Question

The number of integral solutions of
(x + 1)2000 (x - 12)2001/(x - 3)1999 (x - 10)2002 <0 is
(1) Odd
(3) Prime
(2) Even
(4) Composite​

Answer 1

Answer:

4)composite will be the correct option I guess

Answer 2

Answer:

(3) & (4)

Step-by-step explanation:

for x = 10, 3 (the function is not defined because denominator becomes 0)

x≠ -1, 12 (as numenator becomes 0, but we need value less than 0)

(x+1)^2000 is always positive, similarly (x-10)^2002 is always positive.

for value of given eqn, Less than 0

I say that either (x-12)^2001 or (x-3)^1999 become negative, but both cannot be negative at a same time. or else we will get positive value.

Therefore, 3>x<12

x= 4, 5, 6, 7, 8, 9, 11

Now,

Total no. of integral possible values of x=7, which is odd & prime number.