Sample Sessional TEST MATHEMATICS-I for CSE PDF 2023

Student Roll No: MANAV RACHNA INTERNATIONAL INSTITUTE OF RESEARCH & STUDIES SCHOOL OF ENGINEERING AND TECHNOLOGY Sessional Test-I September- 2023 Subject: MATHEMATICS-I for CSE...

Student Roll No: MANAV RACHNA INTERNATIONAL INSTITUTE OF RESEARCH & STUDIES SCHOOL OF ENGINEERING AND TECHNOLOGY Sessional Test-I September- 2023 Subject: MATHEMATICS-I for CSE Department: Applied Sciences Subject Code: BMA-101 Max. Marks: 30 Class/Semester: First Sem. B.Tech. CSE only Time Allowed: 90 minutes Note: Q.1 is compulsory. Attempt any two questions out of questions no. 2 to 4. Qn.1 Qn1:  2 a. Evaluate  0 cos 4  sin 2  d 1 dx b. Examine the convergence of x −1 2 c. Verify the Rolle’s Theorem for f ( x) = x 2 in  −2, 2 d. State Lagrange’s mean value theorem. sin( x 2 ) e. Evaluate: lim x →0 x2 Qn.2 a. Find local maxima and local minima, and also find local maximum and local minimum values of 1 1 following functions. f ( x) = sin x + sin 2 x + sin 3x  x   0,   2 3 x b. Using Lagrange mean value theorem, show that  log( x + 1)  x, x  0. L3 1+ x c. Find nth derivative sin 4 x OR −1 a. Expand y = em sin x by Maclaurin’s theorem, hence show that 1 2 e = 1 + sin  + sin 2  + sin 3  +......... 2 3 b. Calculate the approximate value of 10 to four decimal places by the application of Taylor’s series c. Find the series expansion of Sin 460 Qn.3a.  1 1 2 x  a. Prove   ,  =  dx = 6  3 3  0 1+ x 6 3 3 b.. Find the volume of the solid obtained by revolving one arc of the cycloid 𝑥 = 𝑎(𝜃 + sin 𝜃), 𝑦 = 𝑎(1 + cos 𝜃) about x-axis. OR a. Let f(x)=√x over the interval [1,4]. Find the surface area of the surface generated by revolving the graph of f(x) around the x-axis.  5 b. Find   −   2