Gujarat Technological University 2009-1st Sem B.Pharm acy (Elementry Remedial mathematics) - Question Paper
Seat No. Enrolment No.
(EM-6)
GUJARAT TECHNOLOGICAL UNIVERSITY
B.Pharm. Sem-I Examination December 08/January 09 Elementary (remedial) Mathematics (210006)
DATE: 31 -12-2008,Wednesday TIME: 11.00 am to 2.00 p.m. MAX. MARKS: 80
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1(a) Solve the following system of linear equations using Cramers rule x + 2y + 3z = 6, 2x + 4y + z = 7 and 3x + 2y + 9z = 14
(5)
(5)
(6)
(b) Evaluate A(BC) and (AB)C where
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(c) |
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Q.2(a) Find the mean deviation and standard deviation for the following (8) distribution of the weights of 250 children
Weights 60-61 61-62 62-63 63-64 64-65 65-66 66-67 in kg:
Frequency 10 25 45 55 60 40 15
(b) If the probability that an individual suffers a bad reaction from a (8) certain injections is 0.001, determine the probability that out of 2000 individuals (i) exactly 3 (ii) more than 2 individuals will suffer a bad reaction.
Q.3(a) Find the area of triangle whose vertices are (2, 3), (2, 1), (1, 1) (5)
(c) Find the equation of the locus of points twice as far from (3, 2) as (6) from (1, 1)
Q.4(a) Differentiate the following functions w.r.t. x
(8)
1] y = eax cos(bx + c)
2] x3 + y3 + 3x2 y = a3
(b) Find the nth derivations of the following
(8)
(16)
1] y = sin3 x
2] y = x.log(1 + x)
Q.5 Solve the following differential equations
1] (l + x2 )dy =(l + y2 )dx
2] xdy - ydx = x2 + y2 dx
\dy_
3] (l + x2 + 2 xy - 4 x2 = 0 dx
dx
dy = 2 x(log x +1) dx sin y + y cos y
4]
Q.6(a) Evaluate the following integrals.
(6)
dx
u f-
1
3i f
2] f
dx
Vx+T
+
2x
dx
x2 - 7 x +12
4] f sin2 xdx
4 4
sin x+ cos x
sin 2x
p/2
0
(b) Find all t-ratios of 120
(6)
(4)
(c) If cos q + sin q = 42 cos q, show that cos q - sin q = 42 sinq
Q.7(a) In how many ways can 5 boys and 3 girls stand in a raw so that no (5) two girls are together?
(b) Find the sum of all natural numbers between 200 and 400 which are (5) divisible by 7.
Using binomial expansion, prove that (42 +1 )'-(V2 -1)' = 82 (6)
(c)
2
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Attachment: |
| Earning: Approval pending. |
