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

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is \(\cfrac { 1 }{ 2 } \) cm

    (a)

    3 cm/s

    (b)

    2 cm/s

    (c)

    1 cm/s

    (d)

    \(\cfrac { 1 }{ 2 } cm/s\)

  2. The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \)

    (a)

    \(-4\sqrt { 3 } \)

    (b)

    -4

    (c)

    \(\cfrac { \sqrt { 3 } }{ 12 } \)

    (d)

    \(4\sqrt { 3 } \)

  3. The number given by the Rolle's theorem for the functlon x3-3x2, x∈[0,3] is

    (a)

    1

    (b)

    \(\\ \\ \\ \sqrt { 2 } \)

    (c)

    \(\cfrac { 3 }{ 2 } \)

    (d)

    2

  4. One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

    (a)

    (2,0)

    (b)

    \(\left( \sqrt { 5 } ,1 \right) \)

    (c)

    \(\left( 3,\sqrt { 5 } \right) \)

    (d)

    \(\left( \sqrt { 13 } ,-\sqrt { 3 } \right) \)

  5. If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

    (a)

    2 < t < 5

    (b)

    2 ≤ t ≤ 5

    (c)

    t ≥ 2

    (d)

    t ≤ 2

  6. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

    (a)

    -2

    (b)

    2

    (c)

    1

    (d)

    -1

  7. The angle made by any tangent to the curve y = x5 + 8x + 1 with the X-axis is a

    (a)

    obtuse

    (b)

    right angle

    (c)

    acute angle

    (d)

    no angle

  8. If the slope of the curve 2y2=ax2+b at (1,-1) is - 1, then the values of a, b is

    (a)

    2, 0

    (b)

    0, 2

    (c)

    0, 0

    (d)

    2, 2

  9. The function -3x+12 is ________ function on R.

    (a)

    decreasing

    (b)

    strictly decreasing

    (c)

    increasing

    (d)

    strictly increasing

  10. \(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

    (a)

    1

    (b)

    -1

    (c)

    0

    (d)

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