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Mathematics Test - 10
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Mathematics Test - 10
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  • Question 1/10
    1 / -0

    The value of tan (cos-1(4/5) + tan-1 (2/3)) is equal to

    Solutions

  • Question 2/10
    1 / -0

    What is the total number of different combinations of names, which can be made from the letters of the word MISSISSIPPI, using all the letters at a time?

    Solutions

    Here, we have 1 M, 4 I's, 4 S's and 2 P's,

    Hence, the total number of different combinations of letters of the word MISSISSIPPI are11!/41 x 41 x2! .

  • Question 3/10
    1 / -0

    On the occasion of Diwali, each student of a class sends greeting cards to every other. If there are 20 students in the class, then the total number of greeting cards exchanged by the students is

    Solutions

    Required number = 2 x 20C2 because if A sends to B, then B also sends to A, so it becomes twice for all.

  • Question 4/10
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    If no husband and wife play in the same game, then the number of ways in which a mixed double game can be arranged from among nine married couples is

    Solutions

    Out of 9 men, 2 men can be chosen in 9C2 ways.

    Since no husband and wife are to play in the same game, we have to select 2 women from the remaining 7 women.

    This can be done in 7C2 ways.

    If M1, M2 and W1, W2 are chosen, then a team can be constituted in 2 ways, viz. M1 W1 or M1 W2.

    Thus, number of ways of arranging the game = 9C2 x 7C2 x 2 = 1512

  • Question 5/10
    1 / -0

    The number of ways of painting the faces of a cube with six different colours is

    Solutions

    Since, the number of faces is the same as the number of colours, and the faces are identical, therefore, the number of ways of painting them is 1.

  • Question 6/10
    1 / -0

    What is the number of arrangements that can be made using all the letters of the word 'LAUGH', keeping the vowels adjacent?

    Solutions

    Considering AU as one letter, we have 4 letters: L, AU, G, H, which can be permuted in 4! ways. But, AU can be put together in 2! ways. Thus, the required number of arrangements is 4! × 2! = 48.

  • Question 7/10
    1 / -0

    If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word will be

    Solutions

    Starting with the letter A and arranging the other four letters, there are 4 ! = 24 words. These are the first 24 words. Then, starting with G and arranging A, A, I and N in different ways, there are = 4!/2! 1! 1! = 24/2 = 12 words

    Next, the 37th word starts with I. There are 12 words starting with I.

    This accounts up to the 48th word.

    The 49th word is NAAGI.

    The 50th word is NAAIG.

  • Question 8/10
    1 / -0

    The number of ways of dividing 20 persons into 10 couples is

    Solutions

    Here, the order of the couples is not important. So, required number of ways is 20!/21010!

  • Question 9/10
    1 / -0

    Solutions

  • Question 10/10
    1 / -0

    Directions: The following question has four choices, out of which ONE or MORE is/are correct.

    Solutions

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