Uttar Pradesh Technical University (UPTU) 2007 B.Pharm Advance Mathematics(Special Carryover) - Question Paper

Printed Pages : 4    PHAR- 125

(Following Paper ID and Roll No. to be filled in your Answer Book)

Roll No

B. Pharm.

(SEM. II) EXAMINATION, 2006-07 ADVANCE MATHEMATICS (SPECIAL CARRYOVER EXAMINATION)

[Total Marks : 80

Note : (1) Attempt all the questions.

(2) All questions carry equal marks.

1. Attempt any four of the following :

sin2x

(a) Evaluate : {

a cos x + b sin x

_fe^x(l-sinx)

(b) Evaluate : I ~7Z    rdx

^v    (1 COSXJ

r 3x + 2

(c) Evaluate : J (_{x + 1}j* (*_₂)

(d) Evaluate : J J(_x__A)(_B__x) *

f ^x

(e) Evaluate : I ,

^V '     1 + Sl

(f) Find whether the functions _e^Sx and _e^5x are linearly dependent or linearly independent. If linearly independent, then determine a differential equation having the above functions as independent solutions.

2. Attempt any four of the following :

dy

(a)    Solve : ^y~^x~ ^{= a}

(b)    Solve : (x + 2y^s)- = y

(c)    Solve : y{x²y+ e^x}dx = e^xdy

(d)    Solve : (^x* ⁺

dy x + 2 y + 3

(e)    Solve .    2x + 3j + 4

dy e^y 1

(1) Solve : = j--

dx x x

(b)    Solve : [p² + a²) y = sec ax

dx

(c)    Solve : + 5x + y = e^l

at

- x + 3 y = e^2t dt

4. Attempt any two of the following :

(a)    The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.60 and

standard deviation (13.44)² , find the standard

deviation of second group.

(b)    Find the mean, median, mode and coefficient of variation for the following distribution :

size 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 8 12 12 18 14 0

(c) Find the arithmetic mean, geometric mean and harmonic mean of the following data :

Items	1	2	3	4	5	6	7	8	9
Frequency	1	2	3	4	5	6	7	8	9

(b) The contents of 3 urns A₁,A₂,A_S are as follows :

	White Balls	Black Balls	Red Balls
A 1	1	2	3
A 2	2	1	1
A 3	4	5	3

An urn is selected at random and two balls are drawn. They happen to be white and red. What is probability that they come from urn 2 and

3. Also find the probability that the balls come from urn 1.

(c) A manufacturing company wishes to produce

3 new tablets of different makes and wishes to determine whether one of them is more effective than the others in curing the certain disease. Five months using figures are observed at random on each tablet and results are given below :

Observations	Tablet 1	Tablet 2	Tablet 3
1	25	31	24
2	30	39	30
3	36	38	28
4	38	42	25
5	31	35	28

Use ANOVA and determine whether the tablets are significantly different in their mean effect.

(Given : At 5% level F₂₁₂=3.89)

Z-9925]    4    [1760 ]

Attachment: uttar-pradesh-technical-university--uptu--2007-b-pharm-20209-1.pdf

Earning:   Approval pending.