Download PTU B-Tech CSE-IT 2020 Dec 1st Sem 75362 Mathematics I Question Paper

FirstRanker.com

Roll No. [] HEEE Total No. of Pages : 02
Total No. of Questions : 08

--- Content provided by FirstRanker.com ---

B.Tech. (CSE /IT) (2018 & Onwards) (Sem.-1)
MATHEMATICS-I
Subject Code : BTAM-104-18
M.Code : 75362
Time : 2 Hrs. Max. Marks : 30

--- Content provided by‌ FirstRanker.com ---

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE question(s), each question carries 6 marks.

1. a) Expand f(x)=e^mx upto the term containing x⁴
2. b) Show that f'(x) =sin x (1 + cos x) has a maximum at x = p/3.

2. a) Find the volume of the solid generated by revolving x²/b²+y²/a²=1, a>b about the major axis.

--- Content provided by FirstRanker.com ---

3. b) Using Gamma function evaluate ?₀⁸ x^1/2 exp (—3vx) dx .

3. a) If A={1 2, 1 3}, B={5 4, 1 2} and C={3 5, 2 4}, then show that (AB)C = A(BC).
4. b) Solve the equations using Cramer rule 2x + 3y +4z=11, x+ 5y +7z=15, 3x + 11y + 13z=25.

4. a) Find the rank of the matrix | 1 -8 4, 4 4 7, 1 -8 4|.
5. b) Solve using Gauss elimination method x —y +2z=3, x + 2y +3z=5, 3x — 4y-5z=-13.

--- Content provided by FirstRanker.com ---

5. a) Express v = (2, -5, 3) in R³ as a linear combination of vectors u₁ = (1, -3, 2), u₂=(2,4,-1), u₃=(1,-5,7).
6. b) Determine whether the vectors u₁ = 2 + 4t — 3t² and u₂ = 4 + 8t — 6t² are linearly dependent?

FirstRanker.com

6. a) Suppose the mapping F : R² — R² is defined by F (x,y)= (x + y, x). Using the properties of matrices, show that F is a linear mapping.
7. b) Find the dimension and a basis of the subspace W of P₅ (¢) spanned by U=1+2t -3t² +4t³, v=2+5t² -4t³+ t⁴, w=1+ 4t² +t³+2t⁴.

--- Content provided by FirstRanker.com ---

7. Find the characteristic equation of the matrix |1 3, 5 3| and hence compute A^-1.

8. Reduce the matrix |1 3 7, 3 26 21, 7 21 10| to the diagonal form.

Note: Any student found attempting answer sheet from any other person(s), using incriminating material or involved in any wrong activity reported by evaluator shall be treated under UMC provisions.

Student found sharing the question paper(s)/answer sheet on digital media or with any other person or any organization/institution shall also be treated under UMC.

Any student found making any change/addition/modification in contents of scanned copy of answer sheet and original answer sheet, shall be covered under UMC provisions.

--- Content provided by‌ FirstRanker.com ---

FirstRanker.com