Gujarat Technological University 2011 B.Pharm Elementary (Remedial) Mathematics - Question Paper

GUJARAT TECHNOLOGICAL UNIVERSITY
B. Pharmacy Sem - first Regular / Remedial exam January. 2011
Subject code: 210006
Subject Name: Elementary (Remedial) Mathematics
Date: 13 /01 /2011 Time: 10.30 am – 01.30 pm
Total Marks: 80
Instructions:
1. Attempt any 5 ques..
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q:1 [16]
(a) Solve 4x+1 + x+1 = 3
(b) A 2 digit Number is 4 times the sum and 3 times the
product of its digits. obtain the Number.
(c) Solve by cramer's Rule.
x +2y = 9; 2x-3y = 4
(d) describe the subsequent with suitable Examples.
(1) Diagonal Matrix (2) Transpose of a Matrix.
(3) Symmetric Matrix (4) Upper Triangular Matrix
Q:2 [16]
(a) Expand D = two -1 3
4 one two by Sarrus Method.
1 -1 5
(b) Prove that
1 a b+c
1 b c+a = 0
1 c a+b
(c) Prove that
Sec2? Cos2?
- Cot2? Sin2? = 1-2 Sin2? Cos2?.
(d) If
1 two three four two one 0 obtain AB or BA,
A = two 0 one two & B = three two one Whichever
3 one 0 five one 0 one Exists.
Q:3 [16]
(a) A Population grows at the rate of 5% per year.
How long does it take for the population to double ?
(b) Evaluate : (1) lim x2 -5x + 6
x?2 x2 – 4
(2) Let f(x) = 3x2 + 8x - 4
2x2 +4x -5
calculate lim
x? eight f(x) if it Exists.
(c) describe : Median.
The subsequent Figures show incubation Periods of nine Polio
Cases. obtain the Median of the data.
23,19,21,17,22,18,20,24,16.
2
Q:4 [16]
(a) (1) If Cos A = 15 obtain Sin A & tan A.
17
(2) Prove that
1 + cot? = cot?
1 + tan ?
(3) If A = 30° Verify that tan 2A = two tan A
1 – tan2 A
(4) Evaluate : Sin -1 (Cos p/5)
(5) Prove that
tan-1 4/5 + tan-1 2/3 = tan-1 22/7
(b) obtain 'n' If 11Pn : 12Pn = three : 4
Q:5 [16]
(a) (1) obtain dy if x = at2, y = 2at.
dx
(2) If y = five cos x – three Sin x Prove that d2y + y = 0
dx2
(3) Differentiate x5 + log x + nine w.r.to x
(b) (1) Form the differential formula from xy = Aex + Be-x,
Where A and B are arbitrary Constants.
(2) Solve the differential formula : dy + 2y = 4x.
dx
Q:6 [16]
(a) Solve the subsequent differential Equations.
(1) dy = ex-y + x2 e-y
dx
(2) tan y dy = Sin (x + y) + Sin (x - y).
dx
(3) y 1-x2 dy + x 1-y2 dx = 0.
(b) Evaluate the subsequent Integration.
3
(1) one + Sin x dx. (2) (3x2 + ex) dx
1 + cos x
1
Q:7 [16]
(a) obtain the value of (19)4 by using Binomial Expansion only.
(b) If the distance ranging from A(5,a) & B (2,6) is three 2.
obtain the value of 'a'.
(c) For what velue of x the area of the triangle formed by the vertices
(x,4), (8,2) and (6,7) is 13 units ?
(d) obtain the Number of permutations of five boys and five girls can seat around
a circular table such that boys and girls are at alternate position.
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