Find the value of the expression..1-4+5-8....to 50 terms

can someone please provide some basic funda material on number theory for CAT

can v apply remainder theorem for question:

what will be the remainder when 2^89 is divided by 89?

what is the highest value of x in the expression (167!)/(24!)^x to yield an integral answer?

What is the remainder when 167*234*99*347 by 77?

Find the remainder when 50^51^52 is divided by 11?

What is the remainder when 128^1000 is divided by 153?

25 sets of problem on Data Interpretation- one each for the DI sections of 25 CATALYST tests were prepared by the AMS research team. The DI section of each CATALYST contained 50 questions of which exactly 35 questions were unique,i.e. they had not been used in the DI section of any of the other 24 CATALYSTs. what could be the maximum possible number of questions prepared for the DI sections of all the 25 CATALYSTs put together?

Find the last digit of 112^112^112^112.........

Find the remainder when 15! is divided by 17