In how many ways can 2 cats and 4 dogs be arranged in a row such that all the cats are together

Being a pet owner also brings responsibilities. You need to:

• provide your pet with appropriate food, shelter and care
• register your dog in all council areas and register your cat in some council areas
• have your dog or cat microchipped and ensure its details are up to date so it can be identified and returned to you if lost
• consider having your pet desexed to avoid unwanted litters
• meet new laws regarding standards for safeguarding the welfare of breeding dogs and their puppies
• request a permit from your local council if you want to own:
• a regulated dog (i.e. dangerous, menacing or restricted breed)
• more animals than are allowed in your council area.

Registration

Dogs

In Queensland, all dogs must be registered with the local council:

• before they are 12 weeks old
• within 14 days after moving to a new local council area.

When lodging your completed registration form, you must include the registration fee and state:

• if your dog is a regulated dog - including declared dangerous, declared menacing and restricted dogs
• if your dog has been
• desexed - include a signed certificate from your vet
• micro-chipped - include the permanent identification device (PID) number.

If you intend to use a cat or dog for breeding you may need to tell your local council when you register the animal.

Contact your local council to check if you have to register a working dog. Some types of working dogs are exempt from registration.

Cats

To find out whether cats must be registered in your area check with your local council.

For more information on animal registration, contact your local council.

Microchipping

All dogs and cats born after 10 April 2009 must be microchipped before they are sold or given away. All regulated dogs must be microchipped regardless of when they were born.

Microchips may be implanted only by a vet or other authorised implanter. When your animal is implanted with a microchip, the implanter must provide the microchip's unique number, the animal's information and your contact details to a licensed registry service. It is your responsibility to make sure these records are kept up to date.

When the microchip is read or scanned (harmless to animals) it shows the microchip number which is linked to information about the animal, including its owner and the owner's contact details. This information is important if your animal is lost or impounded.

For more information on microchipping, contact your:

• veterinarian
• Biosecurity Queensland

Once a microchip has been implanted it can be removed only by a veterinary surgeon and only if it's in the animal's best interests.

Desexing

We recommend that you have cats and dogs desexed if they are not intended to be kept for breeding. This prevents an unwanted litter and helps to reduce the number of animals that have to be euthanised. Desexing also helps to prevent male pets from straying during mating seasons. Most council areas offer incentives to desex cats and dogs.

When your cat or dog is desexed, the vet will insert a small tattoo in its ear to identify it as having been desexed.

Animal permits

In Brisbane, you must apply for a:

A breeder or show permit is needed if you want to:

• keep more than 2 dogs for breeding, racing, sale or showing
• keep cats for breeding or showing.

See permits and licensing for animal exhibitors.

Permits may be required for other animals, including race horses. No permits are required to keep chickens and poultry, but there are conditions and limits on their number.

If you live outside the Brisbane City Council area, contact your local council for more information on animal permits.

Animal welfare

If you decide to keep a pet, you have a duty of care to provide for its needs. Before getting an animal, find out if it has any special needs.

You should always make sure you have the time, money, room and capability to care for the type of animal you want before you get it.

Breeding dogs

If your dog becomes pregnant and has a litter you must meet Queensland's animal welfare standards for breeding dogs and their progeny. Within 28 days of the litter being born you must register as a dog breeder.

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1. Sum of three natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist? A. 45 B. 36 C. 54 D. 28

   Correct Answer

   Choice B
   36

2. Sum of three Whole numbers a, b and c is 10. How many ordered triplets (a, b, c) exist? A. 66 B. 78 C. 72 D. 56

   Correct Answer

   Choice A
   66

3. In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty? A. 72 B. 54 C. 45 D. 36

   Correct Answer

   Choice C
   45

4. a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)? A. 8 B. 6 C. 2 D. 4

   Correct Answer

   Choice D
   4

5. A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12? A. 11 B. 12 C. 10 D. 22

   Correct Answer

   Choice A
   11

6. If all words with 2 distinct vowels and 3 distinct consonants were listed alphabetically, what would be the rank of “ACDEF’? A. 4716 B. 4720 C. 4718 D. 1717

   Correct Answer

   Choice C
   4718

7. If we listed all numbers from 100 to 10,000 , how many times would the digit 3 be printed? A. 3980 B. 3700 C. 3840 D. 3780

   Correct Answer

   Choice A
   3980

8. From the digits 2, 3, 4, 5, 6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12? A. 36 B. 60 C. 84 D. 72

   Correct Answer

   Choice B
   60

9. All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations? A. 143 B. 200 C. 157 D. 122

   Correct Answer

   Choice A
   143

10. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's? A. 25 B. 20 C. 35 D. 45

    Correct Answer

    Choice D
    45

11. How many numbers of up to 5 digits can be created using the digits 1, 2, 3 and 5 each at least once such that they are a multiple of 15? A. 24 B. 18 C. 15 D. 12

    Correct Answer

    Choice D
    12

12. How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6? A. 975 B. 960 C. 978 D. 986

    Correct Answer

    Choice C
    978

13. All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"? A. 36 B. 74 C. 42 D. 86

    Correct Answer

    Choice B
    74

14. A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice B
    15⁄23

15. Doctors have devised a test for leptospirosis that has the following property: For any person suffering from lepto, there is a 90% chance of the test returning positive. For a person not suffering from lepto, there is an 80% chance of the test returning negative. It is known that 10% of people who go for testing have lepto. If a person who gets tested gets a +ve result for lepto (as in, the test result says they have got lepto), what is the probability that they actually have lepto?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice C
    1⁄3

16. In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other? A. 6720 B. 2400 C. 4320 D. 1800

    Correct Answer

    Choice B
    2400

17. 2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b? A. 7 B. 9 C. 14 D. 15

    Correct Answer

    Choice A
    7

18. If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice A
    1⁄3

19. N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice C
    13⁄64

20. A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice D
    2⁄3

21. I roll a die four times. In how many outcomes do we have two throws have the same number and the other two something different? A. 720 B. 480 C. 360 D. 350

    Correct Answer

    Choice A
    720

22. In how many ways can be select 5 cards from a card pack such that all 4 suits appear? A. 52728 B. 405646 C. 685464 D. 4056

    Correct Answer

    Choice C
    685464

23. I roll a die 4 times. In how many outcomes will each subsequent throw be greater that the previous one? A. 15 B. 48 C. 30 D. 60

    Correct Answer

    Choice A
    15

24. Find 3 digit numbers such that product of their digits is a natural number less than 5? A. 11 B. 15 C. 13 D. 17

    Correct Answer

    Choice C
    13

25. Find all 3 digit numbers such that sum of their digits is a whole number less than 5? A. 18 B. 20 C. 19 D. 17

    Correct Answer

    Choice B
    20

26. What is sum of all rearrangements of the 4-digit number 3214? A. 66660 B. 55554 C. 60048 D. 65024

    Correct Answer

    Choice A
    66660

27. What is sum of all rearrangements of the 4-digit number 3321? A. 29999 B. 27777 C. 28888 D. 29997

    Correct Answer

    Choice D
    29997

28. Of 22 points on a plane, 8 are on a straight line, 7 are on another straight line and 10 are on a third straight line. How many triangles can be drawn by connecting some three points from these 22?

    A. 22C3

    B. 22C3 - (8C3+ 7C3 +10C3)

    C. 22C3 + (8C3+ 7C3 +10C3)

    D.8C3+ 7C3 +10C3

    Correct Answer

    Choice B
    22C3 - (8C3+ 7C3 +10C3

29. A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?

    A.

    B.

    C.

    D.

    Correct Answer

    Choice D
    17⁄35

30. In how many ways can we rearrange the letters of the word MANANA such that no two A’s are adjacent to each other?

    A. 3! × 5C3

    B. 4! × 4C3

    C. 3 × 4C3

    D. 3! × 4C3

    Correct Answer

    Choice C
    3 * 4C3

31. How many ways are there for arranging letters of the word AMAZING such that the ‘I’ appears between the two ‘A’s? A. 5! ways B. 7! ways C. 8! ways D. 4! ways

    Correct Answer

    Choice A
    5 ! ways

32. In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated? A. 6 × 5! ways B. 7 × 5! ways C. 3 × 3! ways D. 15 × 5! ways

    Correct Answer

    Choice D
    15 * 5 ! ways

33. How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once? A. 191 B. 176 C. 153 D. 189

    Correct Answer

    Choice B
    176