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Mathematics
University
Vector Calculus and Differential Equations Quiz II
20 questions
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- 1. Multiple Choice
Parametric equation of the line joining (0, 0, 0) and (2, 1, 1) can be taken as
x = 2t, y = t, z = t where 0 ≤ t ≤1
x = t2, y = t, z = t where 0 ≤ t ≤1
x = t, y = t2, z = t where 0 ≤ t ≤1
x = t, y = t2, z = t2 where 0≤ t ≤1
- 2. Multiple Choice
If ƒ = x2 i - xy j and C is the straight line joining the points
(0, 0) and (1, 1) then ∫ ƒ. dr is
1
-1
0
2
- 3. Multiple Choice
- 4. Multiple Choice
a2
a3
a
1
- 5. Multiple Choice
The value of ∫∫dxdy over the region bounded by x=0, x=2 and y=0, y=2 is
2
0
3
4
- 6. Multiple Choice
If R is any closed region of the x-y plane bounded by a simple closed curve C then ∫ x dy + y dx is
0
π
1
2
- 7. Multiple Choice
General solution of (D2+9) y= 0 is
y =c1 cos x + c2 sin x +x
y = x
y = c1 cos 3x + c2 sin 3x
none
- 8. Multiple Choice
Complementary function of x2y” –xy’ + 4y = cos (logx) + x sin(log x) is
x
x (c1 cos √3 log x + c 2 sin √3 log x )
x(c1 cos 2√3 log x + c 2 sin2 √3 log x )
x2 (c1 cos√3 log x + c2 sin √3log x )
- 9. Multiple Choice
The particular integral of (D2 + 1) y = x is
x
x2
1
0
- 10. Multiple Choice
True
False
- 11. Multiple Choice
The roots of m3 + 3m2 + 3m +1 = 0 are
1,1,-1
1,1,1
1,0,1
1,2,3
- 12. Multiple Choice
The complementary function of (D2 - 2D + 2) y = x ex is
ex (a + b x + c x2)
ex (a cos x + b sin x)
a ex + b e-x + c e2x
e-x ( a + b x + c x2)
- 13. Multiple Choice
The complementary function of (D3 - 3D2 + 3D - 1) y = x3 is
ex (a + bx + cx2)
e-x (a cosx + b sinx + c)
aex + be-x + ce2x
e-x (a + bx + cx2)
- 14. Multiple Choice
The formula for sin 3x is
4 sinx + 3 sin3x
3 sinx + 4 sin3x
4 sinx - 3 sin3x
3 sinx - 4 sin3x
- 15. Multiple Choice
The formula for cos (A +B) is
cos A cos B + sin A sin B
sin A cos B + cos A sin B
sin A cos B - cos A sin B
cos A cos B - sin A sin B
- 16. Multiple Choice
1/D stands for
Particular Integral
Differentiation
Integration
Complementary Function
- 17. Multiple Choice
If z = log x then θ =
d/dz
d/dy
d/dx
dy/dz
- 18. Multiple Choice
If x Dy = θ y then x2D2y is
(θ2 - θ) y
θ (θ - 1) (θ - 2) y
θ y
θ (θ - 1)
- 19. Multiple Choice
[1/(θ - α)] X =
x-α ∫ x-α+1 X dx
xα ∫ x-α-1 X dx
xα ∫ x-α+1 X dx
x-α ∫ x-α-1 X dx
- 20. Multiple Choice
If Y is the complementary function and u is the particular integral then the general solution of (Dn + a1Dn-1 + a2Dn-2 + ..... + an) y = X is of the form
y = c1Y + c2u
y = Y + u
Y = y + u
Y = c1y+ c2u
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