Expansion part 1

Consider the binomial expansion of (sqrt(x)+(1/(2x^(1/4))))^n n in NN , where the terms of the expansion are written in decreasing powers of x. If the coefficients of the first three terms form an arithmetic progression then the statement(s) which hold good is(are) (A) total number of terms in the expansion of the binomial is 8 (B) number of terms in the expansion with integral power of x is 3 (C) there is no term in the expansion which is independent of x (D) fourth and fifth are the middle terms of the expansion

Assertion: In free expansion of a gas inside an aidabatic chamber Q, W and DeltaU all are zero. Reason: In such an expansion pprop1/V .

The first three terms in the expansion of a binomial are 1, 10 and 40 . Find the expansion.

If the sum of the coefficients in the expansion of (1 + 2x)^(n) is 6561 , the greatest term in the expansion for x = 1//2 , is

Find the decimal expansion of 1/7

The apparent coefficients of volume expansion of a liquid when heated filled in vessel A and B of identical volumes, are found to be gamma_(1) and gamma_(2) respectively. If alpha_(1) be the coefficient of liner expansion for A, then what will be the be the coefficient of linear expansion for B? (True expansion - vessel expansion = app.exp)

Assertion:- During adiabatic expansion of an ideal gas, temperature falls but entropy remains constant. Reason:- During adiabatic expansion, work is done by the gas using a part of internal energy and no heat exchange teakes place the system and the surrounding.

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)