i w m om11 r1 | ww2 1 + 02 1 . ||*1 w1|||0?] ooo

If (w != 1) is a cube root of unity then |[1, 1+i+w^2, w^2], [1-i, -1, w^2-1] , [-i, -i+w-1, -1]| =

Which of the following cannot be valid assignment of probability for elementary events or outcomes of samples space S={w_1, w_2, w_3, w_4, w_5, w_6, w_7}: Elementary events w_1 w_2 w_3 w_4 w_5 w_6 w_7 i. 0.1 0.01 0.05 0.03 0.01 0.2 0.6 ii. 1/7 1/7 1/7 1/7 1/7 1/7 1/7 iii. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 iv. 1/(14) 2/(14) 3/(14) 4/(14) 5/(14) 6/(14) (15)/(14)

Which of the following cannot be valid assignment of probability for elementary events or outcomes of samples space S={w_1, w_2, w_3, w_4, w_5, w_6, w_7}: Elementary events w_1 w_2 w_3 w_4 w_5 w_6 w_7 i. 0.1 0.01 0.05 0.03 0.01 0.2 0.6 ii. 1/7 1/7 1/7 1/7 1/7 1/7 1/7 iii. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 iv. 1/(14) 2/(14) 3/(14) 4/(14) 5/(14) 6/(14) (15)/(14)

If two resistances of value R _ 1 = ( 2.0 pm 0 .1 ) Omega and R _ 2 = ( 12.3 pm 0.2 ) are connected in (i) parallel and (ii) series then find the error in the estimation of equivalent resistance.

If (omega ne1) is a cube root of unity , then {:(1 , 1 + i+ omega^(2) , omega^(2)) , (1-i, -1 , omega^(2) -1) , (-i , -1 + omega - i, -1):}|

If omega is a complex cube root of unity, show that [[1 , omega, omega^2], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]

If 1, omega , omega^2 are cube roots of unity prove that (1 / (1 + 2omega)) - (1 / (1 + omega)) + (1 / (2 + omega)) = 0

An iron bar (L_(1) = 0.1 m , A_(1) = 0.02 m^(2), K_(1) = 79 W m^(-1) K^(-1)) and a brass bar (L_(2) = 0.1 m, A_(2) = 0.02 m^(2) , K_(2) = 109 W m^(-1) K^(-1)) are soldered end to end as shown in Fig. 11.16. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. Obtain expressions for and hence compute (1) the temperature of the function of the two bars, (11) the equivalent thermal conductivity of the compound bar, and (111) the heat current through the compound bar.

An iron bar (L_(1) = 0.1 m , A_(1) = 0.02 m^(2), K_(1) = 79 W m^(-1) K^(-1)) and a brass bar (L_(2) = 0.1 m, A_(2) = 0.02 m^(2) , K_(2) = 109 W m^(-1) K^(-1)) are soldered end to end as shown in Fig. 11.16. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. Obtain expressions for and hence compute (1) the temperature of the function of the two bars, (11) the equivalent thermal conductivity of the compound bar, and (111) the heat current through the compound bar.