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Mathematics Test - 4
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Mathematics Test - 4

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  • Question 1/10
    3 / -1

    A person mistakenly calculated the mean and the median of a sample data of 200 items as 100 and 104, respectively. The maximum value of the individual data was 200. When the data was rechecked, it was found that the value of the maximum sample data was 220. The values of true mean and true median are

    Solutions

    Solution

    Given mean:

    And the median will remain same, i.e. 104.

    Hence, this is the required solution.

  • Question 2/10
    3 / -1

    Consider the following expression:

    The number of values of x which satisfy the given expression is

    Solutions

    Solution

    Here,

    Therefore, 3 such values of x are possible.

    Hence, this is the required solution.

  • Question 3/10
    3 / -1

    If P and Q are two sets such that and  for same set A, then which of the following options is correct?

    Solutions

    Solution

    Given:

    From both the above results,

    P = Q

    Hence, this is the required solution.

  • Question 4/10
    3 / -1

    Evaluate:

    Solutions

    Solution

    Here,

    Hence, this is the required solution.

  • Question 5/10
    3 / -1

    Find the maximum value of 15 cosA + 8 sinA.

    Solutions

    Solution

    As we know that maximum value of

    Thus,

    Maximum value of the given expression is 17.

    Hence, this is required solution.

  • Question 6/10
    3 / -1

    The axis of a parabola is along the abscissa. Its vertex is at origin and it passes through a point P(2, 3). The equation of the parabola is

    Solutions

    Solution

    Given, vertex = (0, 0), point = P(2, 3) and axis is along X axis.

    Since point (2, 3) lies in the first quadrant,

    Therefore, equation of the parabola will be of the form y2 = 4ax , which passes through P(2, 3).

    Hence, this is the required solution.

  • Question 7/10
    3 / -1

    A canonical plastic bottle whose height is 21 m and radius of base is 7 m is being filled with milk at a uniform rate of 5/3 m3/min. When the milk level is 6 m, find the rate at which the level of the milk in the bottle is rising.

    Solutions

    Solution

  • Question 8/10
    3 / -1

    Consider the given expression:

    Differentiate y with respect to x.

    Solutions

    Solution

    Given:

  • Question 9/10
    3 / -1

    Find the area (unit2) bounded by the two curves y = 6 + 5x - 2x2 y = 2x + 3.

    Solutions

    Solution

    We know that y = 6 + 5x - 2x2 makes a parabola and the equation y = 2x + 3 makes a straight line.

    So, Area between two curves ,

  • Question 10/10
    3 / -1

    If 0 < P(X) < 1, 0 < P(Y) < 1 and  then Which of the following is correct?

    Solutions

    Solution

    Here,

    It means X and Y are independent events, so X' and Y' are also independent. Therefore,

    Hence, this is the required solution.

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