1. The scalar product of two vectors A and B is defined as:
दो vectors A और B का scalar product किसके द्वारा परिभाषित किया जाता है?

A. A × B
A × B

B. A · B = AB cos θ
A · B = AB cos θ

C. A · B = AB sin θ
A · B = AB sin θ

D. A + B
A + B

Answer: B. A · B = AB cos θ — A · B = AB cos θ

2. The vector product of two vectors A and B is:
दो vectors A और B का vector product क्या होता है?

A. A × B = AB sin θ n̂
A × B = AB sin θ n̂

B. A × B = AB cos θ
A × B = AB cos θ

C. A × B = A + B
A × B = A + B

D. A × B = A/B
A × B = A/B

Answer: A. A × B = AB sin θ n̂ — A × B = AB sin θ n̂

3. The scalar triple product of vectors A, B and C is:
Vectors A, B और C का scalar triple product क्या है?

A. A × B × C
A × B × C

B. A · (B + C)
A · (B + C)

C. A · (B × C)
A · (B × C)

D. A + B + C
A + B + C

Answer: C. A · (B × C) — A · (B × C)

4. The scalar triple product represents the:
Scalar triple product किसका प्रतिनिधित्व करता है?

A. Area of a triangle
त्रिभुज का क्षेत्रफल

B. Length of a vector
Vector की लंबाई

C. Volume of a parallelepiped
Parallelepiped का आयतन

D. Circumference of a circle
वृत्त की परिधि

Answer: C. Volume of a parallelepiped — Parallelepiped का आयतन

5. If three vectors are coplanar, their scalar triple product is:
यदि तीन vectors coplanar हैं, तो उनका scalar triple product क्या होगा?

A. 1
1

B. −1
−1

C. Maximum
अधिकतम

D. Zero
शून्य

Answer: D. Zero — शून्य

6. A vector field is a physical quantity that has:
Vector field एक ऐसी physical quantity है जिसमें क्या होता है?

A. Magnitude only
केवल magnitude

B. Direction only
केवल direction

C. Both magnitude and direction at each point
प्रत्येक बिंदु पर magnitude और direction दोनों

D. Neither magnitude nor direction
न magnitude न direction

Answer: C. Both magnitude and direction at each point — प्रत्येक बिंदु पर magnitude और direction दोनों

7. Which of the following is a scalar field?
निम्नलिखित में से कौन-सा scalar field है?

A. Temperature field
तापमान field

B. Velocity field
वेग field

C. Force field
बल field

D. Electric field
विद्युत field

Answer: A. Temperature field — तापमान field

8. The gradient operator is denoted by:
Gradient operator को किस symbol से दर्शाया जाता है?

A. ∇
∇

B. Δ
Δ

C. Σ
Σ

D. ∂
∂

Answer: A. ∇ — ∇

9. The gradient of a scalar field φ is written as:
Scalar field φ का gradient किस रूप में लिखा जाता है?

A. ∇ × φ
∇ × φ

B. ∇φ
∇φ

C. ∇ · φ
∇ · φ

D. φ/∇
φ/∇

Answer: B. ∇φ — ∇φ

10. The gradient of a scalar field points in the direction of:
Scalar field का gradient किस दिशा में point करता है?

A. Maximum decrease of the scalar field
Scalar field की maximum decrease की दिशा

B. Zero change of the scalar field
Scalar field में zero change की दिशा

C. Maximum increase of the scalar field
Scalar field की maximum increase की दिशा

D. Random direction
किसी भी दिशा में

Answer: C. Maximum increase of the scalar field — Scalar field की maximum increase की दिशा

11. The divergence of a vector field A is represented by:
Vector field A के divergence को किससे दर्शाया जाता है?

A. ∇ × A
∇ × A

B. ∇ · A
∇ · A

C. ∇A
∇A

D. A × A
A × A

Answer: B. ∇ · A — ∇ · A

12. The divergence of a vector field is a:
Vector field का divergence एक ______ quantity है।

A. Scalar quantity
Scalar quantity

B. Vector quantity
Vector quantity

C. Tensor quantity
Tensor quantity

D. Dimensionless vector
Dimensionless vector

Answer: A. Scalar quantity — Scalar quantity

13. The curl of a vector field A is defined as:
Vector field A का curl किसके द्वारा परिभाषित किया जाता है?

A. ∇ · A
∇ · A

B. ∇A
∇A

C. ∇ × A
∇ × A

D. A · A
A · A

Answer: C. ∇ × A — ∇ × A

14. The curl of a vector field is a:
Vector field का curl एक ______ quantity है।

A. Scalar quantity
Scalar quantity

B. Vector quantity
Vector quantity

C. Constant quantity always
हमेशा constant quantity

D. Dimensionless scalar
Dimensionless scalar

Answer: B. Vector quantity — Vector quantity

15. For an irrotational vector field, the curl is:
एक irrotational vector field के लिए curl का मान क्या होता है?

A. Zero
शून्य

B. One
एक

C. Infinite
अनंत

D. Maximum
अधिकतम

Answer: A. Zero — शून्य

16. The continuity equation expresses the law of conservation of:
Continuity equation किसके conservation law को व्यक्त करती है?

A. Energy
ऊर्जा

B. Momentum
संवेग

C. Mass
द्रव्यमान

D. Angular momentum
कोणीय संवेग

Answer: C. Mass — द्रव्यमान

17. For an incompressible fluid, the continuity equation gives:
Incompressible fluid के लिए continuity equation क्या देती है?

A. ∇ · v = 0
∇ · v = 0

B. ∇ × v = 0
∇ × v = 0

C. ∇v = 1
∇v = 1

D. ∇ · v = 1
∇ · v = 1

Answer: A. ∇ · v = 0 — ∇ · v = 0

18. Bernoulli's theorem is based on the conservation of:
Bernoulli theorem किसके conservation पर आधारित है?

A. Mass only
केवल mass

B. Energy
Energy

C. Charge
Charge

D. Angular momentum only
केवल angular momentum

Answer: B. Energy — Energy

19. Bernoulli's equation for an ideal steady fluid flow is:
Ideal steady fluid flow के लिए Bernoulli equation क्या है?

A. P + ρv² + ρgh = constant
P + ρv² + ρgh = constant

B. P + ½ρv² + ρgh = constant
P + ½ρv² + ρgh = constant

C. P − ½ρv² + ρgh = constant
P − ½ρv² + ρgh = constant

D. P + ½ρv² − ρgh = constant
P + ½ρv² − ρgh = constant

Answer: B. P + ½ρv² + ρgh = constant — P + ½ρv² + ρgh = constant

20. Fourier's law of heat conduction states that heat flow is proportional to:
Fourier's law के अनुसार heat flow किसके proportional होता है?

A. Temperature gradient
Temperature gradient

B. Temperature itself only
केवल temperature

C. Pressure gradient
Pressure gradient

D. Density only
केवल density

Answer: A. Temperature gradient — Temperature gradient

21. The vector triple product A × (B × C) is equal to:
A × (B × C) का मान क्या होता है?

A. B(A · C) − C(A · B)
B(A · C) − C(A · B)

B. A(B · C)
A(B · C)

C. C(A · B) − B(A · C)
C(A · B) − B(A · C)

D. (A × B) × C
(A × B) × C

Answer: A. B(A · C) − C(A · B) — B(A · C) − C(A · B)

22. The vector triple product identity is commonly remembered as:
Vector triple product identity को सामान्यतः किस रूप में याद किया जाता है?

A. BAC − CAB
BAC − CAB

B. ABC − CBA
ABC − CBA

C. ACB − BCA
ACB − BCA

D. ABC + CBA
ABC + CBA

Answer: A. BAC − CAB — BAC − CAB

23. If A · B = 0, then the two non-zero vectors A and B are:
यदि A · B = 0 है, तो दो non-zero vectors A और B कैसी होंगी?

A. Parallel
समांतर

B. Perpendicular
लंबवत

C. Equal
समान

D. Anti-parallel only
केवल anti-parallel

Answer: B. Perpendicular — लंबवत

24. If A × B = 0 for two non-zero vectors, then A and B are:
यदि दो non-zero vectors के लिए A × B = 0 है, तो A और B कैसी होंगी?

A. Perpendicular
लंबवत

B. Equal in magnitude only
केवल magnitude में समान

C. Parallel or anti-parallel
समांतर या anti-parallel

D. Always perpendicular
हमेशा लंबवत

Answer: C. Parallel or anti-parallel — समांतर या anti-parallel

25. The magnitude of A × B is maximum when the angle between A and B is:
A × B का magnitude अधिकतम कब होता है?

A. 0°
0°

B. 30°
30°

C. 45°
45°

D. 90°
90°

Answer: D. 90° — 90°

26. In Cartesian coordinates, the gradient of a scalar field φ is:
Cartesian coordinates में scalar field φ का gradient क्या होता है?

A. ∂φ/∂x + ∂φ/∂y + ∂φ/∂z
∂φ/∂x + ∂φ/∂y + ∂φ/∂z

B. î ∂φ/∂x + ĵ ∂φ/∂y + k̂ ∂φ/∂z
î ∂φ/∂x + ĵ ∂φ/∂y + k̂ ∂φ/∂z

C. î∂φ/∂x − ĵ∂φ/∂y + k̂∂φ/∂z
î∂φ/∂x − ĵ∂φ/∂y + k̂∂φ/∂z

D. ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²
∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²

Answer: B. î ∂φ/∂x + ĵ ∂φ/∂y + k̂ ∂φ/∂z — î ∂φ/∂x + ĵ ∂φ/∂y + k̂ ∂φ/∂z

27. If φ = x² + y² + z², then ∇φ is:
यदि φ = x² + y² + z² है, तो ∇φ क्या होगा?

A. 2x î + 2y ĵ + 2z k̂
2x î + 2y ĵ + 2z k̂

B. x î + y ĵ + z k̂
x î + y ĵ + z k̂

C. 2x + 2y + 2z
2x + 2y + 2z

D. x² î + y² ĵ + z² k̂
x² î + y² ĵ + z² k̂

Answer: A. 2x î + 2y ĵ + 2z k̂ — 2x î + 2y ĵ + 2z k̂

28. For a vector field A = Aₓî + Aᵧĵ + A_zk̂, its divergence is:
Vector field A = Aₓî + Aᵧĵ + A_zk̂ का divergence क्या है?

A. ∂Aₓ/∂x + ∂Aᵧ/∂y + ∂A_z/∂z
∂Aₓ/∂x + ∂Aᵧ/∂y + ∂A_z/∂z

B. ∂Aₓ/∂y + ∂Aᵧ/∂z + ∂A_z/∂x
∂Aₓ/∂y + ∂Aᵧ/∂z + ∂A_z/∂x

C. Aₓ + Aᵧ + A_z
Aₓ + Aᵧ + A_z

D. ∂²Aₓ/∂x² + ∂²Aᵧ/∂y² + ∂²A_z/∂z²
∂²Aₓ/∂x² + ∂²Aᵧ/∂y² + ∂²A_z/∂z²

Answer: A. ∂Aₓ/∂x + ∂Aᵧ/∂y + ∂A_z/∂z — ∂Aₓ/∂x + ∂Aᵧ/∂y + ∂A_z/∂z

29. For A = xî + yĵ + zk̂, the divergence ∇ · A is:
A = xî + yĵ + zk̂ के लिए divergence ∇ · A का मान क्या है?

A. 0
0

B. 1
1

C. 2
2

D. 3
3

Answer: D. 3 — 3

30. The divergence of a uniform vector field is:
Uniform vector field का divergence क्या होता है?

A. Zero
शून्य

B. One
एक

C. Infinite
अनंत

D. Always negative
हमेशा negative

Answer: A. Zero — शून्य

31. For A = yî + zĵ + xk̂, the curl ∇ × A is:
A = yî + zĵ + xk̂ के लिए curl ∇ × A क्या होगा?

A. î + ĵ + k̂
î + ĵ + k̂

B. −î − ĵ − k̂
−î − ĵ − k̂

C. 0
0

D. xî + yĵ + zk̂
xî + yĵ + zk̂

Answer: B. −î − ĵ − k̂ — −î − ĵ − k̂

32. A vector field is called solenoidal when:
किसी vector field को solenoidal कब कहा जाता है?

A. Its curl is zero
उसका curl zero हो

B. Its divergence is zero
उसका divergence zero हो

C. Its gradient is zero
उसका gradient zero हो

D. Its magnitude is zero everywhere
उसका magnitude हर जगह zero हो

Answer: B. Its divergence is zero — उसका divergence zero हो

33. The divergence of the curl of any sufficiently smooth vector field is:
किसी sufficiently smooth vector field के curl का divergence क्या होता है?

A. 1
1

B. −1
−1

C. Zero
शून्य

D. Infinite
अनंत

Answer: C. Zero — शून्य

34. The curl of the gradient of a sufficiently smooth scalar field is:
किसी sufficiently smooth scalar field के gradient का curl क्या होता है?

A. Zero
शून्य

B. One
एक

C. Maximum
अधिकतम

D. Undefined always
हमेशा undefined

Answer: A. Zero — शून्य

35. For an incompressible fluid, the density:
Incompressible fluid के लिए density कैसी होती है?

A. Changes rapidly with pressure
Pressure के साथ तेजी से बदलती है

B. Is effectively constant
Effectively constant होती है

C. Is always zero
हमेशा zero होती है

D. Becomes infinite
Infinite हो जाती है

Answer: B. Is effectively constant — Effectively constant होती है

36. Euler's equation of motion for an ideal fluid relates pressure force with:
Ideal fluid के Euler equation of motion में pressure force किससे संबंधित होती है?

A. Fluid acceleration and body force
Fluid acceleration और body force

B. Only temperature
केवल temperature

C. Only viscosity
केवल viscosity

D. Only heat conduction
केवल heat conduction

Answer: A. Fluid acceleration and body force — Fluid acceleration और body force

37. Euler's equation of motion is applicable to a:
Euler equation of motion किस प्रकार के fluid के लिए लागू होती है?

A. Perfect or ideal fluid
Perfect या ideal fluid

B. Highly viscous solid
Highly viscous solid

C. Rigid body only
केवल rigid body

D. Vacuum only
केवल vacuum

Answer: A. Perfect or ideal fluid — Perfect या ideal fluid

38. In Bernoulli's theorem, P/ρ represents:
Bernoulli theorem में P/ρ किस quantity को दर्शाता है?

A. Kinetic energy per unit mass
Per unit mass kinetic energy

B. Pressure energy per unit mass
Per unit mass pressure energy

C. Potential energy per unit mass
Per unit mass potential energy

D. Heat energy per unit mass
Per unit mass heat energy

Answer: B. Pressure energy per unit mass — Per unit mass pressure energy

39. In Bernoulli's equation, v²/2 represents:
Bernoulli equation में v²/2 क्या दर्शाता है?

A. Pressure head
Pressure head

B. Velocity head
Velocity head

C. Height head
Height head

D. Heat head
Heat head

Answer: B. Velocity head — Velocity head

40. The heat conduction equation in one dimension is obtained by combining Fourier's law with the conservation of:
One-dimensional heat conduction equation Fourier's law को किस conservation principle के साथ combine करके प्राप्त होती है?

A. Mass
Mass

B. Charge
Charge

C. Energy
Energy

D. Angular momentum
Angular momentum

Answer: C. Energy — Energy

41. The vector identity ∇ × (∇φ) for a sufficiently smooth scalar field φ is:
एक sufficiently smooth scalar field φ के लिए ∇ × (∇φ) का मान क्या है?

A. ∇²φ
∇²φ

B. ∇φ
∇φ

C. Zero
शून्य

D. 1
1

Answer: C. Zero — शून्य

42. The Laplacian of a scalar field φ in Cartesian coordinates is:
Cartesian coordinates में scalar field φ का Laplacian क्या होता है?

A. ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²
∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²

B. ∂φ/∂x + ∂φ/∂y + ∂φ/∂z
∂φ/∂x + ∂φ/∂y + ∂φ/∂z

C. ∇ × φ
∇ × φ

D. ∇φ
∇φ

Answer: A. ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z² — ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²

43. Laplace's equation is written as:
Laplace equation को किस रूप में लिखा जाता है?

A. ∇φ = 0
∇φ = 0

B. ∇²φ = 0
∇²φ = 0

C. ∇ · φ = 0
∇ · φ = 0

D. ∇ × φ = 0
∇ × φ = 0

Answer: B. ∇²φ = 0 — ∇²φ = 0

44. Poisson's equation for a scalar potential φ is generally written as:
Scalar potential φ के लिए Poisson equation सामान्यतः किस रूप में लिखी जाती है?

A. ∇²φ = 0
∇²φ = 0

B. ∇φ = ρ
∇φ = ρ

C. ∇²φ = −ρ/ε₀
∇²φ = −ρ/ε₀

D. ∇ × φ = ρ/ε₀
∇ × φ = ρ/ε₀

Answer: C. ∇²φ = −ρ/ε₀ — ∇²φ = −ρ/ε₀

45. Laplace's equation is obtained from Poisson's equation when the charge density is:
Poisson equation से Laplace equation कब प्राप्त होती है?

A. Maximum
अधिकतम

B. Infinite
अनंत

C. Negative
Negative

D. Zero
शून्य

Answer: D. Zero — शून्य

46. Gauss's law relates the electric flux through a closed surface to:
Gauss law closed surface से electric flux को किससे relate करता है?

A. Enclosed charge
Enclosed charge

B. Surface area only
केवल surface area

C. Electric potential only
केवल electric potential

D. Magnetic field only
केवल magnetic field

Answer: A. Enclosed charge — Enclosed charge

47. In integral form, Gauss's law in electrostatics is:
Electrostatics में Gauss law का integral form क्या है?

A. ∮ E · dS = 0
∮ E · dS = 0

B. ∮ E · dS = Q/ε₀
∮ E · dS = Q/ε₀

C. ∮ E × dS = Qε₀
∮ E × dS = Qε₀

D. ∮ E · dS = ε₀Q
∮ E · dS = ε₀Q

Answer: B. ∮ E · dS = Q/ε₀ — ∮ E · dS = Q/ε₀

48. The differential form of Gauss's law is:
Gauss law का differential form क्या है?

A. ∇ × E = ρ/ε₀
∇ × E = ρ/ε₀

B. ∇E = 0
∇E = 0

C. ∇ · E = ρ/ε₀
∇ · E = ρ/ε₀

D. ∇²E = ρ
∇²E = ρ

Answer: C. ∇ · E = ρ/ε₀ — ∇ · E = ρ/ε₀

49. The SI unit of electric flux is:
Electric flux की SI unit क्या है?

A. N/C
N/C

B. C/N
C/N

C. N·m²/C
N·m²/C

D. C/m²
C/m²

Answer: C. N·m²/C — N·m²/C

50. For a point charge q, the electric field at distance r in vacuum is:
Vacuum में point charge q से दूरी r पर electric field क्या होता है?

A. q/(4πε₀r)
q/(4πε₀r)

B. q/(4πε₀r²)
q/(4πε₀r²)

C. q/(4πε₀r³)
q/(4πε₀r³)

D. q r/(4πε₀)
q r/(4πε₀)

Answer: B. q/(4πε₀r²) — q/(4πε₀r²)

51. The divergence theorem converts a volume integral of divergence into a:
Divergence theorem divergence के volume integral को किसमें convert करता है?

A. Line integral
Line integral

B. Surface integral
Surface integral

C. Time integral
Time integral

D. Point value
Point value

Answer: B. Surface integral — Surface integral

52. The divergence theorem is mathematically expressed as:
Divergence theorem का mathematical expression क्या है?

A. ∫V (∇ · A)dV = ∮S A · dS
∫V (∇ · A)dV = ∮S A · dS

B. ∫V A dV = ∮S ∇ · A dS
∫V A dV = ∮S ∇ · A dS

C. ∮S A × dS = ∫V ∇A dV
∮S A × dS = ∫V ∇A dV

D. ∫V ∇A dV = 0
∫V ∇A dV = 0

Answer: A. ∫V (∇ · A)dV = ∮S A · dS — ∫V (∇ · A)dV = ∮S A · dS

53. Stokes' theorem relates the surface integral of curl to a:
Stokes theorem curl के surface integral को किससे relate करता है?

A. Volume integral
Volume integral

B. Line integral around the boundary
Boundary के around line integral

C. Time integral
Time integral

D. Scalar product only
केवल scalar product

Answer: B. Line integral around the boundary — Boundary के around line integral

54. Stokes' theorem can be written as:
Stokes theorem को किस रूप में लिखा जा सकता है?

A. ∮C A · dl = ∫S (∇ × A) · dS
∮C A · dl = ∫S (∇ × A) · dS

B. ∮C A · dl = ∫V (∇ · A)dV
∮C A · dl = ∫V (∇ · A)dV

C. ∮C A × dl = ∫S ∇A dS
∮C A × dl = ∫S ∇A dS

D. ∮C A · dl = 0 always
∮C A · dl = 0 always

Answer: A. ∮C A · dl = ∫S (∇ × A) · dS — ∮C A · dl = ∫S (∇ × A) · dS

55. A conservative force field can be expressed as the negative gradient of:
Conservative force field को किसके negative gradient के रूप में व्यक्त किया जा सकता है?

A. Momentum
Momentum

B. Kinetic energy
Kinetic energy

C. Potential energy
Potential energy

D. Acceleration
Acceleration

Answer: C. Potential energy — Potential energy

56. For a conservative force F, the relation with potential energy U is:
Conservative force F और potential energy U के बीच relation क्या है?

A. F = ∇U
F = ∇U

B. F = −∇U
F = −∇U

C. F = U∇
F = U∇

D. F = U²
F = U²

Answer: B. F = −∇U — F = −∇U

57. In a steady one-dimensional fluid flow through a pipe, the continuity relation is:
Steady one-dimensional fluid flow में pipe के through continuity relation क्या है?

A. Av = constant
Av = constant

B. A/v = constant
A/v = constant

C. A + v = constant
A + v = constant

D. A − v = constant
A − v = constant

Answer: A. Av = constant — Av = constant

58. According to the continuity equation, if the cross-sectional area of a pipe decreases for an incompressible steady flow, the fluid velocity:
Continuity equation के अनुसार incompressible steady flow में pipe का cross-sectional area घटने पर fluid velocity क्या होगी?

A. Decreases
घटती है

B. Becomes zero
Zero हो जाती है

C. Increases
बढ़ती है

D. Remains necessarily unchanged
अनिवार्य रूप से unchanged रहती है

Answer: C. Increases — बढ़ती है

59. In Bernoulli's theorem, if the height remains constant, an increase in fluid speed is accompanied by:
Bernoulli theorem में यदि height constant रहे, तो fluid speed बढ़ने पर क्या होता है?

A. Increase in pressure
Pressure में वृद्धि

B. Decrease in pressure
Pressure में कमी

C. No relation with pressure
Pressure से कोई relation नहीं

D. Infinite pressure
Infinite pressure

Answer: B. Decrease in pressure — Pressure में कमी

60. Fourier's law of heat conduction in one dimension is represented by:
One-dimensional heat conduction के लिए Fourier law किस expression से व्यक्त होता है?

A. Q̇ = kA dT/dx
Q̇ = kA dT/dx

B. Q̇ = −kA dT/dx
Q̇ = −kA dT/dx

C. Q̇ = kA T
Q̇ = kA T

D. Q̇ = −kT/A
Q̇ = −kT/A

Answer: B. Q̇ = −kA dT/dx — Q̇ = −kA dT/dx

61. The scalar triple product of three vectors A, B and C is written as:
तीन vectors A, B और C का scalar triple product किस रूप में लिखा जाता है?

A. A × (B × C)
A × (B × C)

B. (A × B) × C
(A × B) × C

C. A · (B × C)
A · (B × C)

D. A · (B · C)
A · (B · C)

Answer: C. A · (B × C) — A · (B × C)

62. The scalar triple product A · (B × C) represents the:
Scalar triple product A · (B × C) क्या दर्शाता है?

A. Area of a triangle
Triangle का area

B. Volume of the parallelepiped formed by A, B and C
A, B और C से बने parallelepiped का volume

C. Length of a vector
Vector की length

D. Angle between two vectors only
केवल दो vectors के बीच angle

Answer: B. Volume of the parallelepiped formed by A, B and C — A, B और C से बने parallelepiped का volume

63. If three vectors are coplanar, their scalar triple product is:
यदि तीन vectors coplanar हैं, तो उनका scalar triple product क्या होगा?

A. Zero
शून्य

B. One
एक

C. Maximum
अधिकतम

D. Infinite
अनंत

Answer: A. Zero — शून्य

64. A scalar field assigns a scalar quantity to:
Scalar field प्रत्येक point पर क्या quantity assign करता है?

A. Only a direction
केवल direction

B. Only a vector
केवल vector

C. Each point in space
Space के प्रत्येक point पर

D. Only the origin
केवल origin पर

Answer: C. Each point in space — Space के प्रत्येक point पर

65. Temperature distribution T(x,y,z) is an example of a:
Temperature distribution T(x,y,z) किसका example है?

A. Vector field
Vector field

B. Scalar field
Scalar field

C. Tensor field only
केवल tensor field

D. Zero field
Zero field

Answer: B. Scalar field — Scalar field

66. The gradient of a scalar field points in the direction of:
Scalar field का gradient किस direction में point करता है?

A. Maximum decrease of the scalar
Scalar की maximum decrease की direction

B. Maximum increase of the scalar
Scalar की maximum increase की direction

C. Zero change only
केवल zero change

D. Circular motion
Circular motion

Answer: B. Maximum increase of the scalar — Scalar की maximum increase की direction

67. The gradient vector is always normal to a:
Gradient vector हमेशा किसके normal होता है?

A. Equipotential surface
Equipotential surface

B. Random surface
Random surface

C. Coordinate axis
Coordinate axis

D. Time axis
Time axis

Answer: A. Equipotential surface — Equipotential surface

68. The physical dimension of the divergence of velocity is:
Velocity के divergence की physical dimension क्या होती है?

A. T⁻¹
T⁻¹

B. L T⁻¹
L T⁻¹

C. L² T⁻¹
L² T⁻¹

D. T
T

Answer: A. T⁻¹ — T⁻¹

69. A vector field with zero curl is called:
जिस vector field का curl zero हो, उसे क्या कहा जाता है?

A. Solenoidal field
Solenoidal field

B. Irrotational field
Irrotational field

C. Uniform scalar field
Uniform scalar field

D. Harmonic field only
केवल harmonic field

Answer: B. Irrotational field — Irrotational field

70. For an irrotational vector field, the circulation around a closed path is:
Irrotational vector field के लिए closed path के around circulation क्या होता है?

A. Always zero, under suitable conditions
Suitable conditions में हमेशा zero

B. Always infinite
हमेशा infinite

C. Always one
हमेशा one

D. Always negative
हमेशा negative

Answer: A. Always zero, under suitable conditions — Suitable conditions में हमेशा zero

71. The continuity equation expresses the conservation of:
Continuity equation किसके conservation को express करती है?

A. Energy
Energy

B. Mass
Mass

C. Angular momentum
Angular momentum

D. Temperature
Temperature

Answer: B. Mass — Mass

72. For a compressible fluid, the general continuity equation is based on:
Compressible fluid के लिए general continuity equation किस principle पर आधारित है?

A. Conservation of mass
Mass conservation

B. Conservation of charge
Charge conservation

C. Conservation of temperature
Temperature conservation

D. Conservation of pressure
Pressure conservation

Answer: A. Conservation of mass — Mass conservation

73. Bernoulli's theorem is derived from the conservation of:
Bernoulli theorem किसके conservation से प्राप्त होती है?

A. Electric charge
Electric charge

B. Linear momentum only
केवल linear momentum

C. Mechanical energy
Mechanical energy

D. Mass only
केवल mass

Answer: C. Mechanical energy — Mechanical energy

74. Bernoulli's theorem for an ideal steady flow is applicable along a:
Ideal steady flow के लिए Bernoulli theorem किसके along लागू होती है?

A. Streamline
Streamline

B. Random line
Random line

C. Time axis
Time axis

D. Equipotential line only
केवल equipotential line

Answer: A. Streamline — Streamline

75. In Bernoulli's equation, the term gh represents:
Bernoulli equation में gh term क्या दर्शाता है?

A. Pressure energy per unit mass
Per unit mass pressure energy

B. Kinetic energy per unit mass
Per unit mass kinetic energy

C. Gravitational potential energy per unit mass
Per unit mass gravitational potential energy

D. Thermal energy per unit mass
Per unit mass thermal energy

Answer: C. Gravitational potential energy per unit mass — Per unit mass gravitational potential energy

76. The gravitational potential in a charge-free region satisfies:
Charge-free region में gravitational potential किस equation को satisfy करता है?

A. Poisson's equation
Poisson equation

B. Laplace's equation
Laplace equation

C. Wave equation only
केवल wave equation

D. Heat equation only
केवल heat equation

Answer: B. Laplace's equation — Laplace equation

77. In a region containing mass density ρ, the gravitational potential V satisfies Poisson's equation:
Mass density ρ वाले region में gravitational potential V किस Poisson equation को satisfy करता है?

A. ∇²V = 4πGρ
∇²V = 4πGρ

B. ∇²V = −4πGρ
∇²V = −4πGρ

C. ∇V = −4πGρ
∇V = −4πGρ

D. ∇ × V = 4πGρ
∇ × V = 4πGρ

Answer: B. ∇²V = −4πGρ — ∇²V = −4πGρ

78. The gravitational field g is related to gravitational potential V by:
Gravitational field g और gravitational potential V के बीच relation क्या है?

A. g = ∇V
g = ∇V

B. g = V²
g = V²

C. g = −∇V
g = −∇V

D. g = 1/V
g = 1/V

Answer: C. g = −∇V — g = −∇V

79. The electric field E is related to electric potential V by:
Electric field E और electric potential V के बीच relation क्या है?

A. E = −∇V
E = −∇V

B. E = ∇²V
E = ∇²V

C. E = V²
E = V²

D. E = 1/V
E = 1/V

Answer: A. E = −∇V — E = −∇V

80. The thermal conductivity k in Fourier's law determines the ability of a material to:
Fourier law में thermal conductivity k material की किस ability को दर्शाती है?

A. Store electric charge
Electric charge store करने की

B. Conduct heat
Heat conduct करने की

C. Produce mass
Mass produce करने की

D. Resist gravity
Gravity resist करने की

Answer: B. Conduct heat — Heat conduct करने की

81. The magnitude of the vector product A × B is equal to:
Vector product A × B का magnitude किसके बराबर होता है?

A. AB cos θ
AB cos θ

B. AB tan θ
AB tan θ

C. AB sin θ
AB sin θ

D. A/B
A/B

Answer: C. AB sin θ — AB sin θ

82. The direction of A × B is determined by:
A × B की direction किस rule से निर्धारित की जाती है?

A. Right-hand rule
Right-hand rule

B. Left-hand rule only
केवल Left-hand rule

C. Newton's law
Newton's law

D. Lenz's law
Lenz's law

Answer: A. Right-hand rule — Right-hand rule

83. The relation A × B = −(B × A) shows that vector product is:
Relation A × B = −(B × A) दर्शाता है कि vector product कैसा होता है?

A. Commutative
Commutative

B. Associative
Associative

C. Distributive only
केवल distributive

D. Anti-commutative
Anti-commutative

Answer: D. Anti-commutative — Anti-commutative

84. The scalar product satisfies the relation:
Scalar product के लिए कौन-सा relation सही है?

A. A · B = −B · A
A · B = −B · A

B. A · B = B · A
A · B = B · A

C. A · B = A × B
A · B = A × B

D. A · B = 0 always
A · B हमेशा 0

Answer: B. A · B = B · A — A · B = B · A

85. The scalar product A · B is maximum when the angle between A and B is:
Scalar product A · B maximum कब होता है?

A. 0°
0°

B. 45°
45°

C. 90°
90°

D. 180°
180°

Answer: A. 0° — 0°

86. The unit vector in the direction of a vector A is:
Vector A की direction में unit vector क्या होगा?

A. A²
A²

B. |A|A
|A|A

C. A/|A|
A/|A|

D. |A|/A²
|A|/A²

Answer: C. A/|A| — A/|A|

87. The directional derivative of a scalar field φ in the direction of unit vector n̂ is:
Scalar field φ का directional derivative unit vector n̂ की direction में क्या होता है?

A. ∇φ · n̂
∇φ · n̂

B. ∇φ × n̂
∇φ × n̂

C. ∇ · n̂
∇ · n̂

D. φn̂
φn̂

Answer: A. ∇φ · n̂ — ∇φ · n̂

88. The maximum value of the directional derivative of φ at a point is:
किसी point पर φ के directional derivative का maximum value क्या होता है?

A. φ
φ

B. |∇φ|
|∇φ|

C. ∇²φ
∇²φ

D. Zero
Zero

Answer: B. |∇φ| — |∇φ|

89. If ∇φ = 0 throughout a region, then φ is:
यदि किसी region में ∇φ = 0 है, तो φ क्या होगा?

A. Increasing everywhere
हर जगह increasing

B. Decreasing everywhere
हर जगह decreasing

C. Constant throughout that connected region
उस connected region में constant

D. Infinite everywhere
हर जगह infinite

Answer: C. Constant throughout that connected region — उस connected region में constant

90. The physical meaning of divergence of velocity in fluid mechanics is related to the rate of:
Fluid mechanics में velocity के divergence का physical meaning किस rate से संबंधित है?

A. Rotation of the fluid element
Fluid element के rotation की rate

B. Expansion or compression of a fluid element
Fluid element के expansion या compression की rate

C. Heat conduction only
केवल heat conduction

D. Electric charge flow
Electric charge flow

Answer: B. Expansion or compression of a fluid element — Fluid element के expansion या compression की rate

91. The curl of a velocity field is associated with the local:
Velocity field का curl local किस phenomenon से associated होता है?

A. Rotation of the fluid
Fluid के rotation

B. Density conservation only
केवल density conservation

C. Temperature change only
केवल temperature change

D. Pressure measurement only
केवल pressure measurement

Answer: A. Rotation of the fluid — Fluid के rotation

92. In a steady flow, the fluid properties at a fixed point are:
Steady flow में किसी fixed point पर fluid properties कैसी होती हैं?

A. Changing with time
Time के साथ changing

B. Independent of time
Time से independent

C. Always zero
हमेशा zero

D. Infinite
Infinite

Answer: B. Independent of time — Time से independent

93. In an ideal fluid, viscosity is assumed to be:
Ideal fluid में viscosity को कितना माना जाता है?

A. Infinite
Infinite

B. Very large
बहुत बड़ी

C. Zero
Zero

D. Negative
Negative

Answer: C. Zero — Zero

94. In Bernoulli's theorem, the pressure term is commonly called:
Bernoulli theorem में pressure term को सामान्यतः क्या कहा जाता है?

A. Pressure head
Pressure head

B. Velocity head
Velocity head

C. Elevation head
Elevation head

D. Heat head
Heat head

Answer: A. Pressure head — Pressure head

95. The negative sign in Fourier's law indicates that heat flows from:
Fourier law में negative sign किस direction में heat flow को दर्शाता है?

A. Lower temperature to higher temperature
Lower temperature से higher temperature

B. Higher temperature to lower temperature
Higher temperature से lower temperature

C. Zero temperature to infinite temperature
Zero temperature से infinite temperature

D. Random direction
Random direction

Answer: B. Higher temperature to lower temperature — Higher temperature से lower temperature

96. The SI unit of thermal conductivity is:
Thermal conductivity की SI unit क्या है?

A. W m⁻¹ K⁻¹
W m⁻¹ K⁻¹

B. W m K
W m K

C. J m⁻¹
J m⁻¹

D. N m⁻²
N m⁻²

Answer: A. W m⁻¹ K⁻¹ — W m⁻¹ K⁻¹

97. A function satisfying Laplace's equation is called a:
जो function Laplace equation को satisfy करता है, उसे क्या कहा जाता है?

A. Singular function
Singular function

B. Harmonic function
Harmonic function

C. Periodic function only
केवल periodic function

D. Discontinuous function
Discontinuous function

Answer: B. Harmonic function — Harmonic function

98. Gauss's law is particularly useful for calculating electric fields when the charge distribution has:
Gauss law electric field calculate करने में विशेष रूप से useful कब होती है?

A. High symmetry
High symmetry

B. Completely random distribution
Completely random distribution

C. No charge at all
कोई charge नहीं

D. Only time-dependent motion
केवल time-dependent motion

Answer: A. High symmetry — High symmetry

99. For a spherically symmetric charge distribution, the Gaussian surface is generally chosen as a:
Spherically symmetric charge distribution के लिए Gaussian surface सामान्यतः कैसी चुनी जाती है?

A. Cube
Cube

B. Cylinder
Cylinder

C. Sphere
Sphere

D. Plane
Plane

Answer: C. Sphere — Sphere

100. The electric flux through a closed Gaussian surface depends on the:
Closed Gaussian surface से electric flux किस पर depend करता है?

A. Total charge enclosed by the surface
Surface के अंदर enclosed total charge

B. Shape of the surface only
केवल surface की shape

C. Material outside the surface only
केवल surface के बाहर के material

D. Area alone, independent of charge
केवल area, charge से independent

Answer: A. Total charge enclosed by the surface — Surface के अंदर enclosed total charge