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 ____________.
Your Input ________
Answer
Correct Answer is 100
Explanation
5
a
b
b
a
5
For divisible by 55 it shall be divisible by 11 and 5
both, for divisibility by 5 unit digit shall be 0 or 5 but
as the number is six digit palindrome unit digit is 5.
A number is divisible by 11 if the difference between sum of the digits in the odd places and the sum of the digits in the even places is a multiple of 11 or zero.
Sum of the digits in the even place = a + b + 5
Sum of the digits in the odd places = a + b + 5
Difference between the two sums = (a + b + 5 ) - (a + b + 5) = 0
0 is divisible by 11.
Hence, 5abba5 is divisible by 11.
So, required number = 10 $$\times$$ 10 = 100
2
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______________.
Your Input ________
Answer
Correct Answer is 52
Explanation
(i) When '0' is at unit place
Number of numbers = 20
(ii) When 4 or 6 are at unit place
Number of numbers = 32
Total three digit even number = 20 + 32 = 52
3
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
If $${}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}} = {}^q{P_r} - s,0 \le s \le 1$$, then $${}^{q + s}{C_{r - s}}$$ is equal to ______________.