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12th Standard English Medium Maths Subject Application of Differential Calculus Book Back 3 Mark Questions with Solution Part - I

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 30

    3 Marks

    10 x 3 = 30
  1. For the function f(x) = x2, x∈ [0, 2] compute the average rate of changes in the subintervals [0, 0.5], [0.5, 1], [1, 1.5], [1.5, 2] and the instantaneous rate of changes at the points x = 0.5,1, 1.5, 2

  2. A particle moves so that the distance moved is according to the law s(t) = \(s(t)=\frac{t^{3}}{3}-t^{2}+3\). At what time the velocity and acceleration are zero.

  3. A particle is fired straight up from the ground to reach a height of s feet in t seconds, where s(t) = 128t −16t2.
    (1) Compute the maximum height of the particle reached.
    (2) What is the velocity when the particle hits the ground?

  4. The price of a product is related to the number of units available (supply) by the equation Px + 3P −16x = 234, where P is the price of the product per unit in Rupees(Rs) and x is the number of units. Find the rate at which the price is changing with respect to time when 90 units are available and the supply is increasing at a rate of 15 units/week.

  5. A point moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres.
    (i) Find the average velocity of the points between t = 3 and t = 6 seconds.
    (ii) Find the instantaneous velocities at t = 3 and t = 6 seconds.

  6. A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres.

  7. If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = \(\sqrt { 3 } x\) then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres.

  8. A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at 2 cm per second. When the radius is 5 cm find the rate of changing of the total area of the disturbed water?

  9. A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shore line. How fast is the beam moving along the shore line when it makes an angle of 45° with the shore?

  10. Find the equations of tangent and normal to the curve y = x2 + 3x − 2 at the point (1, 2)

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