Continuity and Differentiability

Subject matter experts of JagranJosh have developed chapter wise practice questions of Class 12th as per the relevancy of the chapter in the CBSE board exam. This practice set contains 10 questions with detailed explanations on “Chapter: Continuity and Differentiability” of Mathematics.

  • Q8.Which of the following statements is false?

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  • Q9.Rolle’s theorem holds true for a function f, if f is a real valued function defined on the closed interval [a, b] such that
    (i) it is continuous on [a, b]
    (ii) it is differentiable on [a, b]
    (iii) f (a) = f (b)
    (iv) there exist a real number c ∈ (a,b) such that f’(c) = 0
    Which of the above four conditions is stated wrongly?

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  • Q10.What is the percentage of error in calculating the volume of a cube if an error of 2% is made in measuring the length of the cube?

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  • Q11. It is given that for the function f( x )= x 3 +b x 2 +ax on [ 1, 3 ], Rolles  theorem holds with c=2+ 1 3  then the values of a and b are:

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  • Q12. If f( x )= x 2 sin( 1 x ) where x 0, then the value of the function f at x=0, so that the function is continuous at x=0 is

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  • Q13.Find a real number c between (1, 2) such that Lagrange’s mean value theorem holds true for the function f (x) = x (x – 2) on the interval [1, 2].

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  • Q14. The function given by f(x)={ xsin 1 x ,x0 0,x=0 }is

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