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

**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

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.

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

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**(b)**Solve the following system of linear equations using Cramer's rule

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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.

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-3x1 + 6x2 -11x3 = 14

3x1 - 4x2 + 6x3 = -5

4x1 - 8x2 + 13x3 = -17

**(b)**Using theorems prove that

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| 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

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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

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(i) Find the value of tan 22 1?/2 (ii) Evaluate tan 13

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

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

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**Q.5 (a)**If sin

= 1 and cos = 3 and if 0 , , then prove that + = .

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5

10

2

4

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

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**(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

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

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2--2

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

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**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).

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

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This post was last modified on 05 March 2021