Verbal Reasoning - Mental Ability Questions

Lethargic means "sluggish", kind of inactive

Vital means full of energy, lively

So, they are antonyms.

So, for the 2nd part of the analogy, you are looking for a antonym to trite

Trite means lacking originality or freshness. Overused. Kind of like a cliche

So, an antonym could be original, unique, innovative.

Here Grass is to Erosion and whereas Dam is to Water.

Since Grass prevents Erosion similarly Dam prevents Water flow.

Hence, Grass : Erosion :: Dam : Water.

Sum of place value in a row is 30.

So the letter which comes in place of '?' is 'I'. 

$$\begin{gathered} 2 = 12 + 1 \\ 3 = 22 - 1 \\ 10 = 32 + 1 \\ Now 102 - 1 = 99 \\ 9802 = 992 + 1 \end{gathered}$$

2nd letter to the left of 17th letter from the right means (2 + 17 = ) 19th letter from the right = (26 - 19 + 1 =) 8th letter from the left end , i.e H.  Thus, 8th letter falls into the second section of the reversed sequence. Now, the sequence FGHIJ is reversed and becomes JIHGF. Clearly, position of H remains unchanged. Hence the required letter is H.

Brother of my wife — My brother.in-law; Son of lady's brother is the brother-in-law of the man. 

So lady's brother is man's father-in-law

i.e., the lady is the sister of man's father-in-law. 

Number of students in class = (8 + 1 + 37) = 46

Since Harsh has no brother or sister, so he is his father's only son. Now, wife of my father's son — my wife. 

So, Harsh's wife is the man's mother or the man is Harsh's son.