Gujarat Technological University 2009-1st Sem B.Pharm acy Remedial (Elementry Remedial Methematics) - Question Paper
Seat No.
No._
Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
B. Pharmacy Sem-I Remedial examination March 2009
Subject code: 210006
Subject Name: Elementary (Remedial) Mathematics Date: 18 / 03 / 2009 Time: 02:30pm- 05:30pm
Total Marks: 80
Instructions:
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
16
Q.1
(a) Solve x ( x + 5 ) ( x + 7 ) ( x + 12 ) = - 150
(b) Solve the following simultaneous equations x2 + y2 = 185 ; x + y = 19
(c) Solve the following simultaneous equations using Cramers Rule.
x + y + z = 4 ; 2x - 3y + 4z = 33 ; 3x -2y-2z = 2
then prove that A -5A + 7I = 0
3 1 -1 2
(d) If A =
Q2
16
(a) Expand by SARRUS RULE 3 4 1
2 0 7
1 -3 -2
(b) Using theorems prove that
= xyz ( x - y) ( y- z ) ( z - x )
x y z 222 x y z
3 3 3
x y z
3 5 16 27
Verify that AA-1 = A-1A = I
(c) If A =
(d) Solve by MATRIX INVERSION method.
-3x1 + 6x2 -11x3 = 14 3x1 - 4x2 + 6x3 = -5 4x1 - 8x2 + 13x3 = -17
16
(a) The number N of bacteria in a culture grew at the rate proportional to N. 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 ?
(b) Evaluate : (1) lim x2 - x + 3 (2) lim ( 1 + 2x )y x
x ro 2x3 +1 x 0
(c) Calculate the mean and standard deviation from the following data
|
Value |
90-99 |
80-89 |
70-79 |
60-69 |
50-59 |
40-49 |
30-39 |
|
Frequency |
2 |
12 |
22 |
20 |
14 |
4 |
1 |
Q. 4 16
[ a ]
3
(1) In triangle ABC , cos B = Find sin A , cos A , tan A , sin B , tan B.
-12
(2) If cot 0 = and 0 lies in second quadrant. Find the value of order five trigonometric functions.
(3) Find the value of the following trigonometric ratio :
Sin (- 1125 ) , cot ( 570 )
~ p 9p 3p 5p
(4) Prove that 2 cos . cos + cos + cos = 0
13 13 13 13
10
(5) Find the value of sin 22
2
[ b ] If 2n P3 = 14 n P3 Find n
Q. 5 16
[ a ]
(1) If y = 3 cos (log x) + 4 sin (log x) Prove that x2 y2 + x y1 + y = 0
(2) If y = 500 e7x + 600 e-7x . Show that = 49y
dx2
(3) prove that [ 2x tan-1x - log ( 1+ x2 )] = 2 tan-1 x
dx
[ b ] Evaluate the following Differential
/ 2x2 + 3
(1) y = tan ( e )
(1) x y iy = y + 2 if y (1) = 1
dx
(2) 2xy dy = x2 + 3y2
dx
(3) x (iy + y ) = 1 - y.
dx
[ b ] Evaluate the following Integration.
(1) J tan 3 x dx
4
(2) J (4 - x )3/2 x dx 0
Q. 7 16
1/3
(a) Evaluate ( 998 ) up to five places of decimal.
(b) Show that the vertices of triangle ( 7 , 9 ) , ( 3 , -7 ) , ( -3 , 3 ) from a right angled isosceles triangle.
(c) Find the area of the triangle whose vertices are ( 4 , 4 ), (3 , -2) , (-3 , 16 ).
(d) In a group of students there are 4 girls and 6 boys. In how many ways a 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.
3
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Attachment: |
| Earning: Approval pending. |
