SATHEE: Permutations and Combinations 1 Question 6

Permutations and Combinations 1 Question 6

6. An $n$ -digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$ -digit numbers are to be formed using only the three digits 2,5 and 7 . The smallest value of $n$ for which this is possible, is

$(1998, 2 M)$

(a) 6

(b) 7

(c) 8

(d) 9

Show Answer

Answer:

Correct Answer: 6. (c)

Solution:

Distinct $n$ -digit numbers which can be formed using digits 2,5 and 7 are $3^{n}$ . We have to find $n$ , so that

$\begin{aligned} 3^{n} & \geq 900 \\ \Rightarrow & 3^{n - 2} & \geq 100 \\ \Rightarrow & n - 2 & \geq 5 \end{aligned}$

$\Rightarrow n \geq 7$ , so the least value of $n$ is 7 .

पिछला

अगला

गोपनीयता नीति

द्वारा संचालित Prutor@IITK

sathee@iitk.ac.in

SATHEE का मीडिया कवरेज

खेल स्टोर

ऐप स्टोर

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Permutations and Combinations 1 Question 6

6. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7 . The smallest value of n for which this is possible, is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

6. An $n$ -digit number is a positive number with exactly $n$ digits. Nine hundred distinct $n$ -digit numbers are to be formed using only the three digits 2,5 and 7 . The smallest value of $n$ for which this is possible, is