Assertion -The value of - 51- 3 - 50- 3 - 49- 3 - 48- 3 - 47- 3 - 47- 4 - is equal to - 52- 4 - Reason- n-1Cr- nCr-1-n-1Cr-1

The correct option is C (A) is true but (R) is false,We have, nbsp; ^nC_r + ^nC_r+1 = ^n+1C_r+1 Hence, reason is incorrect. nbsp; ^47C_4+^47C_3 = ^ ...

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Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

Assertion :Th...

Question

Assertion :The value of $(\begin{matrix} 513 \end{matrix}) + (\begin{matrix} 503 \end{matrix}) + (\begin{matrix} 493 \end{matrix}) + (\begin{matrix} 483 \end{matrix}) + (\begin{matrix} 473 \end{matrix}) + (\begin{matrix} 474 \end{matrix})$ is equal to $(\begin{matrix} 524 \end{matrix})$ Reason: $^{n - 1} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1}$

Both (A) & (R) are individually true & (R) is the correct explanation of (A),

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Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

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(A) is true but (R) is false,

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(A) is false but (R) is true.

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Solution

The correct option is C (A) is true but (R) is false,
We have,
$^{n} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1}$
Hence, reason is incorrect.
$^{47} C_{4} +^{47} C_{3} =^{48} C_{4}$
Similarly,
$^{48} C_{4} +^{48} C_{3} =^{49} C_{4}$
Similarly, we can compute for the other terms. Hence, the sum of the given series is $^{52} C_{4}$ .
Hence, the Assertion is true but the Reason is false.

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Similar questions

DIRECTIONS (Qs. 52 AND 53): The following item consist of two statements: one labelled as the Assertion a) and the other as Reason (R). You are to examine these two statements carefully and select the answers to these items using the codes given below:

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

53. Assertion a): Saluva Narasimha put an end to the old dynasty and assumed the royal title.

Reason

(R): He wanted to save the kingdom from further degeneration and disintegration. [2003]

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

52. Assertion a): Shah Alam II spent the initial years as an emperor far away from his capital.

Reason

(R): There was always a lurking danger of foreign invasion from the north-west frontier. [2003]

Q. Assertion(A): Some algae are unicellular.
Reason(R): They belong to the kingdom Monera.

Q. Assertion :the works of most of the Bhakti Saints became immensely popular. Reason: Most of the works were composed in regional languages and could be sung.
(1) A is true but R is false
(2) A is false but R is true
(3) Both A and R are true and R is the correct explanation of A
(4) Both A and R are true but R is not the correct explanation of A

Q. Regarding the assertion and reason, choose the correct option.
Assertion [A]: Deforestation is one main factor contributing to global warming.
Reason [R]: Besides CO₂, methane and CFCs are also greenhouse gases.

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Assertion :The value of (513)+(503)+(493)+(483)+(473)+(474) is equal to (524) Reason: n−1Cr+nCr+1=n+1Cr+1

The correct option is C (A) is true but (R) is false,We have, nCr+nCr+1=n+1Cr+1Hence, reason is incorrect. 47C4+47C3=48C4Similarly, 48C4+48C3=49C4Similarly, we can compute for the other terms. Hence, the sum of the given series is 52C4.Hence, the Assertion is true but the Reason is false.