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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
1.63. please tell me the explaination and option for this
1.63. The number of different 10 x 10 symmetric matrices with each clement Deing either 0 or I is 6) 2100 (i) 250 (ii) 25 iv) 1055 |
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Ujjawal vishal![best-answer]()
since order is 10×10 there are 10 diagonal elements. rest 90 elements are in two parts ,45 elements above diagonal and 45 below. Since matrix is similar, both 45 elements are same (a12=a21,a13=a31.....so on). So, we need to fill 45+10 places i.e 55 place. Since , for each entry their are 2 ways (0 or 1)... so, 55 places can be filled in 2*2*2*........55 times i.e. 2^55 ways. hence option iii