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Mathematics Test 296

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Mathematics Test 296
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  • Question 1
    4 / -1

    If [x] denotes the greatest integer less than or equal to x, then the value of the determinant

    Solution

     

  • Question 2
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    The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

    Solution

     

     

  • Question 3
    4 / -1

    α, β ∈ C are the distinct roots of the equation x2 − x + 1 = 0,

    α101 + β107 is equal to

    Solution

     

  • Question 4
    4 / -1

    Solution

     

  • Question 5
    4 / -1

    Let the vertices of a triangle are 

    the distance between the centroid and the circumcentre of ΔABC

    Solution


     

  • Question 6
    4 / -1

    Solution

    Step 3: Sharpen the lower bound

    The integrand equals 1 only at x = 0 and is strictly less than 1 elsewhere on (0,1], so the integral is strictly smaller than 1:

    I < 1.

     

  • Question 7
    4 / -1

    The smallest positive integer n for which 

    Solution

     

  • Question 8
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    Solution

     

  • Question 9
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    Solution

     

  • Question 10
    4 / -1

    Suppose f is a function satisfying f(x + f(x)) = 4f(x) and f(1) = 4. The value of f(21) is

    Solution

     

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