1. the number having all the three
2. T and S but not C
3. only C

(ii) If the number of students using no book at all is 10, and the number of students using all the three is 20. Show that the information is inconsistent.

 Log₃8Log₉16 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?

A machine depreciates at the rate of 10% of its value at the beginning of a year. The machine was purchased for \$5810 and the scrap value realized when sold was \$2250. Find the number of years that the machine was used.

A machinery in a factory is valued at \$49074 and it is decided to reduce the estimated value at the end of each year by 15 per cent of the value at the beginning of that year. When will the value be (a) \$20,000 (b) 1/10th of the original value?

Find the present value of an annuity of \$1000 p.a. for 14 years following compound interest at 5% p.a.

Calculate the amount and present value of an annuity of \$3000 for 15 years if the rate of interest be 4½% p.a.

How many different arrangements can be made by using all the letters of the word (i) MONDAY; (ii) ORIENTAL? How many of these arrangements begin with A and end with N?

In how many ways can a consonant and a vowel be chosen out of the letters of each of the words (i) LOGARITHM, (ii) EQUATION?

There are 8 vacant chairs in a room. In how many ways can 5 persons take their seats?

There are 50 stations on a railways line. How many different kinds of single first class tickets must be printed so as to enable a passenger to go from one station to another?

How many different numbers of six digits can be formed with the digits 3, 1, 7, 0, 9, 5? How many of these have 0 in ten’s places?

How many different words can be formed with the letters of the word SUNDAY? How many of the words begin with N? How many begin with N and end in Y?

There are four routes for going from A to B and five routes for going from B to C. In how many different ways can a man go from A to C via B

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 3000 and 4000 can be formed with the digits 1, 2, 3, 4, 5, 6?

In how many ways 8 examination papers be arranged in a line so that the best and worst papers never come together?

Six papers are set in an examination of which two are mathematical. In how many different orders can the papers be arranged so that (i) the two mathematical papers are together and (ii) the two mathematical papers are not consecutive?

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?

The figures 1, 2, 3, 4, 5 are written in every possible order. How many of the numbers so formed will be greater than 23000?

Find the number of ways in which n books can be arranged on a shelf so that two particular books are not together.

Find the number of permutations of the letters of the word “SIGNAL’ such that the vowels may occupy only odd positions.

In how many ways can be letters of the word VIOLENT be arranged so that the vowels I, O, E, occupy even places only.

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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?

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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.

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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?

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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?

a(q-r)+b(r-p)+c(p-q)=0

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