Nirma University, Institute of Technology
Department of Mathematics and Humanities
MA305- Mathematics for ICE
Assignment-5
1. Form the partial differential equation by eliminating the arbitrary
constants
a) 2 z  (ax  y) 2  b
b) x 2  y 2  ( z  c) 2 tan 2  , where a, b, c and α
are arbitrary constants.
2. Form the partial differential equation by eliminating the arbitrary
functions
a) z  yf ( x)  xg( y )
b)
F ( x 2  y 2  z 2 , xyz)  0, where f, g, F are
arbitrary functions.
2z
z
x

z
,
y

0
,
z

e
and
 e x .
3. Solve
given
that
when
2
y
y
4. Solve the followings:
a) p  q  log( x  y )
( x2  y 2 )
b) xq  yp  xe
c) p  2q  2 x  e y  1.
5. Find the area A under the normal curve
a) To the left of z= -1.58
b) To the left of z=0.66
c) To the right of z= -1.55
d) Corresponding to z>2.36
e) Corresponding to -0.75 < z < 1.23
f) To the left of z=-2.32 and to the right of z = 1.73
6. Assume that the reduction of a person’s oxygen consumption during a
period of Transcendenta Meditation (T.M.) is a continuous random
variable X normally distributed with mean 37.6 cc/mt and s.d. 4.6
cc/mt. Determine the probability that during a period of T.M. a
person’s oxygen consumption will be reduced by (a) at least 44.5
cc/mt (b) at most 35 cc/mt (c) anywhere from 30 to 40 cc/mt.
7. Find the mean and Standard deviation of a normal distribution in
which 8% of the items are under 40 and 76% are under 60.