Zero Level Binomial Theorem 04
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1 Zeo Level Biomial Theoem 0 Usig biomial theoem, epad the epasios of the Fid the th tem fom the ed i the epasio of followig : (i ( (ii, 0 Fid the th tem fom the ed i the epasio of (iii ( (iv ( a (v ( (vi, 0 Fid the th tem fom the ed i the epasio of (vii, 0 (viii a a Fid the th tem fom the ed i the epasio of (i ( ( ( (i ( (ii 0 Fid the umbe of tems i the epasios of the Fid the middle tem i the epasio of followig : 0 Fid the middle tems i the epasios of the followig: (i ( (ii ( a (iii [( ( ] (iv [( ( ] (i b (ii Usig biomial theoem, epad the followig : 0 a (i ( ( (iii (iv a (ii Fid the middle tems i the epasios of the followig: (iii ( ( (i Evaluate the followig : (ii (i ( ( (ii ( ( (iii ( ( (iv ( ( (iii (iv (v ( ( Wite the geeal tem i the epasios of the Fid the middle tems i the epasios of the followig: followig: ( ( (i (ii, 0 ( Fid the th tem i the biomial epasio of (iii (iv ( Fid the coefficiet of i the epasio of Fid the th tem i the epasio of, whe 0 a Fid the coefficiet of i the epasio of Fid the th tem i the epasio of a Fid the th tem i the epasio of Fid the coefficiet of i the epasio of Fid the th tem i the epasio of a / / / / ( Fid the coefficiet of i the epasio of Fid the th tem fom the ed i the epasio of ( 0 Fid the coefficiet of i the epasio of Class XI, Zoe-II, MP Naga, Bhopal : 0-
2 Fid the coefficiet of i the epasio of Fid the coefficiet of m i the epasio of 0 Fid the tem idepedet of i the epasio of the followig : (i (ii (iii (iv (v (vii / / (i Fid the coefficiet of ( ( Fid the coefficiet of ( ( (vi (viii Class of XI ( ae i AP, fid the value, of Zoe-II, MP Naga, Bhopal : 0- i the epasio of the poduct i the epasio of the poduct Fid, if the coefficiet of th ad th tems i the epasio of a b ( ae equal The d, th ad th tems i the epasio of ( a ae espectivel, 0, ad 0, fid the values of, a, ad Fid a, if the coefficiet of ad i the epasio of ( a ae equal If the coefficiet of ( th tem ad ( th tem i the epasio of ( ae equal fid Fo what value of, the coefficiets of ( th ad ( th tems i the epasio of ( ae equal Pove that the coefficiet of ( th tem i the epasio of ( is equal to the sum of the coefficiet of th ad ( th tems i the epasio of ( The coefficiets of ( th, th ad ( th tems i the epasio of ( ae i the atio : : fid ad 0 The coefficiet of th, th ad th tems i the epasio of ( ae i AP, fid If the coefficiets of d, d ad th tems i the epasio of ( ae i AP, show that 0 If the coefficiet of d, d ad th tems i the epasio I the epasio of ( the biomial coefficiets of thee cosecutive tems ae espectivel 0, ad, fid the value of If thee cosecutive coefficiets i the epasio of ( ae espectivel, ad 0, fid If the coefficiets of thee cosecutive tems i the epasio of ( be, ad, fid If the th, th ad th tems i the epasio of ( a ae espectivel, ad /, fid, a, If the d, d ad th tems i the epasio of ( a ae espectivel 0, 0 ad 0, fid, a, If i the epasio of (, the coefficiet of pth ad qth tems ae equal, pove that p q, whee p q If the coefficiet of ( p th ad ( p biomial epasio of th tems i the ( ae equal, the pove that p 0 If a, b, c ad d i a biomial epasio be the th, th, th ad th tems espectivel, the pove that b ac a c bd c If P occus i the epassio of, pove that its coefficiet is (! p p!! Pove that thee is o tem ivolvig of, whee 0 i the epasio Pove that the tem idepedet of i the epasio of is ( (! If the coefficiet of is a ad the coefficiet b of i betwee a ad b a ae equal, the fid the elatio b If the coefficiet of ad m ( ( i the epasio of ae ad espectivel Fid m ad Fid the value of fo which the coefficiet of the middle tems i the epasios of ( ad ( ae
3 equal, fid Usig biomial theoem, compute the followig : (i ( (ii ( Usig biomial theoem, pove that is divisible b, whee N Usig biomial theoem, pove that is divisible b, whee N 0 Usig biomial theoem, pove that alwas the emaide whe divided b How ma tems ae fee fom adical sigs i the epasio of / / ( Class XI, Zoe-II, MP Naga, Bhopal : 0-
4 ANSWERS (i (ii 0 0 (i (ii (iii ( (iv ( C C, (! [(!], (iii (iv a 0 a 0 a 0 a a (v (vi (vii 0 a a a (viii 0 a a a (i ( (i 0 (ii (i (ii (iii (iv (i (ii (iii 0 0 (i (ii (iii (iv (v C ( C ( C ( C ( ( T 0 0 T T C a T 0 C C (i a b (ii 0 (iii (iv 0 C (i ad (ii (iii, 0, 0 C 0 a 0 C (iv, Class XI, Zoe-II, MP Naga, Bhopal : 0-! m m!! 0 (i 00 (ii ( C (iii (iv (v / (vi C (vii C (viii / (i ( (, a, a /, 0 o,, a /,, a ab m, 0, (i (ii 00
5 VPM Itelliget Mathematics Class - XI Vishal Pakasha Madi B - Bhupeda Sigh Eecise -, Class XI, Zoe-II, MP Naga, Bhopal : 0-
I PUC MATHEMATICS CHAPTER - 08 Binomial Theorem. x 1. Expand x + using binomial theorem and hence find the coefficient of
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