hi nithin,
Actually i dont know where u heard dat it is required to solve all problems in iit ,but i can tell u one thing dat if u score around 60% in ur exam then u can get iit delhi very easily.....
i just gave u a stat which is a message to u how u shud attempt ur paper ..i.e no. of questions is not so important but ur accuracy level is important ..if u attempt arnd 70-75 % problems and u finally make arnd 50-60% then also ur chances of getting into iit is very bright  so dont worry abt the no. of questions u shud attempt rather think hw u can increase ur accuracy level.......
For this i wud tell u one thing dat accuracy can be increased only when if ur concepts are clear and ur knowledge abt the subject is good then u can score high scores with ur high level of accuracy...
Regarding ur 2nd query i wud tell u dat both concepts n solving problems are important n both are complementary type of things ,..i.e without solving problems u can't get deep into the topic n u will find it hard to apply concepts directly in ur xams..
so u shud prefer to 1st clear ur concepts as deep as u can then try some not many problems just to get feel of the topic.....
I think u wud understand wat i wanted to say....
with regards
askiitianexpert pratham