Question

Assertion :Binomial theorem expression can be derived from multinomial theorem by substituting $K=2$ in the expression of the multinomial theorem. Reason: Binomial theorem is the generalization of the Multinomial theorem.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Let

$(1+a+b{)}^2={\sum }_{r=0}^2{}^2{C}_r(a+b{)}^r$

$(1+a+b{)}^2={}^2{C}_0(a+b{)}^0+{}^2{C}_1(a+b)+{}^2{C}_2(a+b{)}^2$

$(1+a+b{)}^2={}^2{C}_0+{}^2{C}_1(a+b)+{}^2{C}_2(a^2+2ab+b^2)$

Above is the general from of binomial expansion

And multinomial expansion is the extend form of binomial expansion