Differential Calculus - Differentiability and Methods of Differentiation Model Question Paper

11th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
    10 x 1 = 10
  1. If \(y={1\over a-z}\) ,then \({dz\over dy}\) is

    (a)

    \((a-z)^2\)

    (b)

    -(z-a)2

    (c)

    (z+a)2

    (d)

    -(z+a)2

  2. If y=mx+c and f(0)=\(f'(0)=1\),then f(2) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    -3

  3. \({d\over dx}(e^{x+5log \ x})\)is

    (a)

    ex.x4(x+5)

    (b)

    ex.x(x+5)

    (c)

    ex\(+{5\over x}\)

    (d)

    ex\(-{5\over x}\)

  4. \(x={1-t^2\over 1+t^2},y={2t\over 1+t^2}\) then \({dy\over dx}\)is

    (a)

    \(-{y\over x}\)

    (b)

    \({y\over x}\)

    (c)

    \(-{x\over y}\)

    (d)

    \({x\over y}\)

  5. The differential coefficient of log10 x with respect to logx10 is

    (a)

    1

    (b)

    -(log10 x)2

    (c)

    (logx 10)2

    (d)

    \(x^2\over100\)

  6. If \(y={(1-x)^2\over x^2}\) ,then \({dy \over dx}\) is 

    (a)

    8

    (b)

    1

    (c)

    4

    (d)

    5

  7. If pv=81,then \({dp\over dv}\) at v=9 is

    (a)

    1

    (b)

    -1

    (c)

    2

    (d)

    -2

  8. If g(x)=(x2+2x+3) f(x) and f(0)=5 and \(lim_{x \rightarrow 0}{f(x)-5\over x}=4\),then g'(0) is 

    (a)

    20

    (b)

    14

    (c)

    18

    (d)

    12

  9. The derivative of f(x)=x|x| at x =−3 is

    (a)

    6

    (b)

    -6

    (c)

    does not exist

    (d)

    0

  10. If is differentiable at x = 1, then

    (a)

    \(a={1\over2},b={-3\over 2}\)

    (b)

    \(a={-1\over2},b={3\over 2}\)

    (c)

    \(a=-{1\over2},b=-{3\over 2}\)

    (d)

    \(a={1\over2},b={3\over 2}\)

  11. 5 x 2 = 10
  12. Show that the greatest integer function \(f(x)=\left\lfloor x \right\rfloor \) is not differentiable at any integer?

  13. Find the derivatives of the following functions using first principle.f(x)=-x2+2

  14. Differentiate the following with respect to x: y=ex+sin x+2

  15. Find the derivatives of the following functions with respect to corresponding independent variables:g(t) = t3cos t

  16. Differentiate the following: F(x)=(x3+4x)7

  17. 5 x 3 = 15
  18. Determine whether the following function is differentiable at the indicated values.f(x) = x | x | at x = 0

  19. Determine whether the following function is differentiable at the indicated values. f(x)=sin|x|at x=0

  20. Find the derivatives of the following functions with respect to corresponding independent variables:\(y={tan \ x-1\over sec \ x}\)

  21. Find F'(x) if F(x)=\(\sqrt{x^2+1}\)

  22. Differentiate the following:y=e−mx

  23. 3 x 5 = 15
  24. Find the slope of tangent line to the graph of f(x) = - 5x2 + 7x at (5, f(5)).

  25. Find the derivatives of the following functions with respect to corresponding independent variables:y = e-x. log x

  26. Differentiate the following: \(y=\sqrt{1+2 \ tan \ x}\)

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