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Given:

Formula used:

Average = Sum of observations/Number of observations

Calculation:

Total number of male participants from all district = 42 + 48 + 46 + 56 = 192

Average number of male participants = 192/4 = 48

∴ The average number of male participants in the voluntary work from all four districts are 48.

Given:

Calculation:

Total number of male participants from Shimla and Kangra = 48 + 56 = 104

Total number of female participants from Chamba and Kullu = 30 + 60 = 90

⇒ Required ratio = 104 : 90 = 52 : 45

∴ The ratio between the total number of male participants from Shimla and Kangra together and the total number of female participants from Chamba and Kullu together is 52 : 45.

Given:

Calculation:

Total participation from the district Chamba = 42 + 30 = 72

Total participation from the district Shimla = 48 + 52 = 100

Total participation from the district Kullu = 46 + 60 = 106

Total participation from the district Kangra = 56 + 20 = 76

From the above districts, the participation from Kullu is maximum, and the participation from Chamba is minimum

⇒ The required difference = 106 – 72 = 34

∴ The difference between the district having the maximum participation and the district having the minimum participation is 34.

Given:

Formula used:

Percentage change = {(Final value – Initial value)/Initial value} × 100

Calculation:

Total number of female participants from district Chamba and Shimla = 30 + 52 = 82

Total number of male participants from district Kangra and Kullu = 46 + 56 = 102

⇒ Percentage change = {(102 – 82)/102} × 100

⇒ (20/102) × 100 = 19.60%

⇒ 19.60% ≈ 20%

∴ The required percentage is 20%.

Given:

Formula used:

Percentage change = {(Final value – Initial value)/Initial value} × 100

Calculation:

Difference between the male voluntary from Shimla and female voluntary from Kangra = 48 – 20 = 28

⇒ Percentage change = {(28/48) × 100} = 58.33%

∴ The required percentage is 58.33%.

The least possible Venn diagram for the given statements is as follows

Conclusion:

I. Some masks are hats → True (As all hats are masks so, Some hats are definitely masks)

II. No caps are covers is a possibility → True (As there is no relation between caps and covers so we cannot say anything here but any possibility can follow here, So it is true)

Hence, Both I and II follow.

Important points:

Some: In this case, Some part is definitely true whereas the rest part can be true if there is the possibility of Some not and All.

Some Not: In this case, Some part is negative that is definite. If the rest part is positive then some part can which is positive will be true otherwise possibility of No will be true. 

Only a few: In this case, The cases of Some and Some Not will follow.

The least possible Venn diagram for the given statements is as follows,

Conclusions

I.Some Pen can be Blue → True (As we know that only a few pen are red that means some part of the pen is red but we don't know rest part of pen whether that is red or not. Hence the possibility is True)

II.Some Red can be Black → True (As we know that only a few red is blue that means some part of the red is blue but we don't know rest part of red whether that is blue or not. Hence the possibility is True)

Hence, conclusion Both I and II follow.

The least possible Venn diagram for the given statements is as follows:

Conclusions:

I. Some scales are eraser → False (It is possible, but there is no definite positive or negative relation is given between the elements, therefore it is false)

II. No scales are eraser → False (It is possible, but there is no definite positive or negative relation is given between the elements, therefore it is false)

Conclusion I and II thus form a complementary pair.

Hence, either conclusion I or II follows.

The least possible Venn diagram for the given statements is as follows

Conclusions

I. No fruit is Orange → False (As there is no relation between fruit and orange, No fruit is orange is possible but not definite. So it is false)

II. Some fruit is not Apple → False (As some fruit is apple means some part of the fruit is in an apple but we don't know about rest part of fruit whether it is in apple or not so it is possible but not definite. So it is false)

Hence, Neither I Nor II follows.

Names of Person: Manoj, Mani, Mohan, Manu, Manju, Meena, Madhu and Mahesh.

Facing direction: All of them are facing North.

1. Four people are sitting between Manju and Manu, but neither of them is sitting at any extreme ends of the row. 

(Here two cases exists, Case - 1: Manu sits to the right of Manoj and four people sit between them. Case - 2: Manu sits to the left of Manju and four people sit between them.)

2. Two people are sitting between Manju and Mohan, who is sitting to the immediate right of Meena.

3. Only one person is sitting between Meena and Madhu, who is not sitting at any extreme ends of the row.

4. Mani is sitting exactly in the middle of Mohan and Manoj.

5. Madhu is sitting second to the left of Mahesh.

(Here Case - 2 gets eliminated, as Madhu can not be placed second to the left of Mahesh.)

Hence, Mahesh is sitting at the extreme right end of the row.