Show that `16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)`

In the circuit shown here, E_(1) = E_(2) = E_(3) = 2 V and R_(1) = R_(2) = 4 ohms . The current flowing between point A and B through battery E_(2) is

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

Write ‘True’ or ‘False’ and justify your answer: The volume of the frustum of a cone (1)/(3)pi h(r_(1)^(2)+r_(2)^(2)-r_(1)r_(2)) where h is the vertical height of the frustum and r_(1),r_(2) are the radii of the ends.

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

If A = {1,2,3} and consider the relation R = {(1,1), (2,2) , (3,3) , (1,2) ,(2,3), (1,3)} . Then R is .......

In the circuit shown in figure, epsilon_(1) = 3 V, epsilon_(2) = 2 V , epsilon_(3) = IV and R = r_(1) = r_(2) = r_(3) = 1 Omega . The current through each branch is...... and potential difference between the points A and B is .......

The differintial eauation of all circle of radius r, is given by (a) {1+(y_(1))^(2)}^(2)=r^(2)y_(2)^(3) (b) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(3) ( c ) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(2) (d) None of these

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

Two resistors of resistances R_(1)=100pm3 ohm and R_(2)=200pm4 ohm are connected (a) series , (b) in parallel. Find the equivalent resistance of the (a) series combination, (b) parallel combination. Use for (a) the relation R = R_(1)+R_(2) and for (b) (1)/(R') = (1)/(R_(1))+(1)/(R_(2)) and (DeltaR')/(R'^(2)) = (DeltaR_(1))/(R_(1)^(2))+(DeltaR_(2))/(R_(2))

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.