NAME_
I_II_III_IV_V_VI_VII_ TOTAL _
September 25
2003
Mathematics 206a
Multivariable Calculus
Examination #1
Mr. Haines
(10) I. Give a coordinate equation for the plane through the point (3, 4, 5) which is
perpendicular to the vector n = i + 3j + 2k .
(10
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_X_TOTAL _
September 30
2005
Mathematics 206a
Multivariable Calculus
Examination #1
Mr. Haines
(10) I. P and Q are points in 3, P has coordinates (1, 1, 1), and Q has coordinates (4, 5, 6).
What is the equation of the pla
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_TOTAL _
March 6
2006
Mathematics 206a
Multivariable Calculus
Examination #2
Mr. Haines
(15) I. Suppose R is the region in the xy-plane bounded by x = 0, x = 2, y = 0, and y = x 2 .
Suppose f ( x) = x 2 + y 2 .
Set up and
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_X_XI_XII_XIII_TOTAL_
_
(5) (5) (5) (12) (10) (10) (8)
(10) (10) (10) (5)
(5)
(5)
April 10
2006
Mathematics 206a
Multivariable Calculus
Final Examination
Mr. Haines
1
2
(5) I. If u = 1 , v = 0 and is the angle between u
NAME_
I_II_III_IV_V_VI_VII_VIII_ TOTAL _
March 25,
2005
Mathematics 206a
Multivariable Calculus
Examination #3
(15) I. Consider the path f : [0, )
2
Mr. Haines
(
A. Sketch a graph of f .
B. Give an integral that computes the total length of this path.
C.
AIEEE/2011/CHEMSITRY
S. No
Questions
1
Solutions
Q.1
the maximum covalent character is shown by the compound :
(a) SnCl2
(b) AlCl3
(c) MgCl2
(d) FeCl2
Sol: 1 (b)
Greater charge and small size of cation cause more polarization and more covalent
character
Q
AIEEE/2012/MATHS
S.
No
Q.1
Questions
sinx
The equation e
e
sinx
Solutions
4 = 0 has
Sol:1 (b)
(a) infinite number of real roots (b) no real roots
esinx esinx =4
1
t t =4
(c) exactly one real root
t2 4t 1 = 0
(d) exactly four real roots
Let esinx = t
4+2
AIEEE/2011/MATHS
S. No
Q.1
Questions
1
Solutions
The lines L1 : y x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q
respectively. The bisector of the acute angle between L1 and L2 intersect L3 at R .
Statement 1 : The ratio PR :RQ equ
AIEEE/2012/PHYSICS
S.
No
Q.1
Questions
A wooden wheel of radius R is made of two semicircular parts (see figure); The
two parts are held together by a ring made of a metal strip of cross sectional area
S and length L. L is slightly less than 2pR. To fit t
AIEEE/2012/CHEMSITRY
S. No
Questions
Solutions
Q.1
Which among the following will be named as dibromidobis (ethylene diamine)
chromium(III) bromide ?
(a) Cr(en)3 Br3
(b) Cr(en)2 Br2 Br
(c) Cr(en)Br4
(d) Cr(en)Br2 Br
Sol:1 (b)
dibromido bis (ethylene
diam
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_X_TOTAL _
November 4
2005
Mathematics 206a
Multivariable Calculus
Examination #2
Mr. Haines
(10) I. Suppose f ( x, y , z ) = ( x + e z + y , yx 2 ) and a = (1, 1, 0). Calculate the total derivative of
f at a .
(10) II. G
NAME_
I_II_III_IV_V_VI_VII_VIII_ IX_X_TOTAL _
February 17
2005
Mathematics 206a
Multivariable Calculus
Examination #2
(12)I. Suppose f ( x, y ) = x sin( xy )
A.
f
( x, y ) =
x
B.
f
( x, y ) =
y
C.
2 f
( x, y ) =
xy
D.
2 f
( x, y ) =
yx
Mr. Haines
(8)II. S
NAME_
I_II_III_IV_V_VI_VII_VIII_ TOTAL _
January 28
2005
Mathematics 206a
Multivariable Calculus
Examination #1
Mr. Haines
(10) I. Give the parametric equation of the line segment connecting the point (1, 2, 3) and the
point (2, 5, 7) . This is a line seg
NAME_
I_II_III_IV_V_VI_VII_ TOTAL _
October 24
2003
Mathematics 206a
Multivariable Calculus
Examination #2
Mr. Haines
(11) I. Find the maximum and minimum values of the function
f ( x, y ) = 1 + x y on the set [0,1] [0,1] .
(21) II. Suppose
f ( x, y, z )
NAME_
I_II_III_IV_V_VI_VII_ TOTAL _
November 19,
2003
Mathematics 206a
Multivariable Calculus
Examination #3
Mr. Haines
(20) I. Let a = (0, 0, 0) , b = (0, 3, 6), and C be the straight line segment connecting a to b.
A. Give a parametrization for C.
B. If
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_X_TOTAL _
April 15
2004
Mathematics 206a
Multivariable Calculus
Final Examination
Mr. Haines
I. (5) If a = 3i - 2j - k and L is the line with parametric equation x = (1, 2, 3) + ta for all t ,
give the equation of any li
NAME_
I_II_III_IV_V_VI_VII_TOTAL
_
April 2
2004
(10) I. Calculate the value of
Mathematics 206a
Multivariable Calculus
Examination #3
1 x x+ y
0 0 0
Mr. Haines
z dzdydx .
(10) II. Give a function f : R 2 3 that is a parametrization of the piece of the sur
NAME_
I_II_III_IV_V_VI_VII_VIII_ TOTAL _
February 6
2004
Mathematics 206a
Multivariable Calculus
Examination #1
Mr. Haines
(10) I. If a = 3i - 2j - k , give the equation of a line through the point (2, 5, 7) that is
parallel to a .
(10) II. Give a coordin
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_TOTAL _
March 10
2004
Mathematics 206a
Multivariable Calculus
Examination #2
Mr. Haines
(5) I. Give an example of vector field on 3 .
(10) II. Find the equation of the tangent plane at the point (0, 1, 1) to the surface
NAME_
i_ii_iii_iv_v_vi_vii_viii_ix_x_xi_xii_xiii_ TOTAL _
December 12,
2003
Mathematics 206a
Multivariable Calculus
Final Examination
Mr. Haines
(3) I. Let a = (1, 3, 7) , b = (0, 3, 6), and C be the straight line segment connecting a to b. Give
a paramet
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_X_XI_TOTAL
_
January 30
2006
Mathematics 206a
Multivariable Calculus
Examination #1
sin x
(20) I. Suppose f ( x, y ) =
y
A.
f
( x, y ) =
x
B.
f
( x, y ) =
y
C.
2 f
( x, y ) =
xy
D.
2 f
( x, y ) =
yx
Mr. Haines
(10) II. P
NAME_
I_II_III_IV_V_VI_VII_VIII_IX_ X_TOTAL _
December 9
2005
Mathematics 206a
Multivariable Calculus
Final Examination
Mr. Haines
(10) I. Give a parametrization of
A. the line segment that connects the points (1, 0, 3) and (4, 5, 5) in 3 .
B. the surface
AIEEE/2011/PHYSICS
S.
No
Q.1
Questions
The transverse displacement y (x,t) of a wave on a string is given by y(x,t)
2
2
=e(ax +bt +2 ab xt ) This represents a
(a) wave moving in x direction with speed
(b) standing wave of frequency
(c) standing wave of fr