SATHEE: Permutations And Combinations Question 324

Permutations And Combinations Question 324

Question: Let P be a prime number such that $ p\ge 11. $ Let $ n=p!+1. $ The number of primes in the list $ n+1, $ $ n+2,n+3,…n+P-1, $ is

Options:

A) $ p-1 $

B) 2

C) 1

D) None of these

Show Answer

Answer:

Correct Answer: D

Solution:

[d] For $ 1\le i\le p-1,p! $ is divisible by $ (i+1) $ Thus, $ n+i=p!+(i+1) $ is divisible by $ (i+1) $ for $ 1\le i\le p-1 $

$ \therefore $ None of $ n+1,n+2,…n+p-1 $ is prime.

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Permutations And Combinations Question 324

Question: Let P be a prime number such that $ p\ge 11. $ Let $ n=p!+1. $ The number of primes in the list $ n+1, $ $ n+2,n+3,…n+P-1, $ is

Options:

Answer:

Solution:

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