Assertion -A- The greatest positive integer which divides n-11n-12n-13n-14- n- N is 24- Reason- R- Product of any r consecutive integers is divisible by r -

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Byju's Answer

Standard XII

Mathematics

Permutation

Assertion :A:...

Question

Assertion :(A): The greatest positive integer which divides $(n + 11) (n + 12) (n + 13) (n + 14) \forall n \in N$ is $24$ . Reason: (R): Product of any $r$ consecutive integers is divisible by $r!$ .

Both (A) & (R) are individually true & (R) is 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 A Both (A) & (R) are individually true & (R) is correct explanation of (A).
Since the reason (R) is obvious.
So the greatest positive integer which divides the product $(n + 11) (n + 12) (n + 13) (n + 14)$ is $4! = 24$

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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]

Q. Assertion (A)
Sum of first n positive integers is given by

S_{n} = \frac{1}{2} n (n + 1) .

Reason (R)
In an AP with first term a and common difference d, the sum of nth terms is given by

S_{n} = \frac{n}{2} [2 a + (n - 1) d] .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a 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).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

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)
The HCF of two number is 9 and their LCM is 2016. If one of the numbers is 54, then the other is 306.
Reason (R)
For any positive integers a and b, we have:

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

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

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Assertion :(A): The greatest positive integer which divides (n+11)(n+12)(n+13)(n+14)∀n∈N is 24. Reason: (R): Product of any r consecutive integers is divisible by r!.

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).Since the reason (R) is obvious.So the greatest positive integer which divides the product (n+11)(n+12)(n+13)(n+14) is 4!=24

Assertion :(A): The greatest positive integer which divides $(n + 11) (n + 12) (n + 13) (n + 14) \forall n \in N$ is $24$ . Reason: (R): Product of any $r$ consecutive integers is divisible by $r!$ .

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).
Since the reason (R) is obvious.
So the greatest positive integer which divides the product $(n + 11) (n + 12) (n + 13) (n + 14)$ is $4! = 24$