matrices JEE 2010 comprehension

ye nahion banta mujhse bhi :P

ask the experts

i asked my maths teacher 1 month back

he said yeh to hua hi nahi kisi se abhi tak
:P

plzz experts here reply!!
prophet sir plzz help!!

those questions are to leave.I don't know how,but one of my friend solved it on 11th April,2010.And told that it took him 1/2 an hour .

:|

the quesns in matrices and det. coming in the recent yrs hav been almost unsolvable!!!

no yaar i don't agree..among determinants and matrices..every question has a hunch as an essential required.like some [3]gout feelings[3] which u have to justify.....its like solving first and then checking if solution fulfilled all requirements of question LOL!!!!!

not so tough

42. CASE 1 matrix is symmetric. so b=c=d (say)
so a²-d²= (a+d)(a-d) is a multiple of p
a+d is multiple of p = (p-1) ways (a+d must necessarily equal p)
a-d is a multiple of p = p ways (ie a=b=c) (a-d must be 0)

CASE 2 matrix is skew symmetric, so a=0 and b=-c and c=-b
so only solution is a=b=c=0 which is included in previous case.

ANS: 2p-1 ways

Will try to post subjective proof for the rest later.
in exam, put p=3 then 5 and rule out options

put p=3 evaluate all possible 27 matrices and then check with the options