1 Prove by M.I. that 6 n+2 + 7 2n+1 is divisible by 43 for each positive integer n. 2 Prove 06 i (i+1) 3 Determine the number of 6 digit integers no leading Os in which i) no digit is repeated ii) no digit is repeated and it is even iii) no digit is repeated and is divisible by 5 4 Find the number of distinguishable permutations of the letters in the following words i)BASIC iv) STRUCTURES v) ENGINEERING ii) CALCULUS iii) MATHEMATICS 5 How many positive integers n can we form using the digits 3,4,4,5,5,6,7 if we want n to exceed 50,00,000