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Question - 1

The gradient of the curve \(y=-2{ x }^{ 3 }+3x+5\) at \(x= 2 \) is

  • A -20
  • B 27
  • C -16
  • D -21

Question - 2

The rate of change of area A of a circle of radius r is

  • A \(2\pi r\)
  • B \(2\pi r\frac { dr }{ dt } \)
  • C \(\pi { r }^{ 2 }\frac { dr }{ dt } \)
  • D \(\pi \frac { dr }{ dt } \)

Question - 3

The velocity v of a particle moving along a straight line when at a distance x from the origin is given by  

\(a+bv^2=x^2\) where a and b are constants. Then the acceleration is

  • A \(\frac { b }{ x } \)
  • B \(\frac { a }{ x } \)
  • C \(\frac { x }{ b } \)
  • D \(\frac { x }{ a } \)

Question - 4

A spherical snowball is melting in such a way that its volume is decreasing at a rate of 1 ​\({ cm }^{ 3 }\)​ ​​ /min. The rate at which the diameter is decreasing when the diameter is 10cms is

  • A \(\frac { -1 }{ 50\pi } \)cm /min
  • B \(\frac { 1 }{ 50\pi } \) cm/min
  • C \(\frac { -11 }{ 75\pi } \) cm/min
  • D \(\frac { -2 }{ 75\pi } \)cm/min

Question - 5

The slope of the tangent to the curve \(y={ 3x }^{ 2 }+3\sin { x } \) at x = 0 is

  • A 3
  • B 2
  • C 1
  • D -1

Question - 6

The slope of the normal to the curve \({ y=3x }^{ 2 }\)at the point whose x coordinate is 2 is

  • A 1/13
  • B 1/14
  • C -1/12
  • D 1/12

Question - 7

The point on the curve \(y = 2x² -6x-4\) at which the tangent is parallel to the x- axis is

  • A \(\left( \frac { 5 }{ 2 } ,\frac { -17 }{ 2 } \right) \)
  • B \(\left( \frac { -5 }{ 2 } ,\frac { -17 }{ 2 } \right) \)
  • C \(\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 2 } \right) \)
  • D \(\left( \frac { 3 }{ 2 } ,\frac { -17 }{ 2 } \right) \)

Question - 8

The equation of the tangent to the curve \(y=\frac { { x }^{ 3 } }{ 5 } \)at the point (-1,-1/5) is

  • A 5y + 3x = 2
  • B 5y – 3x = 2
  • C 3x – 5y = 2            
  • D 3x+3y = 2

Question - 9

The equation of the normal to the curve \(\theta =\frac { 1 }{ t } \)at the point (-3,-1/3 ) is  

  • A 3\(\theta \) =27 t - 80
  • B 5\(\theta \)= 27t - 80
  • C 3\(\theta \)= 27 t + 80
  • D \(\theta =\frac { 1 }{ t } \)

Question - 10

The angle between the curves \(\frac { { x }^{ 2 } }{ 25 } \)+\(\frac { { y }^{ 2 } }{ 9 } \) =1 and  \(\frac { { x }^{ 2 } }{ 8 } \) + \(\frac { { y }^{ 2 } }{ 8 } \)=1 is

  • A \(\frac { \pi }{ 4 } \)
  • B \(\frac { \pi }{ 3 } \)
  • C \(\frac { \pi }{ 6 } \)
  • D \(\frac { \pi }{ 2 } \)
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