`(113^2 +115^2 +117^2 -113 xx115 - 115 xx 117 - 117 xx113)`

185 xx185 - 115 xx 115

The minimum temperature (in ""^(@)C ) during the day at Delhi has been recorded for 30 days, as given below: 11.8, 11.6, 11.6, 11.4, 11.3, 11.4, 11.7, 11.7, 11.3, 11.4, 11.7, 11.7, 11.6, 11.3, 11.5, 11.8, 11.3, 11.3, 11.4, 11.5, 11.3, 11.5, 11.5, 11.8, 11.5, 11.4, 11.3, 11.6, 11.5 Construct a frequency table for the above data.

Assertion : The range of the data 114, 115, 116, 118, 119, 125, 130, 141, 126, 116, 113, 118, 120, and 126, is 100 Reason : The difference between the highest and the lowest value of the data is called range

Without expanding the determinants, prove that |103 115 114 111 108 106 104 113 116|+|113 116 104 108 106 111 115 114 103|=0

Without expanding the determinants, prove that |103 115 114 111 108 106 104 113 116|+|113 116 104 108 106 111 115 114 103|=0

Simplify: (387xx387 + 113xx113 + 2xx387xx113) (87xx87 + 61xx61- 2xx87xx61)

Without expanding the determinants, prove that |(103, 115, 114), (111, 108, 106), (104, 113, 116)|+|(113, 116, 104), (108, 106, 111), (115, 114, 103)|=0

Without expanding the determinants, prove that |(103, 115, 114), (111, 108, 106), (104, 113, 116)|+|(113, 116, 104), (108, 106, 111), (115, 114, 103)|=0