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Seat No.: Enrolment No.
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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
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Instructions:
- Attempt any five questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q1 (a) Solve x(x+5)(x+7)(x+12)=-150 06
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(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 05
x2+y2=185 ; x+y=19
Q.2 (a) Solve by Matrix Inversion method. 06
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-3x1 +6x2-11x3 =14
3x1 -4x2 + 6x3 =-5
4x1-8x2+ 13x3 =-17
(b) Using theorems prove that 05
| x y z |
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| x2 y2 z2 | = xyz(x-y)(y-z)(z-x)| x3 y3 z3 |
(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 06
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| Age | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
| No. of members | 3 | 61 | 132 | 153 | 140 | 51 | 2 |
(b) Calculate the mode and median for the following data. 05
| 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. 05
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?
Q4 (a) Do as directed 06
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(i) Find the value of tan 22.5° (ii) Evaluate tan-1(1)
(b) Cos ? + Sin ? =v2 Cos ?, show that Cos ? - Sin ? =v2 Sin ? 05
(c) Prove that cos4A —sin4A = 1 — 2sin2A 05
Q5 (a) If sina= v(1/10) and cosß = v(9/10) and if 0< a, ß < p/2, then prove that a+ ß = p/2. 06
(b) Solve (xy2 +x)dx + (yx2+y)dy =0 05
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(c) A population grows at the rate of 8% per year. How long does it take for the 05
population to double?
Q.6 (a) If xy=ex-y, prove that dy/dx =log x /(loge x)2 06
(b) Evaluate: ? x2/(1-x2) dx 05
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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 06
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.
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(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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