Log₃8
Log₉16 Log₄10
= 3Log₁₀2

How many numbers between 1000 and 10,000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? How many of them are odd?

There are six students of whom 2 are Indians, 2 Americans and the remaining 2 are Russians. They have to stand in a line so that the two Indians are together, the two Americans are together and so also the two Russians. Show that there are 48 different ways of arranging the students.

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further in how many of these committees

  1. a particular professor is included?
  2. a particular student is excluded?

  1. Find the linear relationship between x and y.
  2. Find the slope of the line, what does it indicate
  3. Find the number of units that must be produced so that
    1. There is neither profit nor loss.
    2. There is a profit of Rs. 1000
    3. There is a loss of Rs. 300; it being given that the selling price is Rs. 8 per unit

  1. Find the linear relationship between x and y.
  2. Find the slope of the line, what does it indicate
  3. It selling price is Rs. 7 per unit. Find the number of units that must be produced so that
    1. There is neither profit nor loss.
    2. There is a profit of Rs. 300
    3. There is a loss of Rs. 300.

12+9+6+.........
is equal to (i) -30, (ii) -100?

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