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12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

    Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. Find the rate of change of the balloon's angle of elevation in radian per second when the balloon is 30 metres above the ground.

    (a)

    \(\cfrac { 3 }{ 25 } radians/sec\)

    (b)

    \(\cfrac { 4 }{ 25 } radians/sec\)

    (c)

    \(\cfrac { 1 }{ 5 } radians/sec\)

    (d)

    \(\cfrac { 1 }{ 3 } radians/sec\)

  2. The tangent to the curve y2 - xy + 9 = 0 is vertical when 

    (a)

    y = 0

    (b)

    \(\\ \\ y=\pm \sqrt { 3 } \)

    (c)

    \(y=\cfrac { 1 }{ 2 } \)

    (d)

    \(y=\pm 3\)

  3. The minimum value ofthe function |3-x|+9 is

    (a)

    0

    (b)

    3

    (c)

    6

    (d)

    9

  4. The point of inflection of the curve y = (x - 1)3 is

    (a)

    (0,0)

    (b)

    (0,1)

    (c)

    (1,0)

    (d)

    (1,1)

  5. The point on the curve y=x2 is the tangent parallel to X-axis is

    (a)

    (1,1)

    (b)

    (2,2)

    (c)

    (4,4)

    (d)

    (0,0)

  6. The value of \(\underset { x\rightarrow \infty }{ lim } { e }^{ -x }\) is

    (a)

    0

    (b)

    (c)

    e

    (d)

    \(\frac{1}{e}\)

  7. The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are

    (a)

    -1, 2

    (b)

    1, \(\frac { 1 }{ 2 } \)

    (c)

    1, 2

    (d)

    none

  8. If the curves y = 2ex and y =ae-x intersect orthogonally, then a = _________

    (a)

    \(\frac { 1 }{ 2 } \)

    (b)

    -\(\frac { 1 }{ 2 } \)

    (c)

    2

    (d)

    2e2

  9. If x + y = 8, then the maximum value of xy is _________

    (a)

    8

    (b)

    16

    (c)

    20

    (d)

    24

  10. The statement " If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

    (a)

    the extreme value theorem

    (b)

    Fermats' theorem

    (c)

    Law of mean

    (d)

    Rolle's theorem

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