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NDA II 2021 Mathematics Test - 49
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NDA II 2021 Mathematics Test - 49
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  • Question 1/10
    2.5 / -0.83

    The function defined by  denotes the greatest integer function) satisfies

    Solutions

    For x ∈ (-1, 0) f(x) = (-1)-1 = -1

    Hence f’(x) = 0

    For x ∈ [0, 1), f(x) = (-1)o = 1

    Hence f’(x) = 0

     

  • Question 2/10
    2.5 / -0.83

    The Sum of the square deviations for 10 observations taken from their mean is 50 is 250. The coefficient of variation is

    Solutions

     

  • Question 3/10
    2.5 / -0.83

    The mean and median of the data x,y,z are 50 and 35 respectively, where 

    Solutions

    We have,

    Mean = 50 and, Median = 35

     

  • Question 4/10
    2.5 / -0.83

    If A is the A.M. of the roots of the equation x2 - 2ax + b = 0 and G is the G.M. of the roots of the equation x2 - 2bx + a2 = 0 then:

    Solutions

     

  • Question 5/10
    2.5 / -0.83

    Solutions

     

  • Question 6/10
    2.5 / -0.83

    Consider the following statements

    1) The middle term of the series arranged in ascending and descending order is called standard deviation.

    2) Frequency polygon can be drawn after drawing histogram.

    3) A frequency polygon is a suitable method for representing the partitioning of the total into subpart.

    Which of the above statements is/are correct?

    Solutions

    Consider statement (1)

    The middle term of the series arranged in ascending and descending order is called a median.

    So statement (1) is incorrect

    Consider statement (2)

    We know that a frequency polygon can be drawn by joining the mid-points of the respective tops of rectangles of a histogram in case of equal class intervals.

    Hence statement (2) is true

    Consider statement (3)

    We know that Pie – chart is a suitable method for representing the partitioning of total into subpart

    So statement (3) is incorrect

     

  • Question 7/10
    2.5 / -0.83

    The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?

    Solutions

    SD will remain same because every observation is decreased by 5 and mean also decreased by 5

    So,there will be no change in standard deviation.

    Now,new mean =45

    And standard deviation is same

    When divided by 4,

     

  • Question 8/10
    2.5 / -0.83

    A train travels 240KM at a uniform speed. If the speed had been 10 KM/H more. It would have taken 1 hrs lesser for the same journey in the same route. What is the speed of the train near to?

    Solutions

    On solving we get x=-54.24 or x=49.2

    Speed cannot be negative. So, the speed is x=49.2

     

  • Question 9/10
    2.5 / -0.83

    The median of the following marks of 9 students in a class, is

    34, 32, 48, 38, 24, 30, 27, 21, 35

    Solutions

    Arranging the data in ascending order of magnitude, we have

    21, 24, 27, 30, 32, 34, 35, 38, 48

    Since there are 9, an odd number of items.

     

  • Question 10/10
    2.5 / -0.83

    Solutions

     

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