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| Roll No. | Total No. of Pages : 02 | Total No. of Questions : 19 |
M.Sc. (Chemistry) (Campus) (2015 to 2017) (Sem.-1)
MATHEMATICS
| Subject Code : CHL-405M | M.Code : 51207 |
| Time : 3 Hrs. | Max. Marks : 70 |
INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains SIX questions carrying FIVE marks each and students have to attempt ALL questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
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SECTION-A
Answer briefly :
- Let u = 2i – j + k and w = i + 2k are two vectors End the cross product v× w and dot product u.w.
- Find the gradient of scalar point function ¢ (x, y, z) = x²yz at the point (1, -1, 2)
- Find X and Y if X + Y =
2 1 1 2 - Define a Hermitian matrix.
- Find
where y = 22 4 -1 2 - Evaluate the integral [(x + 1) x+dx.
- Solve the differential equation dy/dx + y = 2.
- Write down the differential equation of a harmonic oscillator.
- Find the probability of outcome 10 from two throws of a dice.
- In how many ways a committee consisting of 3 men and 2 men can be chosen from 7 men and 5 women?
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1| M-51207
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SECTION-B
- If i + j + k, 2i + 5j, 3i + 2j – 3k and i – 6j – k are the position vectors of points A, B, C and D respectively, then find the angle between AB and CD.
- Solve the following system of equations using matrix method. 2x – 3y + 4z = 8, y - 3z = - 7, x + 2y + 2z = 11
- Find local maximum and minimum values of the function f (x) = 3x² + 4x³ – 12 x² + 12.
- Find the general solution of the following differential equation : (x² + y² + x) dx + 2xydy = 0
- Fit least square straight line to the following data points :
X: 1 2 3 4 5 6 Y: 6 4 3 5 4 2 - Find the product of AB where A =
and B =1 2 3 4 5 6 7 8 - Solve the Huckel Molecular – orbital CH2CHCH22 in terms of the Huckelparameters a and ? : (a – E) c1 + ?c2 = 0
ßc1 + (a – E) C2 + Bc3 = 0
?c2 + (a – E)c3 = 0
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SECTION-C
- Find the Fourier series for f (x) = x + x², - p = x = p.
- Evaluate the integral ? dx/((x+1)(x-2)) by resolving into partial fractions.
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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.
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This download link is referred from the post: VNSGU MBBS Last 15 Years 2010-2025 Previous Question Papers (Veer Narmad South Gujarat University)