Number systems

Q1.Simplify (21^4) - (343^2)

Q2. The unit digit of 25 x 17 x 231 x 43 x 59a is 5 Q2.The unit digit of 25 x 17 x 231 x 43 x 59a is 5. How many possible numbers can come in place of a?

Q3. Two pencils are 24cm and 42cm long Q3.Two pencils are 24cm and 42cm long. If we have to make them of equal size, then the minimum number of similar pencils is

Q4. Which digits should come in place of @ and # if the number 62684@# is divisible by both 8 and 5? D)none

Q5. Find Remainder[ (12 * 13 * 14) / 5 ] B)2 C)3 D)4

Q6.What is the remainder when 64999 is divided by 7? C)3 D)4

Q 7.What is the remainder when 444444 ^ 444 is divided by 7 ? C)3 D)4

Q8.10025-7 is divisible by

Q9. How many keystrokes are needed to type numbers from 1 to 1000 on a standard keyboard ? C)2887 D)2888 E)none

Q10. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? A)44 B)45 C)46 D)Can’t be determine

Q11. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number. A)24 B)42 C)84 D)none

Q12. The last two digits of  998915423 are B)91 C)61 D)None

Q13. Determine the digit in the units position of 13^23 * 27^37 * 19^45. A)7 B)9 C)3 D)none

Q14. Which term of the series 5, 8, 11, 14,.....is 320? A)104th B)105th C)106th D)107th

Q15. If the ratio of the sum of the first 6 terms of a G. P Q15. If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P? A)1/3 B)2 C)9 D)1/9 Explanatory Answer The sum of the first n terms of a G.P. is given by , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P. Therefore, the sum of the first 6 terms of the G.P will be equal to  And sum of the first 3 terms of the G.P. will be equal to   The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1  i.e.   =>   => r3 + 1 = 9  => r3 = 8  => r = 2

Q16. Which of the following has the most number of divisors?

Q17. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is A)4 B)5 C)8 D)6

Q18. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is D)None

Q19.Which of the following fraction is the largest ? 7/8 13/16 31/40 63/80

Q20. The LCM of two number is 4800 and their HCF is 160 Q20.The LCM of two number is 4800 and their HCF is 160. If one number is 480 , then the second number is

Q21. Reduce 128352/238368 to its lowest term A)3/4 B)5/13 C)7/13 D)9/13

Q22)If n is a positive integer and (n + 1)(n + 3) is odd, then (n + 2)(n + 4) must be a multiple of which one of the following? A)Even B)Odd C)Can’t Determined D)None