Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at the temperature of boiling water,the lengths up to which wax melts are $8.4 \ cm$ and $4.2 \ cm$,respectively. If the thermal conductivity of copper is $0.92$,then the thermal conductivity of iron is:

If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

If $\Delta$ is the area of the triangle formed by the positive $x$-axis and the normal and tangent to the circle $x^2+y^2=4$ at $(1, \sqrt{3})$,then $\Delta$ is equal to

Glucose is reabsorbed from the glomerular filtrate by . . . . . . .

An object $2.4 \; m$ in front of a lens forms a sharp image on a film $12 \; cm$ behind the lens. $A$ glass plate $1 \; cm$ thick,of refractive index $1.50$ is interposed between the lens and the film with its plane faces parallel to the film. At what distance (from the lens) should the object be shifted to be in sharp focus on the film (in $; cm$)?

For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval