The main differenc between View and Materialized View states that -

1. View means it stores the SQL statement in the database and let you use it as a table. Everytime you access the view, the SQL statement executes.

2. Materialized view means it stores the results of the SQL in table form in the database. SQL statement only executes once and after that everytime you run the query, the stored result set is used. Advantage include quick query results.

We need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or) 

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

The following arrangements satisfy all 3 conditions.

Arrangement 1: 3 books in a row; 12 rows.

Arrangement 2: 4 books in a row; 9 rows.
Arrangement 3: 6 books in a row; 6 rows.
Arrangement 4: 9 books in a row; 4 rows.
Arrangement 5: 12 books in a row; 3 rows.

Therefore, the possible arrangements are 5.

Let the salary of Karthik 2 years ago be Rs.100
So, Lucky's salary 2 years ago was Rs.50

Karthik's present salary has seen two 10 percent increases. So as Lucky's salary.

So, Karthik's salary 1 year ago = 100 + 10% of 100 = 100 + 10 = 110.
Karthik's present salary = 110 + 10% of 110 = 110 + 11 = 121.

Lucky's salary 1 year ago = 50 + 10% of 50 = 50 + 5 = 55
Lucky's present salary = 55 + 10% of 55 = 55 + 5.5 = 60.5

Lucky's present salary of 60.5 = 50% of Karthik's present salary of 121.

The mother completes the job in x hours.
So, the daughter will take 2x hours to complete the same job.

In an hour, the mother will complete 1/x of the total job.
In an hour, the daughter will complete 1/2x of the total job.

So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.

The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6 th of the task in an hour.

Equating the two information, we get 3/2x = 1/6
By solving for x, we get 2x = 18 or x = 9.

The mother takes 9 hours to complete the job.

We can easily Answer this by taking some values.

The question states that the two fractions, each have values between 0 and 1.

Let us say one of the fraction is 1/2 and the other fraction is 1/3 .

The product of the two fractions is 1/2 x 1/3 = 1/6 .
 is lesser than both 1/2  and 1/3 .

So, the correct answer is that the product is always less than either of the original fractions. 

Let 's' be the number of small packets and 'b' the number of large packets sold on that day.

Therefore, s + b = 5000 ... eqn (1)

Each small packet was sold for Rs.150.
Therefore, 's' small packets would have fetched Rs.150s.

Each large packets was sold for Rs.250.
Therefore, 'b' large packets would have fetched Rs.250b.

Total value of sale = 150s + 250b = Rs. 10.5 Lakhs (Given)

Or 150s + 250b = 10,50,000 ... eqn (2)

Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)

Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000
Or b = 3000

We know that s + b = 5000
So, s = 5000 - b = 5000 - 3000 = 2000.

2000 small packets were sold.