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Mathematics Test - 43
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Mathematics Test - 43
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  • Question 1/10
    5 / -1

    I2 is the matrix

    Solutions

    In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context

     

  • Question 2/10
    5 / -1

    Let A be any m×n matrix, then A2 can be found only when

    Solutions

    The product of any matrix with itself can be found only when it is a square matrix.i.e. m = n.

     

  • Question 3/10
    5 / -1

    Solutions

    To find the determinant we have to cross mutliply the elements and then subtract it.

    cos2θ - (-sin2θ) = 1

     

  • Question 4/10
    5 / -1

    Solutions

     

  • Question 5/10
    5 / -1

    Let f (x) = x4 – 4x, then

    Solutions

     

  • Question 6/10
    5 / -1

    The function f (x) = x3 has a

    Solutions

    f ‘(0) = 0 , f ‘’ (0) = 0 and f ‘’’(0) = 6 . So, f has a point of inflexion at 0.

     

  • Question 7/10
    5 / -1

    Solutions

    By cross checking the options, we can find the answer.

    Hence option 3 is the correct answer and we can check the other choices by the similar argument.

     

  • Question 8/10
    5 / -1

    Solutions

     

  • Question 9/10
    5 / -1

    Solutions

    To calculate the degree or the order of a differential equation, the powers of derivatives should be an integer.

    On squaring both sides, we get a differential equation with the integral power of derivatives.

    ⇒ Order (the highest derivative) = 2

    ⇒ Degree (the power of highest degree) = 2

     

  • Question 10/10
    5 / -1

    Solutions

    y = Acos(αx) + Bsin(αx)

    dy/dx = -Aαsin(αx) + Bαcos(αx)

    d2y/dx2 = -Aα2cos(αx) - Bα2sin(αx)

    = -α2(Acos(αx) + Bsin(αx))

    = -α2 * y

    d2y/dx2 + α2*y = 0

     

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