PYQ




Base āĻāϕ⧇ (>1) āĻš'āϞ⧇ āĻ•ā§‡ā§ąāϞ Exponent āϤ⧁āϞāύāĻž āϕ⧰āĻ• → āϝāĻžā§° Exponent āĻĄāĻžāϙ⧰, āϏ⧇āχ āϏāĻ‚āĻ–ā§āϝāĻžāĻ“ āĻĄāĻžāϙ⧰āĨ¤


āωāĻĻāĻžāĻšā§°āĻŖ:



āϝāĻŋāĻšā§‡āϤ⧁ 9 > 6, āϏ⧇āϝāĻŧ⧇


āĻŽāύāϤ ā§°āĻžāĻ–āĻŋāĻŦ: Base āĻāϕ⧇ → Exponent āϤ⧁āϞāύāĻž āϕ⧰āĻ• → āĻĄāĻžāϙ⧰ Exponent = āĻĄāĻžāϙ⧰ āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤


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Q. If the sum of the digits of a two-digit number is 9 and adding 27 to it reverses its digits, find the unit digit of the number.(āĻāϟāĻž āĻĻ⧁āϟāĻž āĻ…āĻ‚āϕ⧰ āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻ…āĻ‚āĻ• āĻĻ⧁āϟāĻžā§° āϝ⧋āĻ—āĻĢāϞ ⧝āĨ¤ āϏ⧇āχ āϏāĻ‚āĻ–ā§āϝāĻžāϤ ⧍⧭ āϝ⧋āĻ— āϕ⧰āĻŋāϞ⧇ āĻ…āĻ‚āĻ• āĻĻ⧁āϟāĻž āĻ“āϞ⧋āϟāĻž āĻšā§ˆ āϝāĻžāϝāĻŧāĨ¤ āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹ā§° āĻāĻ•āĻ• āĻ…āĻ‚āĻ• āύāĻŋā§°ā§āĻŖāϝāĻŧ āϕ⧰āĻ•āĨ¤)


A. 4  B. 6  C. 3  D. 5


Trick | āĻŸā§ā§°āĻŋāĻ•


Try the options where the sum of the digits is 9. (āϝāĻŋāĻŦā§‹ā§° āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻ…āĻ‚āĻ• āĻĻ⧁āϟāĻžā§° āϝ⧋āĻ—āĻĢāϞ ⧝ āĻšāϝāĻŧ, āϏ⧇āχāĻŦā§‹ā§° āĻĒā§°ā§€āĻ•ā§āώāĻž āϕ⧰āĻ•āĨ¤)



  • 36 + 27 = 63 (Digits are reversed.)

  • 45 + 27 = 72 

  • 54 + 27 = 81 

  • 63 + 27 = 90 


Therefore, the original number is 36. (āϏ⧇āϝāĻŧ⧇, āĻŽā§‚āϞ āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹ āĻšā§ˆāϛ⧇ 36āĨ¤)


Ans | āωāĻ¤ā§āϤ⧰ : Unit digit = 6 | āĻāĻ•āĻ• āĻ…āĻ‚āĻ• = 6


Ans: B. 6