The number of terms independent of x in the expansion of x-1x4+x+1x3 is
-3
0
3
1
Explanation for correct option:Given x-1x4+x+1x3
We know that (x+y)n=C0n路xn+C1n路xn-1路y1+C2n路xn-2路y2+.....+Cn-1n路x1路yn-1+Cnn路ynExpansion of given expression=4C0x4.-1x0+4C1x3.-1x1+4C2x2.-1x2+4C3x1.-1x3+4C4x0.-1x4+3C0x3.1x0+3C1x2.1x1+3C2x1.1x2+3C3x0.1x3=4C0x4-4C1x2+4C2-4C31x2-4C41x4+3C0x3+3C1x+3C21x+3C31x3Therefore only one term is independent of x i.e. C24
Hence option(D) is correct.
Determine whether the following numbers are in proportion or not:
13,14,16,17