The correct answer is option 'B' - cherish.

Explanation:
In the given statement, it signifies that as citizens of free India, we hold both our democracy and our secularism in high regard and value them deeply. The word "cherish" best fits this context as it implies a strong affection, appreciation, and protection towards something important.

Here is a detailed explanation of why the other options are not the correct answers:

a) Promote: While promoting democracy and secularism is important, the sentence suggests that as citizens, we hold these values dear rather than actively promoting them. Therefore, "promote" is not the most appropriate word here.

b) Cherish: This option is the correct answer. "Cherish" means to hold dear or treasure something. As citizens of free India, we cherish both our democracy and our secularism, emphasizing the strong attachment and value we place on these principles.

c) Establish: The word "establish" implies the act of creating or introducing something new. Since democracy and secularism are already established in India, this option does not accurately reflect the citizens' relationship with these values.

d) Champion: While "champion" can mean to support or fight for a cause, it does not convey the same level of personal attachment and value as the word "cherish." Therefore, it is not the most suitable option in this context.

e) Declare: "Declare" means to state or announce something formally. While citizens can declare their support for democracy and secularism, the sentence suggests a deeper emotional connection and appreciation rather than a mere declaration.

In conclusion, the word "cherish" is the most appropriate choice as it conveys the strong affection, appreciation, and protection citizens have towards their democracy and secularism in free India.