The sum of 1/4,1/9,1/16....1/n2 is :
(1)	less than 1	(2)	greater than 1
(3)	equal to 1 or less than 1	(4)	equal to 1/n2 (n + 2)
The right answer is Option (1).
¼ + 1/9 + 1/16 +…+ 1/n2 Consider ¼: ¼ = 1/(2 x 2) < 1/(1 x 2) because ½ < 1 Similarly, 1/9 = 1/(3 x 3) < 1/(2 x 3) Since 1/3 < ½ 1/16 = 1/(4 x 4) < 1/(3 x 4) Because ¼ < 1/3 …………………………………………………….. …………………………………………………….. 1/n2 = 1/(nxn) < 1/(n – 1)n Since 1/n < 1/(n – 1) ¼ + 1/9 + …+ 1/n2 < 1/(1 x 2) + 1/(2 x 3) + … + 1/[(n – 1)n] i.e. ¼ + 1/9 + 1/16 + … + 1/n2 < (1/1 – ½) + (1/2 – 1/3) +…+ [1/(n – 1) – 1/n] i.e. ¼ + 1/9 + 1/16 +… + 1/n2 < 1/1 – 1/n which is less than 1. Hence, the given sum is less than 1 only. Answer: (1) What is the digit in the unit place of  3946252 + 734733 ? (1) 8 (2)  7 (3) 6 (4) 4 The right answer is Option (1). 3946252 + 734733 First we will find the unit digit of 3946252. Divide 46, by 4, we get 2 as remainder. Actual remainder (2)252 Again dividing (2)252  by 4, we get 0 as remainder. And ‘9’ is an odd digit number. So, the last digit of 3946252 will be 1. Last digit of 734733 Þ By dividing 47 by 4, we get 3 or – 1 as a remainder. Now, (– 1) odd, when divided by 4 will give – 1 or 3 as remainder. So, the last digit of 734733 will be. Last digit of 3 ´ 3 ´ 3 = i.e. 7. So, the last digit is 1 + 7 = 8. Answer: (1) The expression 333555 + 555333 is divisible by: (1) 2 (2)  3 (3) 37 (4) All of these The right answer is Option (4). 333555 + 555333 Check it by option. The last digit of 333555 will be odd, and the last digit of 555333 will be odd. odd + odd Þ even So, the last digit is even, which is divisible by 2. Both the numbers are individually divisible by 3. So 333555 + 555333 is divisible by 3. And similarly, both the numbers are divisible by 37, so, 333555 + 555333 is divisible by 37. Hence this expression is divisible by all three numbers.   Answer : (4) Note : If the number consists of same in the multiples of 3, then it is always a multiple of 37 � l ; p� �ߡ ight:150%;font-family:"Arial","sans-serif";color:#333333'> So, the last digit is 1 + 7 = 8. Answer: (1)