Which of the above graphs describe the variation of the ball’s velocity v with time between the time t1 as it hits the bat and t2 as it touches the ground?
I solved it, and my imperfect visualisation gave me c as the right option. Obviously, and unfortunately, it was wrong, as the answer is b.
HOW I DEDUCED MY ANSWER
When the ball hits the bat, it’s velocity is v, which goes on decreasing until it reaches its maximum height where velocity is zero. It then falls down, with the magnitude of velocity increasing in the negative direction. Only c supports this method of representation of the given motion. What is the thought proccess behind arriving at b?
I agree with you that (c) seems to be the best answer to the question you quote.
Note that the graph in (b) shows the absolute value of (c). However, the usual way to use the words in English -- or at least the usage that educators generally insist on -- is that "velocity" means a quantity with a direction (that is, in one dimension is has both a magnitude and a sign) whereas "speed" is the usual word for just the magnitude (or absolute value) of the velocity. So by this standard usage, the graph (c) shows the velocity that you're asked for, whereas (b) shows the speed.
If you're translating the question from a different language than English, something may have been lost in translation.
(In fact all the graphs look wrong to me unless we assume that the ball is hit directly upwards and lands atop the batter. If its velocity has a horizontal component too (which will certainly be the case in most ball-and-bat sports (possibly excepting cricket in which all manner of strange things seem to happen)) that component is not affected by falling, so the speed will never drop to zero, and there should really be a graph looking like the upper branch of a hyperbola, not touching the $t$ axis.)