The density of \(\beta\)-Fe is 7.6 g/cm\(^3\). It crystallizes in a cubic lattice with \( a = 290 \) pm.
What is the value of \( Z \)? (\( Fe = 56 \) g/mol, \( N_A = 6.022 \times 10^{23} \) mol\(^{-1}\))
Arrange the following in the increasing order of number of unpaired electrons present in the central metal ion:
I. \([MnCl_6]^{4-}\)
II. \([FeF_6]^{3-}\)
III. \([Mn(CN)_6]^{3-}\)
IV. \([Fe(CN)_6]^{3-}\)
The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between \( t = 0 \) to \( t = 4s \)?
Let a line passing through the point $ (4,1,0) $ intersect the line $ L_1: \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} $ at the point $ A(\alpha, \beta, \gamma) $ and the line $ L_2: x - 6 = y = -z + 4 $ at the point $ B(a, b, c) $. Then $ \begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix} \text{ is equal to} $