VU Midterm Past Papers
74 solved midterm past paper MCQs for MTH622 (Vectors and Classical Mechanics) at Virtual University, each with the correct answer marked. Use them to learn the VU question style and test your recall. An independent study tool — not affiliated with VU.
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Q1. If φ and ψ are scalar point functions with continuous second order derivatives in a region V bounded by a closed surface S then Green's first identity states that
Q2. The unit vector i is normal to the surface
Q3. Newton's first law is also called
Q4. The ______ is the rate at which the function f(x,y,z) changes at a point (x0,y0,z0) in the direction
Q5. The unit normal to the surface r = 0 is
Q6. Green's theorem states that if R is a simply connected region of the xy-plane bounded by a closed curve C and if M and N are continuous functions of x and y having continuous partial derivatives in R, then
Q7. The entity ∫_S φ dS = -∫_S φ ∇× dS is
Q8. A simple closed curve does not intersect itself anywhere.
Q9. The radial component of velocity for a particle moving in circular path is
Q10. Evaluate ∫ (x + y) dy along the line segment joining (0,0) to (0,1)
Q11. The unit normal to the surface z = 0 is
Q12. If n̂ is the unit normal to the surface S and φ is a scalar point function having continuous partial derivatives then ∫_S φ n̂ dS = ?
Q13. The property ∇·∇×v = 0 always holds.
Q14. According to Stokes' theorem, if S is an open, two-sided surface bounded by a simple closed curve C, and A has continuous first partial derivatives then ∫_C A·dr = ?
Q15. Stoke's theorem can be used to find which of the following?
Q16. Which of the following theorem convert line integral to surface integral?
Q17. A vector is a quantity which is specified by
Q18. If T is a unit vector to a space curve C and s is the arc length then dT/ds is
Q19. ∇·(∇φ) is
Q20. A vector A is called irrotational if
Q21. The Laplace operator is a ____ operator.
Q22. If φ = xy then ∇φ =
Q23. The Laplacian of φ is also called
Q24. If a scalar function φ satisfies the Laplace equation ∇²φ = 0 in a Cartesian region R, then φ is said to be a ____ function in the region R.
Q25. Infinitesimal rotation of a vector field is described by the
Q26. The Stoke's theorem uses which of the following operators?
Q27. ∫ K · A dF =
Q28. If φ and ψ are scalar point functions then ∇(φψ) =
Q29. The volume element dV in Cylindrical polar coordinates is
Q30. For φ = xy, the integral ∫∫∫ φ dV becomes
Q31. The divergence operator when applied to the quantity of a vector field gives a ____ field.
Q32. The unit normal to the surface yz - 1 = 0 is
Q33. If ∇·F = 0, then the vector field F is
Q34. ____ is the way of finding derivative in a specific direction, other than coordinate axes.
Q35. If A = i then ∫∫∫ A dx dy dz =
Q36. ____ is the example of scalar field.
Q37. The relation between spherical and cartesian coordinates is
Q38. The set of all values of scalar point function together forms a
Q39. The value of dF = dx i + dy j + dz k for the curve x = t, y = 2t - 1 and z = 3t² is
Q40. If a scalar function φ satisfies the Laplace equation ∇²φ=0 in a Cartesian region R, then φ is called a function in the region R
Q41. If p and ψ are scalar point functions then ∇·(p∇ψ) =
Q42. dr = dx i + dy j + dz k is called as the differential of
Q43. Curl of a curl of a vector gives a ______
Q44. If V is a solenoid vector point function then
Q45. There exists a continuous vector field V for a scalar potential function φ that satisfies the relation
Q46. The Laplace operator is a ______ order differential operator given by the divergence of the gradient of a given function defined over a space R.
Q47. An ellipse is a simple closed curve.
Q48. The directional derivative f = |∇φ| |a| cos θ is zero, when θ =
Q49. A field which is not irrotational is sometimes called a ______ field.
Q50. Both double and triple integrals can be used to calculate
Q51. I is directly related with mass of the body.
Q52. Let A be a given vector point function which is defined and continuous in a given region R. Then the volume integral of A over the region R can be defined as
Q53. Mathematical perception of the gradient is said to be
Q54. The value of dr = dx i + dy j + dz k for the curve x = t+1, y=2t², z=t³ is
Q55. ∫_C V·dr is independent of the path joining any two points P₁ and P₂ in a given region if that region is
Q56. If A is a differentiable vector function and φ is a differentiable scalar function of position (x,y,z), then (A × ∇)φ =
Q57. The two dimensional Laplace operator in polar coordinates (r,θ) can be expressed as ∇²φ =
Q58. The set of all values of scalar point function φ in a region together forms a
Q59. ∫ dr × B = k becomes
Q60. For φ = xy, the integral ∭ ∇²φ dV =
Q61. The surface integral of a vector field is called the flux of the vector field through the surface.
Q62. Gradient of a scalar function represents a normal vector to the surface.
Q63. A particle moves in a plane such that at any time t its distance from the origin is r = 2t + 4 and its angle with positive x-axis is θ = √t. Find the radial and transverse components of velocity.
Q64. The directional derivative = |∇φ| cos θ can be zero, when θ =
Q65. If ∇·V = 0 everywhere in some region of R³, then V is called a solenoidal vector point function in the region.
Q66. If a particle of mass 2 units has position vector r = t²i + t³j - t⁴k, then find the force acting on the particle.
Q67. ∫∫∫ dV =
Q68. The Green's theorem in plane can be written in tangential form as
Q69. Temperature is the example of scalar field.
Q70. If F = zyi - xj - y²k, then the integral for work done by the force on the curve C in the xy-plane, y = 2x, from (0,0) to (1,2) is
Q71. An integral where the function is evaluated along a curve is called line integral.
Q72. A curl has divergence.
Q73. If |U| = 1, then the vector field U is
Q74. If A is rotational and ∇×A = (c-1)i + (a-4)j + (b-2)k, then the value of a must be