**UGC-NET CS 2017 Nov – II**

**Q1****. If the time is now 4 O’clock, what will be the time after 101 hours from now ?**

- 9 O’clock
- 8 O’clock
- 5 O’clock
- 4 O’clock

**Ans.** 1. 9 O’clock

**Explanation: **We know that there are 24 hours in a day. So we will take mod for 101 hours i.e. (101 mod 24) = 5. So residue is 5. On adding these remaining 5 hours to the present time will give We know that there are 24 hours in a day, so we will take mod for 101 hours ie (101 mod 24) = 5. So residue is 5. On adding these remaining 5 hours to the present time will give 9 O'CLOCK time.

**Q2. Let m=(313) _{4} and n=(322)_{4}. Find the base 4 expansion of m+n.**

- (635)
_{4} - (32312)
_{4} - (21323)
_{4} - (1301)
_{4}

**Ans.** 4. (1301)_{4}

**Explanation: We have m=(313) _{4} and n=(322)_{4} convert m and n into decimal:**

m = 3*4^{2}+ 1*4^{1}+ 3*4^{0}m = 48 + 4 + 3 m = 55. Now n=3*4^{2}+ 2*4^{1}+2*4^{0}n = 48 + 8 +2 n = 58. m + n = 55 + 58 m + n = 113

**Now we have to convert 113 in to base 4:**

ie step 1-113 % 4 = 1 113 / 4 = 28 step 2- 28 % 4 = 0 28 / 4 = 7 step 3- 7 % 4 = 3 7 / 4 = 1 step 4- 1 % 4 = 1 1 / 4 --> will not divide it in quant. So we have to stop here.

**The answer will be Residue from step 4 to step 1 inorder i.e. 1301 Ans-(1301) _{4}**