Assertion :The expression $n! (10 - n)!$ is minimum for $n = 5$ Reason: The expression $^{2 m} C_{r}$ attains maximum value for $m = r$ .

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),
$∵ n! (10 - n!) = 10! (\frac{n! (10 - n)!}{10!}) = \frac{10!}{^{10} C_{n}}$ will be minimum If $^{10} C_{n}$ is maximum and its maximum value occurs at $n = \frac{10}{2} = 5$
$∴$ $^{10} C_{5} =^{2 m} C_{r} =^{2 \times 5} C_{5} \Rightarrow m = r$

Suggest Corrections

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)

\frac{1242}{49}

is a non-terminating, repeating decimal.
Reason (R)
The rational number

\frac{p}{q}

is a terminating decimal if q = (2m × 5n) for some whole numbers m and n.

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

Q. Assertion (A)
The polynomial p(x) = x³ + x has one real zero.

Reason (R)
A polynomial of nth degree has at most n zeros.

(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.

Join BYJU'S Learning Program

Assertion :The expression n!(10−n)! is minimum for n=5 Reason: The expression 2mCr attains maximum value for m=r.

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),∵n!(10−n!)=10!(n!(10−n)!10!)=10!10Cn will be minimum If 10Cn is maximum and its maximum value occurs at n=102=5 ∴ 10C5=2mCr=2×5C5⇒m=r

Assertion :The expression $n! (10 - n)!$ is minimum for $n = 5$ Reason: The expression $^{2 m} C_{r}$ attains maximum value for $m = r$ .