When something is dilapidated, it is run down. This does not mean that it is totally destroyed. Nevertheless, a dilapidated piece of property is in poor shape.  The word comes from roots that literally mean with stones fallen down. While such a piece of property might be inexpensive or ugly, this is not what "dilapidated" means.  "To be dilapidated" is to be in a state of disrepair or ruin. Thus, the best option is "battered." While this can be used to describe someone who has been physically injured, it also can be used to describe something that has been worn down by use or over-exposure to poor conditions. Thus, someone can have a "battered old car."

For this question, you have to be very careful to match the synonym most closely. The options provided all are related to the word "irate." Note that "irate" means the state of being extremely angry. Thus, "enraged" is the best option among those provided for "irate."  All of the other ones are too weak for so strong an emotion.

"Pensive" is an adjective meaning performing reflection or deep and serious thought. "Contemplative" is a similar adjective meaning engaged in the act of thinking as well. The words "annoyed," "disturbed," "distracted," and "confused" are all antithetical to "pensive."

"Jocular" is an adjective meaning exhibiting a joyous or jesting mood. "Playful" means wanting to play or be amused, and is a close synonym. "Annoying," "obvious," "blank," and "beautiful" are all adjectives unrelated to playfulness or joking.

"Petulant" is an adjective meaning rude or bad tempered, often in a childish or immature way. "Peevish" means grumpy and has the same connotation of childishness, "feckless" means cowardly or incompetent, "fastidious" means careful and neat, "quiescent" means agreeable, and "mendacious" means lying.

"Crestfallen" means dejected, feeling sad, disappointed and hopeless. To provide further help, "lifeless" means without life; "miserly" means stingy, not inclined to spend money; "ebullient" means enthusiastic; "ruffled" means disturbed. 

"Enervating" means tiring, causing one to feel drained of energy. It is opposite in meaning to "invigorating" which means energizing. To provide further help, to "brandish" means to flourish or wave around; "demoralizing" means taking away morale, making one feel less enthusiastic; "placating" means soothing, comforting. 

Vulnerable means susceptible to physical or emotional harm.

Reticent means not readily revealing thoughts or feelings, or reserved.

"Urbane" means cultured or civilized. "Metropolitan" means urban or concerning a city. "Urgent" means needing immediate attention. "Resolute" means determined or strong-willed. "Succinct" means short and to the point.