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, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

Find the value of the determinant |[101 ,102 ,103],[ 104 ,105 ,106],[ 107, 108, 109]|

The weights in grams of 50 oranges picked at random from a consignment are as follows: 131, 113, 82, 75, 204, 81, 84, 118, 104, 110, 80, 107, 111, 141, 136, 123, 90, 78, 90, 115, 110, 98, 106, 99, 107, 84, 76, 186, 82, 100, 109, 128, 115, 107, 115, 119, 93, 187, 139, 129, 130, 68, 195, 123, 125, 111, 92, 86, 70, 126

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.

The weights in grams of 50 oranges picked at random from a consignment are as follows: 131,113,82,75,204,81,84,118,104,110,80,107,111,141, 136,123,90,78,90,115,110,98,106,99,107,84,76,186,82, 100,109,128,115,107,115,119,93,187,139,129,130,68, 195,123,125,111,92,86,70,126 Form the grouped frequency table by dividing the variable range into intervals of equal width, each corresponding to 20gms in such a way that the mid-value of the first class corresponds to 70 gms.

From the prices of shares X and Y below, find out which is more stable in value X 35 54 52 53 56 58 52 50 51 49 . Y 108 107 105 105 106 107 104 103 104 101

From the prices of shares X and Y given below: find out which is more stable value: X: 35 54 52 53 56 58 52 50 50 49 Y: 108 107 105 105 106 107 104 103 104 101

Which of the following is correct: (a) The element Mendelebium (d) has been named is the honour of Mendeleev. What is the atomic number of that element? (i) 100 , (ii) 101 , (iii) 102 , (iv) 103 (b) The element Seaborgium (Sg) has been nemed in the honour of Glenn T . Seaborg. What is the atomic number of that elements? (i) 104 , (ii) 105 , (iii) 106 , (iv) 107 (c ) Glenn T . Seaborg was awarded Nobel Prize in 1951 for the discovery of which element // elements? (i) Uranium (U) (ii) Elelments from 90 to 93 (iii) Elements from 94 to 102 (iv) elements from 103 to 106

Following is the distribution of I.Q. of 100 students. Find the median I.Q. I.Q. 55-64 65-74 75-84 85-94 95-104 105-114 115-124 125-134 135-144 No. of Students: 1 2 9 22 33 22 8 2 1

A meter bridge is set- up as shown in figure, to determine an unknown resistance X using a standard 10 Omega resistor. The galvanometer shows null point when tapping - key is at 52 cm mark. The end -corrections are 1 m and 2 cm respectively for the ends A and B . The determined values of X is . (a) 10.2 Omeaga (b) 10.6 Omega (c) 10.8 Omega (d) 11.1 Omega .