®
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
速
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
速
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