Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Find the number of palindrome words formed by taking 2 or more letters from the word ‘RESONANCE’ (palindrome words are those which read the same forward and backward).
A) 87
B) 57
C) 84
D) 26

Answer
VerifiedVerified
480.3k+ views
2 likes
like imagedislike image
Hint:
For palindromes, words must be the same when read forward and backward. So first we have to check for the repeating letters. Here there are two repeating letters. So we can find combinations of two, three, four and five.

Complete step by step solution:
Number of letters in the given word ‘RESONANCE’ is 9.
We can see that two letters N and E are occurring two times and the rest of the five letters R,S,O,A and C are occurring one time.
We are asked to find the number of palindrome words formed by taking 2 or more letters at a time.
We can consider two letter words first.
There are only two possibilities: NN and EE.
Now consider three letter words.
Possibilities are NRN, NEN, NSN, NON, NAN, NCN, ERE, ESE, EOE, ENE, EAE, ECE.
There is 12 in total.
Now consider four letter words.
There are only two cases: NEEN and ENNE
Now consider five letter words.
Possibilities are NEREN, NESEN, NEOEN, NEAEN, NECEN, ENRNE, ENSNE, ENONE, ENANE, ENCNE.
There is 10 in total.
In total there are 2+12+2+10=26 possibilities.

The answer is option D.

Note:
To find the words choose the repeating letters and fix them in the beginning and end tail. Then we can make different choices for the middle letter. Considering all possibilities we get the answer.
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
Social scienceSocial science
ChemistryChemistry
MathsMaths
BiologyBiology
EnglishEnglish
₹38,500 (9% Off)
₹35,000 per year
Select and buy