The correct answer is option 'B' - triplet.

In nuclear magnetic resonance (NMR) spectroscopy, the 29Si NMR spectrum provides information about the chemical environment and bonding of silicon atoms in a molecule. The observed splitting patterns in the NMR spectrum can be used to determine the number of chemically distinct silicon environments in the molecule.

To understand why the correct answer is a triplet, we need to analyze the structure of the molecule X[Ph3SiH2]. This molecule contains a silicon atom bonded to three phenyl (Ph) groups and two hydrogen (H) atoms.

The silicon atom in this molecule has four different substituents: three phenyl groups and one hydrogen atom. These substituents create four different environments for the silicon atom, resulting in four distinct signals in the 29Si NMR spectrum.

Now, let's consider the splitting pattern of the signals. The hydrogen atoms directly bonded to the silicon atom (H2) will cause splitting in the 29Si NMR spectrum. The number of hydrogen atoms that are magnetically coupled to the silicon atom determines the splitting pattern observed.

In this case, the hydrogen atoms (H2) are adjacent to two chemically equivalent phenyl groups. Therefore, the H2 protons will experience coupling from two neighboring protons, resulting in a triplet splitting pattern in the 29Si NMR spectrum.

The triplet splitting pattern arises because the two adjacent protons can be either aligned with the external magnetic field or against it. These two spin states will have slightly different energy levels, leading to two different resonance frequencies. The silicon signal is then split into three peaks with an intensity ratio of 1:2:1, corresponding to the three possible spin combinations.

In summary, the 29Si NMR spectrum of X[Ph3SiH2] exhibits a triplet splitting pattern because the hydrogen atoms (H2) are adjacent to two chemically equivalent phenyl groups. The triplet splitting pattern arises due to the coupling of these hydrogen atoms with their neighboring protons, resulting in three distinct resonance peaks.