Download PTU M-Sc -Chemistry 1st Semester May 2019 75119 NUMERICAL METHODS FOR CHEMISTS Question Paper

Roll No.

Total No. of Pages : 02

Total No. of Questions : 15

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M.Sc.(Chemistry) (2018 Batch) (Sem.-1)

NUMERICAL METHODS FOR CHEMISTS

Subject Code : CHL406B-18

M.Code: 75119

Time: 3 Hrs.

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Max. Marks : 50

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of FIVE questions carrying TWO marks each.
2. SECTION-B contains EIGHT questions carrying FOUR marks each and students have to attempt any SIX questions.
3. SECTION-C will comprise of two compulsory questions with internal choice in both these questions. Each question carries EIGHT marks.

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SECTION-A

1. Illustrate the associative law of matrix multiplication using an example.
2. Prove that any square matrix can be expressed as a sum of symmetric and skew-symmetric matrix.
3. Define Bohr's radius.
4. How are differential equations applicable in kinetics?

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5. Explain conditional probability with example.

SECTION-B

1. Express A = 2-2-4 -134 as the sum of a symmetric and skew-symmetric matrix. 1-2-3
2. Obtain the inverse of the following matrix : 20-1 A=5 1 0 01 3
3. Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = -3 and at x = 5.

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4. Find the derivative of f given by f (x) = sin¯¹ x assuming it exists.
5. Find the general solution of the differential equation dy/dx - y = cos x.
6. Show that the differential equation (x – y) dy – (x + y) dx = 0 is homogeneous and solve it.
7. An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
8. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

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SECTION-C

1. a) Show that ?= x+y y+z z+X Z X y =0. 111
   b) Find the area of the region closed between the two circles x² + y² = 4 and (x – 2)² + y² = 4
2. a) Find the general solution of the differential equation dy/dx = (x + 1)/(2 -y), (y ? 2).
   Or
   

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   b) Use method of least squares to fit a straight line to the data
   X: 2 4 6 8 10 12
   Y: 7.32 8.24 9.20 10.19 11.01 12.05

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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