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12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. Let C be the circle with centre at(1,1) and radius =1. If T is the circle centered at(0, y)
    passing through the origin and touching the circleC externally, then the radius of T is equal to

    (a)

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

    (b)

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

    (c)

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

    (d)

    \(\frac { 1 }{ 4 } \)

  2. If \(\vec { a } ,\vec { b } ,\vec { c } \) are three unit vectors such that \(\vec { a } \) is perpendicular to \(\vec { b } \) and is parallel to \(\vec { c } \) then \(\vec { a } \times (\vec { b } \times \vec { c } )\) is equal to

    (a)

    \(\vec { a } \)

    (b)

    \(\vec { b} \)

    (c)

    \(\vec { c } \)

    (d)

    \(\vec { 0 } \)

  3. If the distance of the point (1,1,1) from the origin is half of its distance from the plane x + y + z + k =0, then the values of k are

    (a)

    \(\pm 3\)

    (b)

    \(\pm 6\)

    (c)

    -3, 9

    (d)

    3, 9

  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 u(x, y) = x2+ 3xy + y - 2019, then \(\frac { \partial u }{ \partial x } \)(4, -5) is equal to

    (a)

    -4

    (b)

    -3

    (c)

    -7

    (d)

    13

  6. If \(\int _{ a }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } } \)then a is

    (a)

    4

    (b)

    1

    (c)

    3

    (d)

    2

  7. The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

    (a)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0\)

    (b)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }+y=0\)

    (c)

    \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }=0\)

    (d)

    \(\frac { { d }^{ 2 }x }{ { dy }^{ 2 } }=0\)

  8. Integrating factor of the differential equation \(\frac { dy }{ dx } =\frac { x+y+1 }{ x+1 } \) is 

    (a)

    \(\frac{1}{x+1}\)

    (b)

    x+1

    (c)

    \(\frac { 1 }{ \sqrt { x+1 } } \)

    (d)

    \({ \sqrt { x+1 } } \)

  9. Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k2 , where k is the face that comes up k = {1, 2, 3, 4, 5}.
    The expected amount to win at this game in Rs. is

    (a)

    \(\cfrac { 19 }{ 6 } \)

    (b)

    \(-\cfrac { 19 }{ 6 } \)

    (c)

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

    (d)

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

  10. If \(f(x)=\left\{\begin{array}{ll} 2 x & 0 \leq x \leq a \\ 0 & \text { otherwise } \end{array}\right.\) is a probability density function of a random variable, then the value of a is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

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