Switching from user mode to kernel mode ($T1$) is known as a mode switch, which happens during system calls, interrupts, or exceptions.
In a mode switch ($T1$), the execution shifts to kernel space within the context of the same process, meaning the memory mapping, page tables, and TLB remain completely unchanged.
Switching between two separate user processes ($T2$) is a full process context switch, which is a much more complex operation managed entirely by the operating system scheduler.
A process context switch ($T2$) requires saving the registers of the old process, loading the registers of the new process, switching the control of memory by changing address translation tables (page tables), and dealing with TLB invalidation.
Since a process context switch ($T2$) includes a change in memory management structures along with multiple mode switches to execute the scheduler code, it inherently takes significantly more overhead and time than a simple mode switch ($T1$).
Therefore, the time taken for a mode switch is strictly less than the time taken for a process context switch:
$$T1 < T2$$
Correct Option: C