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12th Standard English Medium Maths Subject Application of Differential Calculus Book Back 1 Mark Questions with Solution Part - II

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 5

    1 Marks

    5 x 1 = 5
  1. The function sin4 x + cos4 x is increasing in the interval

    (a)

    \(\left[ \frac { 5\pi }{ 8 } ,\frac { 3\pi }{ 4 } \right] \)

    (b)

    \(\left[ \frac { \pi }{ 2 } ,\frac { 5\pi }{ 8 } \right] \)

    (c)

    \(\left[ \frac { \pi }{ 4 } ,\frac { \pi }{ 2 } \right] \)

    (d)

    \(\left[ 0,\frac { \pi }{ 4 } \right] \)

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

    (a)

    1

    (b)

    \(\sqrt { 2 } \)

    (c)

    \(\frac { 3 }{ 2 } \)

    (d)

    2

  3. The number given by the Mean value theorem for the function \(\frac { 1 }{ x } \), x ∈ [1, 9] is

    (a)

    2

    (b)

    2.5

    (c)

    3

    (d)

    3.5

  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. The maximum product of two positive numbers, when their sum of the squares is 200, is

    (a)

    100

    (b)

    \(25\sqrt { 7 } \)

    (c)

    28

    (d)

    \(24\sqrt { 14 } \)

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