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Consider an example question from a nursery/KG class:

Question: 16 comes in the table of:
(a) 2
(b) 4
(c) 8
(d) 3

Student A: (a), (b)
Student B: (a)

Student B has learnt the table of 2 only.
Student A has learnt the tables of 2 and 4.

The grading system awards both of them -1 mark.

Student C forgets the tables and leaves the question. The grading system awards him/her 0 mark.
22% marks were allotted to the questions of the similar type in JEE 2006.

Similar type of grading - though without negative marking - is reported in matching type of questions (13%).

In numerical questions, even if a student gets the concept right, solves the whole problem, but makes small error towards the end in calculation gets zero marks (13%).

The question here is, "Is the grading system fair"? After all shouldn't the student who knows more get more? Also, why should a student be penalised for knowing at least some part of the answer correctly? The grading in mains earlier years involved partial marks which was fair in the sense that if a question had four steps and a student who had done the problem correctly upto three steps used to get some marks.

Leaving aside this issue with grading in some questions it was good to see that the quality of questions was not diluted and some refinements can make JEE a great exam in the coming years. IIT need to be congratulated for an attempt to introduce the concept of quality objective based testing.

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$