As the secret was kept between the speaker and Sam.

Correct Option: D

Option (d) is correct, as the secret was kept between the speaker and Sam. Option (a) is wrong, because then the statement becomes redundant. Option (b) is incorrect. Option (c) is wrong, because amongst is used in the case when more than two people or entities are involved.
The correct word is filled in the above given sentence :-
Sam asked me to keep this secret between us .So , option D is correct .

As we can say that ,
Launch refers to introducing something to the public for the first time.

Correct Option: C

As we can say that ,
Option (c) is correct, because a product is launched. Launch refers to introducing something to the public for the first time. Start means to just begin or set in motion, it is synonymous with ‘begun’; whereas, commissioned means ‘to give an official approval’.
Therefore , option C is correct word .

When a ship founders, it fills with water and sinks. Similarly the carriage foundered (that is, sank) in the snowdrift (deep pile of snow formed by the wind). The trapped (sunk) carriage then had to be freed from the snowdrift. In other words, it had to be extricated.

Correct Option: D

When a ship founders, it fills with water and sinks. Similarly the carriage foundered (that is, sank) in the snowdrift (deep pile of snow formed by the wind). The trapped (sunk) carriage then had to be freed from the snowdrift. In other words, it had to be extricated.
The correct word is filled in the above given sentence :-
The carriage foundered in a snowdrift and it took two hours to extricate it.