Here the given numbers are 

567  284  696  865  738

When 1 is added to the last digit of each of the above numbers, it becomes as follows :

568  285  697  866  739

After reversing the order of digits , we get

865  582  796  668  937

Now , when the numbers are arranged in ascending order their order becomes as follows:

582  668  796  865  937

Hence , the fourth number is 865 (a number formed by 567). Therefore option(1) is correct answer.

Second, fourth and the sixth digits of the number are 3, 1 and 6. Using these digits only once we can make 361, which is a perfect square number. Hence, our answer is 19 x 19 = 361

Given Number :  7 6 5 3 4 2 1 8 

New Number :    8 7  6 4 5 3 2 9

Ascending Order :  2 3 4 5 6 7 8 9 

Fifth digit in the above ascending order arrangement is '6' . Hence option(1) is the correct answer.

5th to the right of 12th digit from the right end means (12 - 5 = ) 7th digit from the right.ie 3.

Three persons A, B, C can be arranged in a queue in six different ways, ie ABC, CBA, BAC, CAB, BCA, ACB. But since there are only 3 persons ahead of C, so C should be in front of the queue. Thus, there are only two possible arrangements, ie CBA and CAB.

We may consider the two cases as under:

Case I:  ←3C↔8B↔5A→21

Clearly, number of persons in the queue = (3+1+8+1+5+1+21=) 40

Case II:  ←3C A↔5B

Number of persons between A and C                  

= (8 - 6) = 2   

∵[C↔8B A→21B]

Clearly number of persons in the queue = (3+1+2+1+21) = 28

Now, 28 < 40. So, 28 is the minimum number of persons in the queue.                                                     

A > C  -----(i),   B > D  -----(ii),  E < B  --------(iii),  E > C  ---------(iv),  C > D  ---------(v)

from (i) and (v),   we get    A > C > D   ---------(I)

from (iii) and (iv), we get    B > E > C    --------(II)

From (I) and (II) , it is clear that 'D' is the thinnest.

No. of boys up to the 34th rank = 34-18 = 16

 Total no of boys = 180x1/2+1 = 60

 number of boys after the rank of Rupesh = 60 - 16 = 44

Total days from 25th June to 15th August = 5 + 31 + 15 = 51 days

51/7  = 7 weeks and 2 days 

August 15 = Wednesday + 2 = Friday