Tiêu đề ENG-MATHS-3-2021.pdf ✅

Page 1 of 2 GURUKULA KANGRI (DEEMED TO BE UNIVERSITY), HARIDWAR END SEMESTER EXAMINATION-2021 CLASS – B.Tech SEMESTER – III SUBJECT NAME – Engineering Mathematics-III SUBJECT CODE- BEM-C302 TIME: 3 HOUR MAX. MARKS: 70 MIN. PASS: 40% NOTE: QUESTION PAPER IS DIVIDED INTO TWO SECTIONS A AND B. ATTEMPT BOTH SECTIONS AS PER GIVEN INSTRUCTIONS. SECTION-A (SHORT ANSWER TYPE QUESTIONS) INSTRUCTIONS: ANSWER ANY FIVE QUESTIONS IN ABOUT 150 WORDS EACH. EACH QUESTION CARRIES SIX MARKS. (5 X 6 = 30 MARKS) Q.1. Find inverse Laplace transform of tan−1 2 s 2 . Q.2. Find the value of ∫ cos 6t−cos4t t ∞ 0 dt Q.3. Find f(x) whose Fourier cosine transform is sinaλ λ . Q.4. Evaluate ∫ x 2 (x2+a2)(x2+b2) ∞ 0 dx and hence find ∫ ( x 1+x2 ) ∞ 2 0 dx. Q.5.Find the inverse Z transform of 4z2−2z z 3−5z2+8z−4 . Q.6. Determine u2 where U(z) = 2z2+3z+4 (z−3)3 . Q.7. Show that the function w = x x 2+y2 − iy x 2+y2 is an analytic function. Find dw dz . Q.8. Evaluate ∫ z 2dz C where C is a (i) Straight line segment from z=0 to z= 2+i (ii) Straight line from (0, 0) to (2, 0) and then from (2, 0) to (2, 1). Q.9. Use Newton Raphson method to find the real root of the equation 3x = cosx + 1, correct to 5 decimal places. Q.10. Use iteration method to find root of equation x 3 + x2 − 1 = 0, correct to 4 decimal places.