CAT Exam Model Paper 4 with solutions for free online practice

f(0) > 0 and f(1) < 0 implies that one root for f(x) = 0 lies between x = 0 and x = 1.
f(6) + f(8) = 0 implies that f(6) and f(8) are of opposite sign but same absolute value. Hence another root for f(x) = 0 must lie between x = 6 and x = 8.
As f(1) < 0, f(6) must also be less than zero, otherwise we’ll have more than 2 roots for f(x) = 0.
Hence f(8) > 0 and f(6) < 0.
Further f(7).f(9) > 0 implies that both f(7) and f(9) are greater than zero.
So the second root for f(x) = 0 must lie between x = 6 and x = 7.
So f(x) would look like

As f(1), f(2) and f(3) are less than zero,
f(1).f(2).f(3) < 0 is true.
As f(3), f(5) < 0 and f(7), f(9) > 0,
f(3).f(5).f(7).f(9) > 0 is true.
As f(7), f(8) > 0,
f(7).f(8)<0 is false.
f(0), f(9), f(10) > 0 and f(1) < 0, but since we don’t know the magnitude of any of these four we cannot judge if f(0) + f( 1) + f(9) + f( 10) is greater than zero or not.