Yeah, there was negative marking, but I met someone who cleared last year interview, he said that everyone at that interview have attempted 23 questions or more.
So, for last year maybe PEA cut-off would have been 22 or 23 questions right.
Assuming, 4 marks per question, and -1 for wrong answers, it would imply, 22 attempted questions with only one wrong answer.
I know, the same anxiety I had when I started solving it. But then RTI reply becalmed me. To the best of my knowledge in ISI exam, there is a different marking scheme all together. There is no negative mark, but you get an extra mark for each unattempted question. But somehow both are one n the same thing.
I don't know theorem but you can have a look at my approach.
Let g(x)= f(x)-x
so g(0)=f(0)>=0
g(1)= f(1)-1 <=0 since f(x) lies in [0,1]
so g varies from less than 0 to more than 0 in interval [0,1]
since f(x) and x both are continuous so there is atleast a point where g(x)=0
See in question we have to show f(x)=x but the definition f is not defined.so in order to prove them I assumed a new function and proved it to be Zero. Since question had little info so we have to make one. Some questions on functions have solutions like this( assumption of a new function)
18. The domain in the second region will be a subset of first part. Thus, all its points would have been considered in first region's analysis too. So, optimum in second is less than equal to optimum in first.
14. It is given that this is true for all values of a, b,c. Thus take a=1 b=2 and c=1. The value of k evaluated from all three options will not lie between 1 and 2. Thus, none of these