of( I + ax the coefficients ofxr and xa are the same. Find the
)10,

11. The expansion of( 1 + px )r0 in ascending powers ofx is given by

l+2x * li x2 + ..-Find the value ofp and n.
8
1 5. Let m and n be positive integers with mS n. If in the expansion of ( 1 + 2x
),' . the

J
coefficient of x' is times the coefficient of x ''-1. show.that m and n satisfies
2
4n-7m+4=0

Hence, find the value olm and n rhat satisfies the above equation
ANSWERS

l. (a)40320 (b) 120960 (c) 5040 (d) jt4
(e) 56 (f) l00l (g) t344

(n t)(n -2) " n+1
-
2. (a) l0 (b) 8i6 (c) (d) (n+2xn+l)n (e) (n+2xn+l) (fl
; \a--gt n+3
-
6 (a) 192tt2 (b) -960prro-ro (c) 210 (d) 31a928x7 1e) 5arb'yr
i
7 2l6x + 243x
6. I 6x + 2lx2-50 xr
9. (a) 96059601 (b) i 12s50881
10 r 8.89568
I I (a) l9 a48l (b) 1 3.032 I
12. I 06l5
l] 4i1
Il. n:16.p= l,/3