Q. How many integers lie between 250^2 and 251^2 ? (250^2 āĻ†ā§°ā§ 251^2 ā§° āĻŽāĻžāĻœāĻ¤ āĻ•āĻŋāĻŽāĻžāĻ¨āĻŸāĻž āĻĒā§‚ā§°ā§āĻŖāĻ¸āĻ‚āĻ–ā§āĻ¯āĻž āĻ†āĻ›ā§‡ ?)

Q. How many integers lie between 2502 and 2512 ? (2502 āĻ†ā§°ā§ 2512 ā§° āĻŽāĻžāĻœāĻ¤ āĻ•āĻŋāĻŽāĻžāĻ¨āĻŸāĻž āĻĒā§‚ā§°ā§āĻŖāĻ¸āĻ‚āĻ–ā§āĻ¯āĻž āĻ†āĻ›ā§‡ ?)


Soln


2502 = 62500, 2512 = 63001


Number of integers between them / āĻŽāĻžāĻœāĻ¤ āĻĨāĻ•āĻž āĻĒā§‚ā§°ā§āĻŖāĻ¸āĻ‚āĻ–ā§āĻ¯āĻžā§° āĻ¸āĻ‚āĻ–ā§āĻ¯āĻž:


63001- 62500 -1 = 501-1= 500


Ans / āĻ‰āĻ¤ā§āĻ¤ā§°: (C) 500


Shortcut Trick / āĻšāĻŽā§ āĻ•ā§ŒāĻļāĻ˛


Between n2 and (n+1)2, the number of integers is 2n.


n2 āĻ†ā§°ā§ (n+1)2 ā§° āĻŽāĻžāĻœāĻ¤ āĻĨāĻ•āĻž āĻĒā§‚ā§°ā§āĻŖāĻ¸āĻ‚āĻ–ā§āĻ¯āĻžā§° āĻ¸āĻ‚āĻ–ā§āĻ¯āĻž = 2n


Here / āĻ‡āĻ¯āĻŧāĻžāĻ¤, n = 250 


So / āĻ¸ā§‡āĻ¯āĻŧā§‡, 2 × 250 = 500 


Ans / āĻ‰āĻ¤ā§āĻ¤ā§°: 500


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Practice Set










1. How many integers lie between 1002and 1012 ?
A) 198 B) 199 C) 200 D) 201


2. How many integers lie between 1502 and 1512 ?
A) 298 B) 299 C) 300 D) 301


3. How many integers lie between 2002 and 2012 ?
A) 398 B) 399 C) 400 D) 401


4. How many integers lie between 3252 and 3262 ?
A) 648 B) 649 C) 650 D) 651


5. How many integers lie between 5002 and 5012?
A) 998 B) 999 C) 1000 D) 1001


6. How many integers lie between 7502 and 7512 ?
A) 1498 B) 1499 C) 1500 D) 1501


7. How many integers lie between 9992 and 10002?
A) 1996 B) 1997 C) 1998 D) 1999


8. How many integers lie between 1252 and 1262 ?
A) 248 B) 249 C) 250 D) 251


9. How many integers lie between 4252 and 4262 ?
A) 848 B) 849 C) 850 D) 851


10. How many integers lie between 8752 and 8762 ?
A) 1748 B) 1749 C) 1750 D) 1751