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Mathematics Test 285
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Mathematics Test 285
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  • Question 1/10
    4 / -1

    Solutions

     

  • Question 2/10
    4 / -1

    If λ ∈ R is such that the sum of the cubes of the roots of the equation x2 + (2 - λ) x + (10 - λ) = 0 is minimum, then the magnitude of the difference between the roots of this equation is

    Solutions

     

  • Question 3/10
    4 / -1

    If tan A and tan B are the roots of the quadratic equation 3x2 - 10x - 25 = 0, then the value of 3 sin2 (A + B) - 10 sin (A + B) × cos (A + B) - 25 cos2 (A + B) is

    Solutions

    Since tan A and tan B are roots of the equation 3x2 - 10x - 25 = 0, therefore tan A + tan B = 10/3.

     

  • Question 4/10
    4 / -1

    If the system of linear equations

    x + ky + 3z = 0

    3x + ky - 2z = 0

    2x + 4y - 3z = 0

    has a non-zero solution (x, y, z), then xz/y2 is equal to

    Solutions


     

  • Question 5/10
    4 / -1

    Solutions

     

  • Question 6/10
    4 / -1

    If β is one of the angles between the normals to the ellipse x2 + 3y2 = 9 at the points (3 cos θ, √3 sin θ) and (-3 sin θ, √3 cos θ); θ ∈ (0, π/2), then 2 cot β/sin2θ is equal to

    Solutions

     

  • Question 7/10
    4 / -1

    Solutions

    ∴ From the above diagram of f(x), f(x) is surjective but not injective.

     

  • Question 8/10
    4 / -1

    The number of four-lettered words that can be formed using the letters of the word BARRACK is:

    Solutions

    B's - 1

    A's - 2

    R's - 2

    C's - 1

    K's - 1

    The number of four-lettered words can be formed from (2 identical, 2 identical) or (2 identical, 2 different) or 4 different letters.

     

  • Question 9/10
    4 / -1

    Solutions

     

  • Question 10/10
    4 / -1

    A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws , is

    Solutions

    Required Probability = 5/6 x 1/6 + (5/6)3 x 1/6 + (5/6)5 x 1/6 + ....

    = 1/6 x 5/6 / (1-25/36)

    = 5/11

     

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