If the sides be a,b,c, than find `(r_(1)- r)(r _(2)+r_(3)).`

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)

Find the magnitude and direction of r_(1)-r_(2) when |r_(1)|=5 and points North-East while |r_(2)|=5 but points North-West.

The sides of a square shaped frame, Shown in the diagram are made of wires of resistances r_(1) and r_(2) The frame is places in a uniform magnetic field, which is perpendicular to the plane of figure and is increasing at a constant rate. The resistance that should be connected across the diagonal of frame, so that this wire is warmed up at greatest rate is given by R=(n r_(1)r_(2))/(r_(1)+r_(2)) . Find n.

Prove that if two bubbles of radii r_(1) and r_(2)(r_(1)ltr_(2)) come in contact with each other then the radius of curvature of the common surface r=(r_(1)r_(2))/(r_(2)-r_(1))

In DeltaABC, let b=6, c=10and r_(1) =r_(2)+r_(3)+r then find area of Delta ABC.

The formula –G Mm (1//r_(2) – 1//r_(1)) is more/less accurate than the formula mg (r_(2) – r_(1)) for the difference of potential energy between two points r_(2) and r_(1) distance away from the centre of the earth.

Two resistance R_(1) and R_(2) are made of different material. The temperature coefficient of the material of R_(1) is alpha and of the material of R_(2) is -beta . Then resistance of the series combination of R_(1) and R_(2) will not change with temperature, if R_(1)//R_(2) will not change with temperature if R_(1)//R_(2) equals

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.

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 .......

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