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  1. Using a bicycle promotes physical health by improving cardiovascular fitness, building muscle strength, and reducing stress levels. Environmentally, it is a sustainable mode of transport that reduces air pollution and carbon emissions. Bicycles also help minimize noise pollution and traffic congestiRead more

    Using a bicycle promotes physical health by improving cardiovascular fitness, building muscle strength, and reducing stress levels. Environmentally, it is a sustainable mode of transport that reduces air pollution and carbon emissions. Bicycles also help minimize noise pollution and traffic congestion in urban areas. They require fewer resources for manufacturing and maintenance compared to motor vehicles, making them an eco-friendly and health-conscious transportation choice.

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  2. (a) The electron distribution in an aluminium atom is 2, 8, 3. https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/

    (a) The electron distribution in an aluminium atom is 2, 8, 3.

    https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/

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  3. The optimal value of the objective function in LPP is always obtained at the corner points of the feasible region. This is because the objective function is linear, and at one of the corner points due to the property of linear programming, the maximum or minimum occurs. Check this for more: https://Read more

    The optimal value of the objective function in LPP is always obtained at the corner points of the feasible region.

    This is because the objective function is linear, and at one of the corner points due to the property of linear programming, the maximum or minimum occurs.

    Check this for more:
    https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-12

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  4. To find the condition on p and q, we substitute the coordinates of the corner points 1, 1 and 3, 0 into the objective function Z = px + qy. 1. For point (1, 1): Z = p(1) + q(1) = p + q 2. For point (3, 0) Z = p(3) + q(0) = 3p For the minimum value of Z to occur at (3, 0) and (1, 1), the objective fuRead more

    To find the condition on p and q, we substitute the coordinates of the corner points 1, 1 and 3, 0 into the objective function Z = px + qy.

    1. For point (1, 1):
    Z = p(1) + q(1) = p + q

    2. For point (3, 0)
    Z = p(3) + q(0) = 3p

    For the minimum value of Z to occur at (3, 0) and (1, 1), the objective function value at (1, 1) must be greater than at (3, 0). So we require,
    p + q ≥ 3p
    q ≥ 2p

    Therefore, the constraint on p and q is q = 2p.

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