Page 96 - Ganit Kaushal

14. State whether the following statements are True (T) or False (F).

(a) In the game of heights, the child at the corner can never say 1.
(b) In the game of heights, the child at the corner can never say 0.

(c) In the game of heights, the child at the corner can never say 2.
(d) Applying the Kaprekar procedure to a four-digit number repeatedly, we always reach 6714.
(e) The Collatz sequence always ends at the number 2.

(f) The 5th term of the Collatz sequence starting with 15 is 36.
(g) The sum of a four-digit number and a two-digit number sometimes gives a six-digit number.

(h) The sum of two 5-digit numbers can sometimes give a 6-digit number.
(i) The product of the place values of two 3s in 435638 is 9000000.
(j) The sum of the place value and face value of 5 in 62578 is 505.

(k) The difference between the largest and smallest five-digit palindromes is a palindrome.
Subjective/Competency Based Questions
15. Write the Collatz sequence starting with 15.

16. Write the greatest 4-digit number using different digits, where the tens digit is the smallest natural
number, and the units digit is five times the tens digit.
17. Find 8 times the difference of the place values of 5 in 450253.
18. What must be added to the largest 4-digit number to get the smallest number of five different digits
formed by 1, 2, 0, 3, 4?

19. How many supercells are there in the adjoining grid? What is the number 16,200 39,344 29,765
in that supercell? If you exchange two digits of one of the numbers, there 23,609 62,871 45,306
will be four supercells. Figure out which digits to swap. (NCERT)
19,381 50,319 38,408
20. We are a group of five-digit numbers between 5000 and 75,000 such that
all of our digits are odd. Who is the largest number in our group? Who is the smallest member in our
group? Who among us is closest to 50,000? (NCERT)

21. Write one 5-digit number and two 3-digit numbers such that their sum is 18,670.
22. What is the difference between the smallest 6-digit number with five different digits and the greatest
5-digit number with four different digits?

23. Write all four-digit numbers that can be formed with the digits 2 and 5, using both digits an equal
number of times. Also find their sum.
24. How many hundreds should be multiplied to make 1 million?

25. Which one is greater, the sum of the first fifteen whole numbers or the product of the first fifteen
whole numbers?
26. Round off the given numbers to the nearest tens:
(a) 898 (b) 1225 (c) 87653

27. Round off the given numbers to the nearest hundreds:
(a) 877 (b) 2225 (c) 87653

94 Mathematics-6