The phrase "besides the mark" is wrong. It should either be "off the mark" or "beside the mark". The other three usages of the word are correct.

According to Oxford Dictionary (http://www.oxforddictionaries.com/) LICENTIOUS means promiscuous and unprincipled in sexual matters:
""the ruler’s tyrannical and licentious behaviour""
synonyms: dissolute, dissipated, debauched, degenerate, salacious, immoral, wanton, decadent, depraved, profligate, impure, sinful, wicked, corrupt, indecent, libertine; lustful, lecherous, lascivious, libidinous, prurient, lubricious, lewd, promiscuous, unchaste, carnal, fleshly, intemperate, abandoned; ribald, risqué, smutty, dirty, filthy, coarse, perverted

According to Oxford Dictionary (http://www.oxforddictionaries.com/) RAMSHACKLE means (especially of a house or vehicle) in a state of severe disrepair.
""a ramshackle cottage""
synonyms: tumbledown, dilapidated, derelict, ruinous, falling to pieces, decrepit, neglected, gone to rack and ruin, run down, crumbling, decaying, disintegrating, rickety, shaky, unsteady, broken down, unsound, unsafe;

According to Oxford Dictionary (http://www.oxforddictionaries.com/) MORIBUND means (of a thing) in terminal decline; lacking vitality or vigour.
""the moribund commercial property market""
synonyms: declining, in decline, on the decline, waning, dying, stagnating, stagnant, decaying, crumbling, atrophying, obsolescent, on its last legs;

In option c), the word should be bough, which means the main branch of a tree.

According to Oxford Dictionary (http://www.oxforddictionaries.com/) FOMENT means instigate or stir up (an undesirable or violent sentiment or course of action).
""they accused him of fomenting political unrest""
synonyms: instigate, incite, provoke, agitate, excite, stir up, whip up, arouse, inspire, encourage, urge, actuate, initiate, generate, cause, prompt, start, bring about, kindle, spark off, trigger off, touch off, fan the flames of;

The word in the first blank should be something that is associated with slaves. ‘Allegiance’ is not apt, and option (D) can be ruled out. In the second blank, the word should talk about the nature of “the shadow of law”. Among the options, the best word to describe this is ‘portentous’. The word ‘loyalty’ in option (B) also fits perfectly well in the first blank. So, option (B) is the correct answer.

According to Oxford Dictionary (http://www.oxforddictionaries.com/) INSOUCIANT means showing a casual lack of concern.
""an insouciant shrug""
synonyms: nonchalant, untroubled, unworried, unruffled, unconcerned, lacking concern, indifferent, blasé, heedless, relaxed, calm, equable, equanimous, serene, composed, casual, easy, easy-going, airy, breezy, carefree, free and easy, free from care, free from worry, happy-go-lucky, light-hearted, frivolous, unserious; informalcool, laid back, upbeat
""he had an insouciant attitude to their money problems""
antonyms: anxious, concerned

The sentence indicates that a mighty will is something that is very eagerly sought by people. Hence, the appropriate word would be fervently

From the given options, mow down (meaning overwhelm, crush) and ludicrous (meaning unreasonable, silly) are most appropriate words to fill in the blanks.

According to Oxford Dictionary (http://www.oxforddictionaries.com/) LICENTIOUS means promiscuous and unprincipled in sexual matters:
""the ruler’s tyrannical and licentious behaviour""
synonyms: dissolute, dissipated, debauched, degenerate, salacious, immoral, wanton, decadent, depraved, profligate, impure, sinful, wicked, corrupt, indecent, libertine; lustful, lecherous, lascivious, libidinous, prurient, lubricious, lewd, promiscuous, unchaste, carnal, fleshly, intemperate, abandoned; ribald, risqué, smutty, dirty, filthy, coarse, perverted

Reprobate means an unprincipled person. Synonyms are rogue, rascal, scoundrel, good-for-nothing, villain, wretch, unprincipled person, rake, profligate, degenerate, debauchee, libertine.

According to Oxford Dictionary (http://www.oxforddictionaries.com/) RAMSHACKLE means (especially of a house or vehicle) in a state of severe disrepair.
""a ramshackle cottage""
synonyms: tumbledown, dilapidated, derelict, ruinous, falling to pieces, decrepit, neglected, gone to rack and ruin, run down, crumbling, decaying, disintegrating, rickety, shaky, unsteady, broken down, unsound, unsafe;

According to Oxford Dictionary (http://www.oxforddictionaries.com/) ABNEGATION means the action of renouncing or rejecting something.
""abnegation of political power""
synonyms: renunciation, rejection, refusal, abandonment, abdication, surrender, giving up, relinquishment, abjuration, repudiation, denial, eschewal, disavowal, casting aside
""to ignore these issues would be a serious abnegation of their responsibilities""

According to Oxford Dictionary (http://www.oxforddictionaries.com/) LIMPID means (of a person's eyes) unclouded; clear.
"the limpid grey eyes gazed trustfully at her"
Synonyms: clear, transparent, glassy, glass-like, crystal clear, crystalline, see-through, translucent, pellucid, unclouded, uncloudy

According to Oxford Dictionary (http://www.oxforddictionaries.com/) DECREPITUDE means the state of being decrepit.
""he had passed directly from middle age into decrepitude""
synonyms: feebleness, enfeeblement, infirmity, weakness, frailty, debilitation, debility, sickliness, incapacitation, malaise;

The word in the first blank should be something that is associated with slaves. ‘Allegiance’ is not apt and option d) can be ruled out. In the second blank, the word should talk about the nature of “shadow of law”. Among the options, the best word to describe this is ‘portentous’. The word ‘loyalty’ in option b) also fits perfectly well in the first blank. So, option b) is the correct answer.

From the given options, mow down (meaning overwhelm, crush) and ludicrous (meaning unreasonable, silly) are most appropriate words to fill in the blanks.

Axiomatic means something that is self-evident

Flawed means something that is not perfect. The remaining mean something that is affected or unnatural

'Glanced pointedly' and 'glanced earnestly' are inappropriate usages. Though both 'nonchalantly' and 'casually' fit in the first blank, the word 'blatant' cannot be used in the second blank. This rules out option a). Option d) is the correct answer.

Fortuity means a chance occurrence. The remaining terms are used to refer to source or origin of things

The sentence indicates that in spite of doubts Akshay agreed to the deal. Hence the appropriate option would be option C.

Ostensible, Feigned and Specious refer to things that appear to be one thing but are something else - i.e. insincere or superficially true. Flagrant is something that is conspicuously or obviously offensive. Hence, the correct option is c.