Questions asked by Arnab C.

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• 1.Show that n(n+1)(n+2) is divisible by 6. 2.Show that #1^2015+2^2015+3^2015+4^2015+5^2015+6^2015# is divisible by 7. How do I solve these?
  
• Suppose there are m Martians & n Earthlings at a peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martians there is at least one Earthling?(see detail)
  
• What happens if I use #cos# repeatedly?
  
• The hollow metallic bob of a simple pendulum is filled with water. Water comes out drop by drop through a small hole at the bottom of the bob. How will the time period change?
  
• Why is the aqueous solution of aluminium chloride acidic?
  
• Prove that there are infinitely many distinct pairs (a, b) of co-prime integers #a>1# and #b>1# such that #a^b+b^a# is divisible by #a+b#?