BTech Engineering Mathematics-I Past Paper 2023-24 PDF

Printed Page: 1 of 2 Subject Code: KAS103T 0Roll No: 0 0 0 0 0 0 0 0 0 0 0 0 0 BTE...

Printed Page: 1 of 2 Subject Code: KAS103T 0Roll No: 0 0 0 0 0 0 0 0 0 0 0 0 0 BTECH (SEM I) THEORY EXAMINATION 2023-24 ENGINEERING MATHEMATICS-I TIME: 3HRS M.MARKS: 100 Note: 1. Attempt all Sections. If require any missing data; then choose suitably. SECTION A 1. Attempt all questions in brief. 2 x 10 = 20 Qno. Question Marks CO a. 10 101 2 1 20 202 Find the Rank of the matrix. b. Define singular and non singular matrix. 2 1 c. Define Rolle’s theorem. 2 2 d. If = , find. 2 2 e. Find the stationary point of f(x,y) = x3+y3+3axy. 2 3 f. If u = sin ( + ) , then find the value of +. 2 3 g. Evaluate. 2 4 h. Write the formula of area and volume by integration. 2 4 i. Find the unit normal vector at the surface = + at (1, 2). 2 5 j. State Stokes theorem. 2 5 SECTION B 2. Attempt any three of the following: 10x 3 = 30 a. Find the Eigen values and Eigen vectors of the following 10 1 3 10 5 matrix: !−2 −3 −4'. 3 5 7 , b. If y = ( )*+ show that (1-x2) yn+2 - (2n+1) x yn+1 - (n2+m2) yn = 0 , 10 2 also calculate yn(0). c. If -,., / are the roots of the equation (0 − )1 + (0 − )1 + 10 3 ( ,2,3) (0 − )1 = 0 , find ( , ,4). d. Change the order of integration 5( , ). 10 4 e. Verify the Greens theorem to evaluate the line integral ∫ (2y2 dx + 3x 10 5 dy), where C is the boundary of the closed region by y = x and y = x2. SECTION C 2 −1 1 3. Attempt any one part of the following: 10x 1 = 10 a. 10 1 Find inverse by elementary transformation A = !−1 2 −1' 1 −1 2 b. Investigate for what values of 0 and 6 do the system of the equation + 10 1 + = 6, + 2 + 3 = 10, + 2 + 0 = 6 has i) no solution ii) unique solution iii) infinite no. of solution. 1|Page  Printed Page: 2 of 2 Subject Code: KAS103T 0Roll No: 0 0 0 0 0 0 0 0 0 0 0 0 0 BTECH (SEM I) THEORY EXAMINATION 2023-24 ENGINEERING MATHEMATICS-I TIME: 3HRS M.MARKS: 100 4. Attempt any one part of the following: 10x 1 = 10 a. If y 9 + y 9 = 2x prove that (x − 1)yCD + (2n + 1)xyCD + 10 2 (n − m )yC = 0 b. Verify Lagrange’s Mean value theorem for the function f(x) = x3 10 2 in [-2,2] 5. Attempt any one part of the following: 10x 1 = 10 a. Expand x +3y -9x-9y+26 in powers of ( − 1) and ( − 2) by Taylor’s 10 2 2 3 theorem up to second degree term. b. In estimating the number of bricks in a pile which is measured to be (5 10 3 m × 10 m × 5 m), the count of bricks is taken as 100 bricks per m3. Find the error in the cost when the tape is stretched 2 % beyond its standard length. The cost of bricks is 2000 Rs. per thousand bricks. 6. Attempt any one part of the following: 10x 1 = 10 G √ G a. Evaluate ( + ) by changing into polar Co- 10 4 ordinates. b. Calculate the volume of solid bounded by the surface x=0,y=0,x+y+z=0 10 4 and z=0. 7. Attempt any one part of the following: 10x 1 = 10 a. Prove that ( − + 3 − 2 )H + (3 +2 )I + (3 −2 + 10 5 2 )J is both solenoidal and irrotational. b. Using Green’s Theorem evaluate K ( + ) + ( + ) , 10 5 where C is the square formed by the lines = ±1, = ±1. 2|Page