UPSC NDA 2 2016 Mathematics Solved Paper

Case I
When unit digit can be 1,3,5 or 7 & digit at thousand's place can be 1,2,3,4,5,6,7 or 8.
No. of ways digits can be filled are:

7

8

7

4

Total no’s=7×8×7×4=1568
Case II
When unit digit can be 9 & digit at thousand’s place can be 1,2,3,4,5,6,7 or 8.
No. of ways digits can be filled are:

8

8

7

1

Total no’s =8×8×7×1=448
Case III
When unit digit can be 1,3,5 or 7 & digit at thousand's place can be 9.
No. of ways digits can be filled are:

1

8

7

4

Total no’s=1×8×7×4=224∴ Number of odd digits between 1000 & 9999 with no
digit repeated=1568+448+224
=2240