# Download PTU B.Pharma 2020 Dec 3rd Sem 46221 Pharmaceutical Mathematics Question Paper

Download PTU I. K. Gujral Punjab Technical University (IKGPTU) B.Pharma (Bachelor of Pharmacy) 2020 December 3rd Sem 46221 Pharmaceutical Mathematics Previous Question Paper

Roll No.
Total No. of Pages : 03
Total No. of Questions : 24
B.Pharma (2012 to 2016) (Sem.?3)
PHARMACEUTICAL MATHEMATICS
Subject Code : BPHM-301
M.Code : 46221
Time : 3 Hrs. Max. Marks : 80
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is C OMPULSORY co nsisting of FIFT EEN questio ns carrying TWO
marks eac h.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt ANY FOUR questio ns.
3 .
SECT ION-C contains FOUR q uestions carrying T EN marks eac h an d s tud ents
have to atte mpt ANY THREE q uestions.
SECTION-A
Solve the following :
1
4
3
1.
Define singular matrix and show that A =
6
8
5 is singular matrix.
2 8
6
1
3
5
2.
Without expanding show that the value of determinant is zero 2
6
10 .
31 11 38
7
0
3 0
3.
Find X and Y if X + Y =
and X ? Y =
.
2
5
0
3
4.
Find the length of an arc of a circle of radius 5 cm subtending a central angle measuring
15?.
sin A +sin 3A
5.
Prove
tan 2A.
cos A + cos 3A
6.
Find the differential coefficient of 6x + 1 w.r.t x by using first Principle.
7.
Differentiate the function (x + a)m (x + b)n.
1 | M - 4 6 2 2 1
( S 4 ) - 5 6 8

2
x 3x 4
8.
Integrate the function
.
x
dx
9.
Evaluate
.
x (1 x )
10. The mean of 100 students were found to be 40. Later on it was discovered that a score of
53 was misread as 83. Find the correct mean.
11. For a set of 10 observations, mean = 5, S.D = ?2 and C.V = 60%. Comment.
12. Is there any fallacy in the statement? The mean of a Binomial Distribution is 20 and its
standard deviation is 7.
13. Write relation between mean, median and mode.
14. Calculate the standard deviation of first 7 natural numbers.
15. During war 1 ship out of 9 was sunk on an average in making a certain voyage. What was
the probability that exactly 3 out of a convoy of 6 ships would arrive safely?
SECTION-B
2 1
1
6
4 6
16. If A =
, B
, C
verify (AB)C = A(BC).
3
4
3 4
3 5
1?
17. Prove tan 11
2 1.
4
18. Calculate the mean and standard deviation for the following distribution :
Marks :
20-30
30-40
40-50
50-60
60-70
70-80
80-90
No of students :
3
6
13
15
14
5
4
dy
2
3at
3at
19. Find
for the function in parametric form x
, y
.
dx
3
3
1 t
1 t
2
d y
dy
20. If y = a cos (log x) + b sin (log x) then show that 2
x
x
y 0.
2
dx
dx
2 | M - 4 6 2 2 1
( S 4 ) - 5 6 8

SECTION-C
21. Using Cramer's rule solve the following system of equations :
x ? y + 3z = 6
x + 3y ? 3z = ?4
5x + 3y + 3z = 10
22. In an examination taken by 500 candidates the average and standard deviation of marks
obtained (normally distributed) are 40% and 10%. Find approximate
a) How many will pass if 50% is fixed as a minimum?
b) What should be minimum if 350 candidates are to pass?
c) How many have scored above 60%?
(Given P (0 Z 1) = 0.3415, P (0 Z 2) = 0.4772, P (0.2) = 0.53)
23. a) Evaluate
x
e sin xdx
3x 1
b) Evaluate
dx
2
(x 2) (x 2)
24.
a) Differentiate
2
log (x 1 x ).
1
b) Prove that cos 20? cos 40? cos 60? cos 80? =
.
16
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