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NDA I 2022 Mathematics Test - 19
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NDA I 2022 Mathematics Test - 19
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  • Question 1/10
    2.5 / -0.83

    Solutions

    Now,

     

  • Question 2/10
    2.5 / -0.83

    If n = 100! , then what is the value of the following?

    Solutions

     

  • Question 3/10
    2.5 / -0.83

    If x + y = 20 and P = x y, then what is the maximum value of P?

    Solutions

     

  • Question 4/10
    2.5 / -0.83

    If a + b + c = 18 and ab + bc + ca = 107; then find a³ + b³ + c³ - 3abc?

    Solutions

    As we know,

    (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

    By putting the values given in the question, we get

    (18)² = a² + b² + c² + 2(107)

    ⇒ a² + b² + c² = 324 – 214 = 110

    Now, a³ + b³ + c³ – 3abc = (a + b + c){a² + b² + c² – (ab + bc + ca)}

    = 18(110 – 107) = 54

     

  • Question 5/10
    2.5 / -0.83

    Solutions

    Trick to find adj for 2×2 order=Exchange the leading diagonal elements and multiply the non leading diagonal elements by minus sign without exchanging them.

     

  • Question 6/10
    2.5 / -0.83

    What is the order of the product

    Solutions

     

  • Question 7/10
    2.5 / -0.83

    A and B are two matrices such that AB = A and BA = B then what is B2 equal to?

    Solutions

    Given:

     

  • Question 8/10
    2.5 / -0.83

    (If I is the identity matrix)

    Solutions

     

  • Question 9/10
    2.5 / -0.83

    How many distinct matrices exist with all four entries taken from {1, 2}?

    Solutions

    With 4 entries we can make three matrix such that

    For the 4 entries we have two choices 1 or 2, so total number of ways = 2 x 2 x 2 x 2 = 16

    So, total number of matrices = 16 x 3 = 48.

     

  • Question 10/10
    2.5 / -0.83

    A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3 and 4 without repetition of digits, What is the number of ways this can be done?

    Solutions

    Since sum of digits = 10(which is not divisible by 3)

    So, no numbers can be formed.

     

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