Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Help me please, - Consider the statement : is prime. Then which one of the following is true? - Mathematical Induction - JEE Main

Consider the statement : "P(n)=n^2-n+41 is prime." Then which one of the following is true?

  • Option 1)

     

    Both P(3) and P(5) are true.

  • Option 2)

     

    P(3) is false but P(5) is true. 

  • Option 3)

     

    Both P(3) and P(5) are false

  • Option 4)

     

    P(5) is false but P(3) is true.

Answers (1)

best_answer

 

Steps of Mathematical Induction (Verification step) -

Step 1: Verification step

Actual verification of the proposition of the starting value n=1

- wherein

2^{3n}-1 is divisible by 7

Put n=1, It Satisfies.

 

 

Steps of Mathematical Induction (Induction Step) -

Step 2: Induction Step

Assuming the proposition to be true for n=k, and proving it is true for value     n=k+1

-

 

 

Steps of Mathematical Induction (Generalization Step) -

Combine Verification step and Induction step

p(1) is true and p(n) is true for n+1 assuming it is true for n

-

P(n): n^{2}-n+41  is  prime

put n=3

P(3) =  9 - 3 + 41 = 47 which is prime 

put n = 5 

P(5) =  25 - 5 + 41 = 61 which is prime 


Option 1)

 

Both P(3) and P(5) are true.

Option 2)

 

P(3) is false but P(5) is true. 

Option 3)

 

Both P(3) and P(5) are false

Option 4)

 

P(5) is false but P(3) is true.

Posted by

admin

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question