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NDA II 2021 Mathematics Test - 57
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NDA II 2021 Mathematics Test - 57
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  • Question 1/10
    2.5 / -0.83

    Solutions

     

  • Question 2/10
    2.5 / -0.83

    A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/ min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is

    Solutions

    Let any time t, h cm be the thickness of ice. Then,

     

  • Question 3/10
    2.5 / -0.83

    If the value of a third-order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is?

    Solutions

    Here, determinant of matrix = 16 and order = n = 3

    Determinant formed by replacing

    each of its elements by its cofactor = determinant of the transpose of adjoint

    = determinant of the adjoint of matrix

    (∵ The determinant of a square matrix is the same as the determinant of its transpose.)

     

  • Question 4/10
    2.5 / -0.83

    The function  is not defined at x = π. The value of f(π) so that f(x) is continuous at x = π is

    Solutions

     

  • Question 5/10
    2.5 / -0.83

    The adjoint of the matrix

    Solutions

     

  • Question 6/10
    2.5 / -0.83

    Solutions

     

  • Question 7/10
    2.5 / -0.83

    What is cot2x cot4x – cot4x cot6x – cot6x cot2x equal to?

    Solutions

     

  • Question 8/10
    2.5 / -0.83

    Let g(x) is a function defined on (-1,1). If the area of the equilateral triangle with two of its vertices at (0,0) and {x, g(x)} is √3/4 , then the function is:

    Solutions

     

  • Question 9/10
    2.5 / -0.83

    If ω is an imaginary cube root of unity, then (1 + ω - ω2)7 equals.

    Solutions

    Given: ω is an imaginary cube root of unity.

     

  • Question 10/10
    2.5 / -0.83

    A square is inscribed in the circle  and its sides are parallel to the coordinate axes then one vertex of the square is :

    Solutions

    The centre of the circle is (1,-2), and it is given that the sides of the inscribed square are parallel to the coordinate axes. So the x and y coordinate cannot be 1 and -2. Hence the choices A, B and C are not possible.

     

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