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HIGHER MATH

HIGHER MATHS CLASS - 1 PREMUTATION AND COMBINATION

DIRECTIONS for questions 1 to 38: Choose the correct alternative. 1.

2.

There are 10 toy cars, 10 toy buses and 10 toy guns. A child has an option to select one toy of each kind. How many choices does he have? 1] 1 2] 30 3] 3 4] Cannot be determined. There are 10 toy cars, 10 toy buses 10 toy guns in which each particular toy is of a different kind. A child has to select one toy of each kind. How many choices does he have?

3.

1] 1000 2] 30 3] 3 How many three-digit numbers are even?

4] Cannot be determined.

4.

1] 400 2] 900 3] 500 4] 450 How many three-digit odd numbers are formed by using the digits 0, 1, 2, 3, 4 exactly once?

5.

1] 16 2] 30 3] 36 4] 18 How many three-character codes can be formed using the English alphabets and the digits?

6.

1] 260 2] 36 3] 46656 4] None of these Five boys and five girls want to sit in a row. In how many ways can they sit such that no two boys sit together?

7.

1] 720 2] 2 × 6 × 5! 3] 6(5!) 2 4] None of these Five boys and five girls want to sit in a row. In how many ways can they sit such that all boys sit together?

8.

1] 2 × 6 × 5! 2] 30 3] 720 4] 6! × 5! How many numbers greater than 6000 and less than 10000 are their in which all the digits are different?

9. 10.

11.

1] 2016 2] 9000 3] 9!/5! 4] None of these If a polygon has 35 diagonals, find the number of sides in the polygon? 1] 10 2] 30 3] 35 4] Cannot be determined. If there are 8 points in a plane of which 3 are collinear then find the number of different lines that can be form? 1] 1 2] 11 3] 26 4] None of these The 24 probables include 10 batsmen,7 bowlers,5 all rounders and 2 wicket keepers.In how many ways can a playing eleven of 5 batsmen, 1 allrounder,1 wicketkeeper and 4 bowlers be chosen such that the captain,a bowler is sure to play.? 1] 50400

2] 3008

3] 16050

1

4] Cannot be determined.

IMS-34-UG-AL-HM-Class-1

®

HIGHER MATH

12.

How many words can be formed using all the letters of the word ELEPHANTA such that all the vowels are together? 1] 17280

13.

3] 4320

4] none

How many words can be formed using the letters of the word TRIVANDRUM such that no two vowels are together? 1] 7! × 8! × 3!

14.

2] 720

2] 30

3] 3000

4] (8! × 7!)/5!

In a packet there are 10 identical sweets. Find how many choices does a person have in selecting the number of sweets? 1] 11

2] 100

3] 1

4] Cannot be determined.

DIRECTIONS for questions 15 to 18: When two non-identical unbiased die are rolled; 15. What is the probability of getting sum of digits as 7 or 10? 1] 16.

1 6

3]

3 36

4]

1 4

1 12

2]

11 12

3]

1 9

4] none of these

What is the probability of getting sum of digits as odd? 1]

18.

2]

What is the probability of getting sum of the digits as greater than 10? 1]

17.

1 18

1 2

2]

5 11

3]

3 11

4] none of these.

What is the probability of getting sum of digits as a prime number? 1]

1 15

2]

4 9

3]

1 18

4]

1 36

DIRECTIONS for questions 19 and 20: If an unbaised dice with digits 1, 1, 1, 2, 3, 4 is rolled 19. What is the probability that it shows 1? 1] 20.

1 2

2]

1 6

3]

1 4

4] none of these.

What is the probability that it shows 3?

1 1 1 2] 3] 4] none 6 3 4 If three coins are tossed 21. What is the probability that at least two of them show head?

1]

1]

1 2

IMS-34-UG-AL-HM-Class-1

2]

1 4

3]

2

1 8

4]

2 7

HIGHER MATH

22.

What is the probability that at least one shows tail? 1]

23.

1 8

2]

1 4

3]

3 8

4]

7 8

4]

1 8

What is the probability of exactly one coin shows head? 1]

1 4

2]

2 7

3]

3 8

DIRECTIONS for questions 24 to 28: A standard pack of cards has 52 cards has 4 suits (Hearts, clubs, spades and diamonds) each suit has 13 cards, (ace, king queen, jack and 2-10) 24. One card is drawn at random .What is the probability that it is a king? 1] 25.

30.

3 52

4]

1 13

1 17

2]

1 13

3]

3 13

4] none of these

1 52

2]

15 52

3]

1 17

4]

4 13

1 26

2]

2 13

3]

1 17

4]

1 13

If two cards are drawn one after another with replacement then what is the probability that the cards are either a king or a spade. 1]

29.

3]

If two cards are drawn at random then what is the probability that both cards are spades? 1]

28.

1 26

One card is drawn at random .What is the probability that it is a diamond or a king? 1]

27.

2]

One card is drawn at random .What is the probability that it is a diamond but not a king? 1]

26.

5 52

1 52

2]

3 52

3]

3 28

4] None

What is the sum of all 4 distinct digit numbers that can be formed by the digits 1, 2, 3, 4, 5? 1] 609993 2] 309999 3] 399960 4] 360990 A family has two children. What is the probability that both the children are boys given that at least one of them is a boy? 1]

1 4

2]

3 4

3]

3

1 2

4] None

IMS-34-UG-AL-HM-Class-1

HIGHER MATH

31.

A candidate is to be selected for each of three posts. For the first post there are 5 candidates for the second post there are 8 and for the third there are 7.What is the probability for selecting a candidate for at least one post assuming he has applied for all three posts? 1]

32.

4 5

2 5

2]

1 5

3]

1 6

4]

2 3

89 156

2]

49 156

3]

40 156

4] None

3 10

2]

1 5

3]

3 5

4]

4 9

9 24

2]

1 24

3]

23 24

4]

13 24

3 8

2] 1

3]

1 24

4]

23 24

A box contains 8 red balls, 10 blue balls & 4 white balls. Each ball is of different size if a ball is selected at random. What is the probability that the red ball selected is the smallest red ball? 1]

38.

4]

There are 4 envelopes and 4 letters if the letters are placed at random what is the probability that none of the letters are placed in the right envelope? 1]

37.

2 5

There are 4 envelopes and 4 letters if the letters are placed at random what is the probability that none of the letters are placed in their respective envelopes? 1]

36.

3]

100 students appeared for two examinations 60 passed in first and 50 passed in second and 30 passed in both then find the probability that a student selected at random has failed in both the examinations? 1]

35.

3 5

There are two bags, bag I contains 5 red and 7 white balls and bag II contains 7 red and 5 white balls. One ball is transferred from bag I to bag II and then a ball is drawn from bag II. What is the probability that it is a red ball? 1]

34.

2]

A dice is rolled three times and the sum of three numbers appearing is 15. What is the probability that the first roll was four? 1]

33.

1 5

1 22

2]

1 8

3]

1 14

4] None

If a four digit number is formed using all the digits 1,2,5,7 exactly once, what is the probability that the number is divisible by 25? 1]

1 24

IMS-34-UG-AL-HM-Class-1

2]

1 12

3]

4

1 6

4] None

Higher Math_Class_1_stu

HIGHER MATH DIRECTIONS for questions 1 to 38: Choose the correct alternative. IMS-34-UG-AL-HM-Class-1 1 ®