Assertion -If f x -xn then f 1 -f- 1 -1-f- 1 -2-f- 1 -3-nf 1 -n-2n Reason- If 1-x n-r-0nnCrxr- then -r-0nnCr-2n

Assertion (A) Addition reaction of water to but-1-ene in acidic medium yields butan-1-ol.
Reason (R) Addition of water in acidic medium proceeds through the formation of primary carbocation.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

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Assertion :If f(x)=xn then f(1)+f′(1)1+f′′(1)2!+f′′′(1)3!+...+nf(1)n!=2n Reason: If (1+x)n=n∑r=0nCrxr, then n∑r=0nCr=2n

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertionf(x)=f(1)+f′(1)(x−1)+f′′(1)2!(x−1)2+....+fn(1)n!(x−1)nf(x)=xn⟹ put x=2⟹f(1)+f′(1)1+f′′(1)2!+⋯+fn(1)n!=2n(1+x)n=n∑r=0CrxrPut x=1⟹n∑r=0Cr=(1+1)n=2n

Assertion :If $f (x) = x^{n}$ then $f (1) + \frac{f^{'} (1)}{1} + \frac{f^{''} (1)}{2!} + \frac{f^{'''} (1)}{3!} + . . . + \frac{^{n} f (1)}{n!} = 2^{n}$ Reason: If ${(1 + x)}^{n} = n \sum r = 0^{n} C_{r} x^{r}$ , then $n \sum r = 0^{n} C_{r} = 2^{n}$