Assertion - - r-0 n r-1 nCr-n-22n-1 Reason- - r-0 n r-1 nCr-1-xn-nx1-xn-1

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Standard XII

Mathematics

Existence of Limit

Assertion : ...

Question

Assertion : $\sum_{r = 0}^{n} {r + 1}^{n} C_{r} = (n + 2) 2^{n - 1}$ Reason: $\sum_{r = 0}^{n} {r + 1}^{n} C_{r} = (1 + x)^{n} + n x (1 + x)^{n - 1}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$n \sum r = 0 r + 1^{n} C_{r} = (n + 2) 2^{n - 1}$
$= n 2^{n - 1} + 2^{n}$
$\Rightarrow n s u m + (1 + x)^{m}$
$\Rightarrow n 2^{n - 1} + 2^{n}$
Reason $= n \sum r = 0 r + {1.}^{n} C_{r} = (1 + x)^{n} + n x (1 + x)^{n - 1}$

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Similar questions

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

The correct answer is :(a) /(b) /(c) /(d)

Q. Assertion: The compressibility factor for

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H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

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Assertion (A) Bond angle in ethers is slightly less than the tetrahedral angle.
Reason (R) There is a repulsion between the two bulky (- R) groups.
(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.

Assertion (A) Order of the reaction can be zero or fractional.

Reason (R) We cannot determine order from balanced chemical equation.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

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Assertion :∑nr=0r+1nCr=(n+2)2n−1 Reason: ∑nr=0r+1nCr=(1+x)n+nx(1+x)n−1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertionn∑r=0r+1nCr=(n+2)2n−1 =n2n−1+2n⇒n sum+(1+x)m⇒n2n−1+2nReason =n∑r=0r+1.nCr=(1+x)n+nx(1+x)n−1

Assertion : $\sum_{r = 0}^{n} {r + 1}^{n} C_{r} = (n + 2) 2^{n - 1}$ Reason: $\sum_{r = 0}^{n} {r + 1}^{n} C_{r} = (1 + x)^{n} + n x (1 + x)^{n - 1}$