The value of $k$ such that the line $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$ lies in the plane $2x - 4y + z = 7$ is:

Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600 \ K, T_B = 800 \ K, T_C = 2200 \ K$,and $T_D = 1200 \ K$,the work done per cycle is ..... $kJ$.

If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0$,then $c$ is equal to

How many nodal tissues (specialized cardiac musculature) are present in the human heart?

$Fe$ is made passive by

Two slabs $A$ and $B$ of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of $A$ and $B$ are $k_1$ and $k_2$ respectively. $A$ steady temperature difference of $12^{\circ} C$ is maintained across the composite slab. If $k_1 = \frac{k_2}{2}$,the temperature difference across slab $A$ is (in $^{\circ} C$)