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.
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( 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
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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
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
3 | M - 4 6 2 2 1
( S 4 ) - 5 6 8
This post was last modified on 14 February 2021