Directions: In this question, a sentence has been divided into 5 parts. The part given as bold is the starting fragment of the sentence. You need to rearrange the rest of the parts in a meaningful sequence and choose the option that gives the correct sequence. 
Important for :
1
very aware of the fact that China is quietly (A) / with a sense of urgency (B) / The Indian government needs to be / and must take steps to counter it (C) / extending its influence in Ladakh (D)
» Explain it
D
1st fragment:

The Indian government needs to be …

Clearly, either an adjective or a verb (with ing) follow here.

Now, if we place the fragment D next, it doesn’t make any sense and will make the context absurd. Thus, we can place fragment A next.

Connectors: 

A to D

very aware of the fact that China is quietly (A)

extending its influence in Ladakh (D)

Now, between B and C, if we choose to place fragment B next, it once again won’t be logical in the context of the sentence.

Therefore, fragment C comes next and B comes at the end.

The proper sequence of the fragments will be:

ADCB

Option D is hence the correct answer.
2
After realizing that conventional tools / with his new students, Vishnu Sharma decided (A) / 50 stories that focused on five strategies (B) / and techniques of teaching will not work (C) / to write a collection of more than (D)
» Explain it
B
1st fragment:

After realizing that conventional tools …

Clearly, fragment C follows as it has the key word ‘techniques’ in it.

Connectors:

C to A:

and techniques of teaching will not work (C)

with his new students, Vishnu Sharma decided (A)

A to D:

with his new students, Vishnu Sharma decided (A)

to write a collection of more than (D)

Clearly, B comes at the end.

The proper sequence will therefore be:

CADB

Option B is hence the correct answer.
3
In Chennai, citizens have petitioned / of a large canal to remove (A) / the tribunal to stop pollution of the Cooum river, (B) / as well as to ensure proper dredging (C) / silt and improve flow (D)
» Explain it
C
1st fragment:

In Chennai, citizens have petitioned …

Evidently, fragment B comes next as a petition is done to ‘tribunal’ (a body established to settle certain types of dispute).

Connectors:

B to C:

the tribunal to stop pollution of the Cooum river, (B)

as well as to ensure proper dredging (C)

Here, the word ‘dredging’ which means ‘to bring up or clear (something) from a river’ clearly implies it in line with the fragment B.

C to A:

as well as to ensure proper dredging (C)

of a large canal to remove (A)

Clearly, the fragment D comes at the end.

The proper sequence will therefore be:

BCAD

Option C is hence the correct answer.
4
to be the first beneficiary of this system (A) / recording facility (B) / to launch the "Dial 100" and (C) / in its control rooms, and Bangalore is likely (D) / The State Police Department is set
» Explain it
E
1st fragment:

The State Police Department is set …

At first glance either of the two fragments A and C seems to be the next fragment, but presence of ‘this’ in fragment A makes it a weaker choice as we are not sure which ‘system’ is being referred to here.

Clearly, fragment C follows next.

Connectors:

C to B:

to launch the "Dial 100" and (C)

recording facility (B)

Clearly, both “Dial 100” and ‘recording facilities’ are new features that the State Police Department is introducing in the sentence.

B to D:

recording facility (B)

in its control rooms, and Bangalore is likely (D)

Clearly, fragment A comes at the end.

The proper sequence will therefore be:

CBDA

Option E is hence the correct answer.
5
for games designed (A) / produced promising results (B) / Over the past year, / several small pilot studies have (C) / to help children with autism (D)
» Explain it
A
1st fragment:

Over the past year, …

The 1st fragment doesn’t help much here but if we observe, we find that only the fragment C has a noun phrase with verb ‘have’ following it. Clearly, fragment C comes next.

Connectors:

C to B:

several small pilot studies have (C)

produced promising results (B)

B to A:

produced promising results (B)

for games designed (A)

Clearly, fragment D comes at the end.

The proper sequence will therefore be:

CBAD

Option A is hence the correct answer.