To understand why the correct answer is option 'D', let's break down the given information and analyze it step by step.

Horizontal and Vertical Tangencies:
A stationary closed Lissajous pattern on an oscilloscope means that the pattern formed by the two inputs (horizontal and vertical) remains constant over time. In this case, the pattern has 3 horizontal tangencies and 2 vertical tangencies.

Frequency of the Horizontal Input:
The frequency of the horizontal input is given as 3 kHz. This means that the horizontal input signal completes 3000 cycles in one second.

Relationship between Horizontal and Vertical Inputs:
In a Lissajous pattern, the shape of the pattern depends on the frequency and phase relationship between the horizontal and vertical inputs. The shape of the pattern can change depending on the ratio of the frequencies of the two inputs.

Horizontal Tangencies:
The number of horizontal tangencies in the Lissajous pattern is related to the frequency ratio between the horizontal and vertical inputs. In this case, there are 3 horizontal tangencies, which means that the frequency ratio is 3:1.

Vertical Tangencies:
Similarly, the number of vertical tangencies is also related to the frequency ratio between the inputs. In this case, there are 2 vertical tangencies, which means that the frequency ratio is 2:1.

Finding the Frequency of the Vertical Input:
We know that the frequency ratio between the horizontal and vertical inputs is 3:1 for horizontal tangencies and 2:1 for vertical tangencies. To find the frequency of the vertical input, we need to find a common multiple of both ratios.

The common multiple of 3 and 2 is 6. Therefore, the frequency ratio between the horizontal and vertical inputs is 6:2, which can be simplified to 3:1.

Since we are given that the frequency of the horizontal input is 3 kHz, the frequency of the vertical input can be calculated as follows:

Frequency of vertical input = Frequency of horizontal input / Frequency ratio
Frequency of vertical input = 3 kHz / 3
Frequency of vertical input = 1 kHz

Therefore, the frequency of the vertical input is 1 kHz, which matches with option 'D'.