Assertion: The term independent of x in the expansion of (x+(1/x)+2)m is ((4 m) !/(2 m !)2) Reason: The coefficient of x 6 in the expansion of (1+ x ) n is n C 6

Question

Assertion: The term independent of x in the expansion of (x+(1/x)+2)m is ((4 m) !/(2 m !)2) Reason: The coefficient of x 6 in the expansion of (1+ x ) n is n C 6 (A) Assertion is correct, reason is correct; reason is a correct explanation for assertion. (B) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (C) Assertion is correct, reason is incorrect (D) Assertion is incorrect, reason is correct

Tardigrade Admin · Accepted Answer

(x+(1/x)+2)m=((x2+2 x+1/x))m=((1+x)2 m/xm) Term independent of x is coefficient of xm in the expansion of (1+ x )2 m = 2 m C m =((2 m ) !/( m !)2) Coefficient of x6 in the expansion of (1+x)n is n C6

Q. Assertion : The term independent of x in the expansion of (x+x1​+2)m is (2m!)2(4m)!​ Reason : The coefficient of x6 in the expansion of (1+x)n is nC6​

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct

(x+x1​+2)m=(xx2+2x+1​)m=xm(1+x)2m​ Term independent of x is coefficient of xm in the expansion of (1+x)2m=2mCm​=(m!)2(2m)!​ Coefficient of x6 in the expansion of (1+x)n is nC6​

Q. Assertion : The term independent of $x$ in the expansion of $(x + \frac{1}{x} + 2)^{m}$ is $\frac{( 4 m )!}{( 2 m ! ) ^{2}}$
Reason : The coefficient of $x^{6}$ in the expansion of $(1 + x)^{n}$ is $^{n} C_{6}$