Resolve into partial fractions for the following : \(\frac{2 x^2-5 x-7}{(x-2)^3}\)

Resolve into partial fractions for the following : \(\frac{x^2-6 x+2}{x^2(x+2)}\)

Resolve into partial fractions for the following : \(\frac{1}{\left(x^2+4\right)(x+1)}\)

Show that the middle term in the expansion of (1 + x)²ⁿ is \(\frac { 1.3.5....(2n-1){ 2 }^{ n }.{ x }^{ n } }{ n! } \)

How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?