Engineering Mathematics I Past Paper PDF - MAT 1151 - 2018

Question Paper Exam Date & Time: 21-Dec-2018 (08:30 AM - 11:30 AM) FIRST SEMESTER B.TECH END SEMESTER MAKEUP EXAMINATIONS, DECEMBER 2018 Engineering Mathematics - I [MAT 1151 - 2018 -PHY/CHM] Engineering Mathematics - I [MAT 1151...

Question Paper Exam Date & Time: 21-Dec-2018 (08:30 AM - 11:30 AM) FIRST SEMESTER B.TECH END SEMESTER MAKEUP EXAMINATIONS, DECEMBER 2018 Engineering Mathematics - I [MAT 1151 - 2018 -PHY/CHM] Engineering Mathematics - I [MAT 1151 - 2018 -PHY] Marks: 50 Duration: 180 mins. A Answer all the questions. Instructions to Candidates: Answer ALL questions, Missing data may be suitably assumed 1) (3) A) B) (3) C) (4) 2) (3) A) B) (3) Page #1  C) (4) 3) (3) A) B) (3) C) (4) 4) (3) A) B) Define maximal linearly independent set of vectors. Prove (3) that a set of non-zero orthogonal vectors are linearly independent. C) (4) Page #2  Find the root of the equation x e x = cos x in the interval 5) (3) A) (0,1) using the method of false position. Carry out four iterations correct to four decimal places B) Using Gram-Schmidt process, construct an orthonormal (3) basis vectors from : (2, 3, 0), (6, 1, 0) and (0, 2, 4) C) (4) -----End----- Page #3 Question Paper Exam Date & Time: 19-Nov-2018 (08:30 AM - 11:30 AM) FIRST SEMESTER B.TECH END SEMESTER EXAMINATIONS, NOV 2018 Engineering Mathematics - I [MAT 1151 - 2018 -PHY/CHM] Engineering Mathematics - I [MAT 1151 - 2018 -CHM] Marks: 50 Duration: 180 mins. A Answer all the questions. Instructions to Candidates: Answer ALL questions Missing data may be suitably assumed 1) (3) A) B) (3) C) (4) 2) (3) A) B) (3) C) (4) 3) (3) A) Page #1  B) (3) C) (4) 4) (3) A) B) (3) C) (4) 5) (3) A) B) (3) Page #2 C) (4) -----End----- Page #3  Reg. No. FIRST SEMESTER B.TECH. (COMMON TO ALL BRANCHES) END SEMESTER EXAMINATIONS, November, 2017 SUBJECT: ENGINEERING MATHEMATICS-I [MAT 1101] REVISED CREDIT SYSTEM 15/11/2017 Time: 3 Hours MAX. MARKS: 50 Instructions to Candidates:  Answer ALL the questions.  Missing data may be suitably assumed. Solve by Gauss Seidel method. Carry out 4 iterations correct up to 4 decimal places 10x – y + 2z = 6 1A. –x +11y – z +3w = 25 4 2x – y +10z – w = – 11 3y – z + 8w = 15 Construct an orthonormal basis from the following set of vectors (0,1,0), 1B. (2,3,0) and (0,2,4) for E3. 3 Find a root of the equation xe-x = cos x using method of false position 3 1C. correct to four decimal places [1, 2] carry out 3 iterations. 2A. Find the real root of f(x)=0, if f(– 1)=2, f(2)= – 2, f(5)=4 and f(7)=8 by 4 Lagrange’s method. Find by Taylor’s series method of order four the value of y at x = 0.3 to four 2B. 3 dy decimal places from  2 y  3xe x , y(0)=0. dx Solve xy  y  x sin x with y( )  0. 3 2C. 3 Page 1 of 2 MAT 1101  Find the eigen values and corresponding eigen vectors of 3A.  3 1 2  4   1 6  A=  3  2 2  2 3B. d2y dy 3 Solve  2  xe x dx 2 dx The velocities of a car (running on a straight road) at intervals of 10 kms are given below. S in kms 0 10 20 30 40 50 60 3C. 3 V in kms/hr 47 58 64 65 61 52 38 Apply Simpson’s 3/8th rule to find the time taken by the car to cover 60kms. (i) Prove that a maximal linear independent set of vectors forms a basis. 4 4A. (ii) “V is a vector space over a field F.” What do you mean by a field here? 4B. Solve ( D 2  2D  1) y  e x log x by variation of parameters. 3 d2y Evaluate at x=1.5 from the following table. 4C. dx 2 3 x 1 1.2 1.4 1.6 y 47 58 64 65 5A. Solve x + y + z = 0, x– 2y + 2z = 4, x + 2y– z=2 by Gauss Jordan method. 4 Using Runge-Kutta method of fourth order, solve for y at x = 1.5 given that 𝑑𝑦 2𝑥−𝑦 2 3 5B. = with x0 = 1, y0 = 0 and h = 0.5. 𝑑𝑥 𝑥 2 +𝑦 d2y dy 5C. Solve x 2 x 2  4 y  cos(log x)  x sin(log x) 3 dx dx ******** Page 2 of 2 MAT 1101