JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Permutations and Combinations

WhatsApp Email

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is

Answer: 100

Solution

A six-digit palindrome has the form

\overline{ab cc ba}

with

a \neq = 0

. Divisibility by

11

holds automatically, since the alternating digit sum

(a - b + c) - (c - b + a) = 0

. Divisibility by

5

needs the last digit

a \in {0, 5}

, and since

a

is also the leading digit,

a = 5

. The digits

b

and

c

are each free with

10

choices, giving

10 \times 10 = 100

such palindromes.

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Permutations and Combinations →

More JEE Main questions on Permutations and Combinations

The number of strictly increasing functions f from the set ${1, 2, 3, 4, 5, 6}$ to the set $(1, 2, 3, \dots, 9)$ such that $f (i) \neq = i$ for $1 \leq i \leq 6$ , is equal to :
JEE Main 2026View solution →
Let $S = {(m, n) : m, n \in {1, 2, 3, \dots .., 50}}$ . If the number of elements ( $m, n$ ) in S such that $6^{m} + 9^{n}$ is a multiple of 5 is p and the number of elements …
JEE Main 2026View solution →
The largest $n \in N$ , for which $7^{n}$ divides 101!, is:
JEE Main 2026View solution →
Let ABC be a triangle. Consider four points $p_{1}, p_{2}$ , $p_{3}, p_{4}$ on the side AB , five points $p_{5}, p_{6}, p_{7}, p_{8}, p_{9}$ on the side BC and four points …
JEE Main 2026View solution →
Let S be the set of the first 11 natural numbers. Then the number of elements in $A = {B \subseteq S : n (B) \geq 2$ and the product of all elements of B is even $}$ is
JEE Main 2026View solution →
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.
JEE Main 2026View solution →