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 ?

1. 9 O’clock
2. 8 O’clock
3. 5 O’clock
4. 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.

1. (635)₄
2. (32312)₄
3. (21323)₄
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*42 + 1*41 + 3*40
m = 48 + 4 + 3
m = 55.
Now n=3*42 + 2*41 +2*40
    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