Log₃8
Log₉16 Log₄10
= 3Log₁₀2

A man left $18000 with the direction that it should be divided in such a way that his 3 sons aged 9, 12 and 15 years should each receive the same amount when they reached the age of 25. If the rate of interest is 3½% p.a., what should each son receive when he is 25 years old?

Find how many words can be formed of the letters of the word "FAILURE". The four vowels always coming together.

In how many ways 10 examination papers be arranged so that the best and worst papers never come together.

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?

How many different words can be formed with the letters of HARYANA? In how many of these
  1. H and N are together,
  2. begin with H and end with N?

If all the permutations of the letters of the word CHALK be writtern down as in a dictionary, what is the rank of the word?

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?

In how many ways can 21 white balls and 19 black balls be arranged in a row so that no two black balls may be together?

  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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