Download GTU B.Pharma 2018 Summer 1st Sem 210006 Elementary (Remedial) Mathematics Question Paper

Download GTU (Gujarat Technological University) B.Pharma (Bachelor of Pharmacy) 2018 Summer 1st Sem 210006 Elementary (Remedial) Mathematics Previous Question Paper

Seat No.: _____ Enrolment No. _____________
GUJARAT TECHNOLOGICAL UNIVERSITY
B. Pharm. - SEMESTER?1 ? EXAMINATION ? SUMMER -2018
Subject Code: 210006 Date: 05/05/2018
Subject Name: Elementary (Remedial) Mathematics
Time: 02:30 PM TO 05:30 PM
Total Marks: 80
Instructions:


1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Solve x ( x + 5 ) ( x + 7 ) ( x + 12 ) = - 150
06

(b) Solve the following system of linear equations using Cramer's rule
05
x + y + z = 4, 2x - 3y + 4z = 33 and 3x -2y -2z = 2

(c) Solve the following simultaneous equations
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x2 + y2 = 185 ; x + y = 19



Q.2 (a) Solve by Matrix Inversion method.
06
-3x1 + 6x2 -11x3 = 14
3x1 - 4x2 + 6x3 = -5
4x1 - 8x2 + 13x3 = -17

(b) Using theorems prove that
05
| 2 2 2 |= xyz (x - y) ( - z ) (z ? x )
3 3 3

(c) A two digit number is four times the sum and three times the product of its
05
digits. Find the number.



Q.3 (a) Calculate the mean and standard deviation from the following data
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Age
20-30
30-40
40-50 50-60 60-70
70-80
80-90
No. of
3
61
132
153
140
51
2
members

(b) Calculate the mode and median for the following data.
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Class
0-10
10-20
20-30
30-40
40-50
Frequency 10
14
19
17
13

(c) The number N of bacteria in a culture grew at the rate proportional to N.
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The value of N was initially 100 and increased to 332 in one hour. What will be
the value of N after 1.5 hours?



Q.4 (a) Do as directed
06
(i) Find the value of tan 22 1?/2 (ii) Evaluate tan 13
12

(b) Cos + Sin = 2 Cos , show that Cos - Sin = 2 Sin
05

(c) Prove that cos4A ? sin4A = 1 ? 2sin2A
05



Q.5 (a) If sin
= 1 and cos = 3 and if 0 , , then prove that + = .
06
5
10
2
4

(b) Solve (2 + ) + (2 + ) = 0
05

(c) A population grows at the rate of 8% per year. How long does it take for the
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population to double?



Q. 6 (a) If xy = ex - y, prove that dy/dx = log x /(log ex)2
06

(b) Evaluate: 3-5
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2--2

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(c) Solve : (x2 ? y2) dy =2xy dx
05



Q.7 (a) In a group of students there are 4 girls and 6 boys. In how many ways a
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committee of five members can be formed such that
I. There are at least 3 girls
II. There are at the most 3 boys in the committee.

(b) Find the equation of the line passing through the points (2, 3) and (5, -2).
05

(c) Find the area of the triangle whose vertices are (4, 4), (3, -2), (-3, 16).
05
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