Q1. What is the rank of the word JAIPUR if all the words formed by the letters of JAIPUR are arranged in ascending order?
(a) 241
(b) 242
(c) 122
(d) 123
(e) None of these
Q2. In how many ways 3 numbers can be selected from the set of numbers 1, 2, 3….20 such that the selected numbers are in ascending order.
Q3. How many squares (off all possible dimensions) are there on a chessboard?
(a) 65
(b) 64
(c) 204
(d) 1296
(e) None of these
Q4. In how many ways 3 playing cards can be selected from a deck of 52 cards such that there is at least one face card.
Q5. Two teams of 11 students each are formed from 20 students such that exactly three students are common between the two teams. In how many ways can the two teams be formed?
Q6. If all the words which can be formed by using the letters of the word INDIA are arranged in alphabetical order, find the rank of the word INDIA.
Q7. A bag contains 3 red balls, 4 green balls and 3 yellow balls. Three balls are randomly selected, find the probability that all the three balls are not of the same colour.
Q8. Three numbers are randomly selected from the set of natural numbers {1, 2, 3, …..50}, find the probability that these numbers are in AP.
Q9. In a bolt factory machines A, B and C manufacture respectively 25%, 35% and 40% of the total product. Of their output 5, 4, 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What are the probabilities that it was manufactured by machine A.
Q10. If the letters of the word ‘REGULATION’ be arranged at random, the probability that there will be exactly 4 letters between R and E
ANSWERS :
S1. Ans.(b)
Sol. List of the words comes before JAIPUR in dictionary is
A- - - - - total words = 5! = 120
I- - - - - total words = 5! = 120
JAIPRU 1 word
JAIPUR
Hence the rank of the word JAIPUR is 120 + 120 + 1 + 1 = 242.
S2. Ans.(b)
Sol. Let us first solve the question in how many ways 3 numbers can be selected and written in a line.
- - -
The answers is 20 × 19 × 18 as first place can be filled in 20 ways, 2nd place can be filled in 19 ways and the 3rd place can be filled in 18 ways. Since we want numbers to be in ascending order, hence out of every 6 permutations only I can be taken. Required number of ways
S3. Ans.(c)
Sol. There are 64 squares of dimension 1 × 1, there are 49 squares of dimensions 2 × 2, counting in the same way, we get total number of squares in a chess board as:
64 + 49 + 36 + 25 + ….. 4 + 1 = 204
S4. Ans.(b)
Sol. There are 12 face cards, hence the required number of ways
S6. Ans.(c)
Sol. All the words which appear before INDIA are:
A(- - - -) = 4!/2! = 12
D(- - - -) = 4!/2! = 12
IA(- - -) = 3!=6
ID(- - -) = 3! = 6
II(- - - - ) = 3! = 6
INA(- -) = 2! = 2
INDAI = 1
INDIA
Rank = 46th.
S8. Ans.(a)
Sol. Suppose the three selected numbers are a, b and c. If these numbers are in AP, then
2b = a + c, thus a + c must be an even number. This is possible only if both a & c are odd or both are even. There are 25 odd numbers are 25 even numbers. Hence a and c can be selected in
S10. Ans.(b)
Sol. Given that there are 4 letters between R and E, suppose this combination R - - - - E is denoted by X, then the total number of arrangement of X and other four remaining alphabets are:
5!.2!.4! (as R and E can be permuted)
Also, the four letters that come between R and E can be selected in 8_(C_4 ) ways.
Required number of permutations
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