IIT-JEE Exam

For 3i^3 matrices M and N, which of the following statement(s) is (are) NOT correct ?
(A) NTMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric
(B) MN, NM is skew symmetric for all symmetric matrices M and N
(C) MN is symmetric for all symmetric matrices M and N
(D) (adj M) (adj N) = adj(MN) for all invertible matrices M and N

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IIT-JEE Other Question

Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4 ,1/4,1/8. Then the probability that the problem is solved correctly by at least one of them is A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are
option
a) 24
b) 32
c) 45
d) 60