Download GTU B.Pharma 2018 Summer 1st Sem 818807 Remedial Mathematics Question Paper

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Seat No.: Enrolment No.

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GUJARAT TECHNOLOGICAL UNIVERSITY

Pharm D — 1^st Year EXAMINATION - SUMMER - 2018

Subject Code: 818807 Date: 01/06/2018

Subject Name: Remedial mathematics

Time: 10:30am TO 01:30pm Total Marks: 70

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Instructions:

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

Q.1

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(a) Given A(2,4), B(6,8), C(a+4,2a+b)and CA | BC, find a. 06

(b) Expand by SARRUSRULE | 3 4 1 2 0 7 1 -3 -2 | 04

(c) If cos? +sin? = v2 cos?, show that cos? — sin? = v2sin? 04

Q.2

(a) Solve the following simultaneous equations using cramer’s rule. 06

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x+y+z =4, 2x-3y+4z=33, 3x-2y-2z=2.

(b) Prove that sin 5 x - sin 3 x cos x = 2sinx 04

(c) Show that points (1, 1), (2,3) and (3,5) are collinear. 04

Q.3

(a) Using theorems prove that | x y z x^2 y^2 z^2 x^3 y^3 z^3 | = xyz(x-y)(y-z)(z-x) 06

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(b) Evaluate lim _x?8 x 2 - 3 x + 3 2 x 3 + 1 04

(c) Prove that sin10° sin 30° sin50° sin70° = 1/16. 04

Q.4

(a) Solve the differential equation: 06

xy' = y+2 if y(1) =1.

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(b) Solve (xy² +x) dx.+ (yx^*+y) dy = 0. 04

(c) Solve the following differential equation 04

(1+x²) dy = x²ydx

Q.5

(a) If y= x 2 x + cos x find d y d x 06

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(b) Solve: 2xy d z d x -z =x²+3y² 04

(c) Evaluate lim _x?0(1 + 2x)^1/x 04

Q.6

(a) Solve the following differential equation: 06

d y d x = 2 x ( log x + 1 ) sin y + y cos y

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(b) Evaluate: ?sin⁶x cos⁴x dx 04

(c) Solve : L^-1( s s 2 + 4 s + 8) 04

Q.7

(a) Evaluate: ? 2 x 2 - 7 x + 12 dx 06

(b) Find the Laplace transform of cos2t. 04

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(c) Evaluate: ?₀^p/2sin⁶ x dx. 04

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