Page 3 - CBQ-CL-6-CH-3 NUMBER PLAY

9 Case study based questions.

The concept of palindromic numbers involves numbers that read the same forwards and backwards.
Examples of such numbers include 121, 1331, and 12321. These numbers are symmetrical and have

interesting mathematical properties. Palindromes are not just visually appealing; they also exhibit
unique behaviours when manipulated through certain mathematical processes. For instance, you
can create a palindrome by reversing the digits of a number and adding it to itself until a palindromic
number is obtained. This process often leads to surprising results and highlights the beauty of
symmetry in numbers.

(i)What is the defining characteristic of a palindromic number?
(a) It is divisible by 10.
(b) It has no repeated digits.
(c) It reads the same forwards and backwards.
(d) It is always a prime number.
(ii)Which of the following is an example of a palindromic number?
(a) 123 (b) 112 (c) 1331 (d) 245
(iii) What happens when you reverse the digits of a number and add it to itself?
(a) The result is always a prime number.
(b) The result is always a multiple of 10.
(c) You may obtain a palindromic number.

(d) The result is always larger than the original number.
(iv) Describe a mathematical process that can result in a palindromic number.
10 Assertion (A): A cell in a number table is called a supercell if it is greater than all its immediate
neighbours.
Reason (R): A number is coloured as a supercell even if it is smaller than any one of its adjacent cells.
(a) Both assertion and reasons are true and the reason is the correct explanation of assertion.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion.

(c) Assertion is true and the reason is false.
(d) Assertion is false and the reason is true.

11 Assertion (A): The number 6174 is called the Kaprekar constant.
Reason (R): Repeatedly arranging digits of a 4-digit number in descending and ascending order and

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