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JEE Advanced Model Paper 7 with solutions for online practice

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Passage-4

Let ‘p’ be an odd prime number and Tp = {A = [

a.b
c	a

] / a , b , c ∊ {0 , 1 , 2 , ..... , (p - 1)}} . Then answer the following

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Question : 38

Total: 66

The number of symmetric matrices A in Tp such that trace of A is not divisible by p butdet A is divisible by p is

(p - 1) (p2 - p - 1)
p3 - (p−1)2
(p−1)2
2 (p - 1)

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