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
- monotonically increases
- monotonically decreases
- increases to a maximum value and then decreases
- decreases to a minimum value and then increases
Q2) The value of is
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
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
Q8) For a spherical surface , the unit outward normal vector at the point is given by
Q9) At x=0, the function has
- a maximum value
- a singularity
- a mimimum value
- a point of inflexion
Q10) Voriticity vector of a flow field is given as . The vorticity vector at (1,1,1) is