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Mathematics Tes...

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    Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.Statement 1: f′(4) = 0Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)

  • Question 3
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    The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

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    A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

  • Question 6
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    Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

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    All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

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  • Question 9
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    The number of values of k, for which the system of equations (k + 1)x + 8y = 4k kx + (k + 3)y = 3k − 1 has no solution, is

  • Question 10
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    The area bounded between the parabolas x^2 = y/4 and x^2 = 9y, and the straight line y = 2 is

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