Out of 13 marks in Engineering maths, 4-5 marks will be covered by the topic of calculus in GATE exam. So a good knowlegde about the concepts in calculus is essential. Here are 10 basic level questions from Calculus. Try them out and check whether you remember the basic concepts of calculus or not.

Q1) As x is increased from  to , the function 

  1. monotonically increases
  2. monotonically decreases
  3. increases to a maximum value and then decreases
  4. decreases to a minimum value and then increases

Q2) The value of  is

  1. 0
  2. 1/2
  3. 1/4
  4. undefined

Q3) Consider a spatial curve in 3D space given in parametric form by x(t)=cos(t), y(t)=sin(t), z(t)=t, . The length of the curve is ________.

Q4) Curl of a vector at x=y=z=1 is

  1. -3i
  2. 3i
  3. 3i-4j
  4. 3i-6j

Q5) The value of  is____________.

Q6) The value of , where C is region bounded by x = 0, y = 0 and x+y=1 is _____________. 

Q7) The area enclosed between the straight line y=x and the parabola  in the xy plane is

  1. 1/6
  2. 1/3
  3. 1/4
  4. 1/2

Q8) For a spherical surface , the unit outward normal vector at the point  is given by

Q9) At x=0, the function  has

  1. a maximum value
  2. a singularity
  3. a mimimum value
  4. a point of inflexion

Q10) Voriticity vector of a flow field is given as . The vorticity vector at (1,1,1) is

  1. 4i-j
  2. 4i-k
  3. i-4j
  4. i-4k