BTECH First Year/First Semester 2024-25 Tutorial Sheet T3 PDF

Bachelor of Technology – First Year(All Branches) BABU BANARASI DAS NORTHERN INDIA INSTITUTE OF TECHNOLOGY Affiliated to Dr. A.P.J. Abdul Kalam Technical University (AKTU Code : 056) AKTU Code :...

Bachelor of Technology – First Year(All Branches) BABU BANARASI DAS NORTHERN INDIA INSTITUTE OF TECHNOLOGY Affiliated to Dr. A.P.J. Abdul Kalam Technical University (AKTU Code : 056) AKTU Code : 056 Approved by All India Council for Technical Education (AICTE) Sector II, Dr Akhilesh Das Nagar, Faizabad Road, Lucknow (UP) – India, 226028 Website : www.bbdniit.ac.in BTECH FIRST YEAR / FIRST SEMESTER / 2024-25 TUTORIAL SHEET: T3 Name of Subject: Engineering Mathematics I Subject Code: BAS 103 Unit Covered: III NBA Subject Code: C132 Q# Question Description CO 1 1 e a sin x CO3 Expand by Maclaurin’s theorem. in the neighbourhood of 1,1 up to and inclusive of y 2 Expand the function tan 1 x CO3 second degree terms. Hence compute f 1.1,0.9. 3 Find maximum and minimum value of x3  y3  3axy. CO3 4 Show that the rectangular solid of maximum volume that can be inscribed in a CO3 sphere is a cube. 5 Find the shortest distance from the point (1, 2,-1) to the surface CO3 x 2  y 2  z 2  24. A rectangular box, open at the top is to have a given capacity. Find ,by 6 Lagrange’s method of multipliers, the dimension of the box requiring least CO3 material for its construction  r ,  ,   Find the value of the Jacobian where x  r sin  cos  , y  r sin  sin  , 7   x, y , z  CO3 z  r cos. x y xz Show that u  ,v  are not functionally independent. Find the 8 xz yz CO3 relation between them. x y z If  ,  , be the roots of the equation    1 in k then prove 9 ak bk ck ( x, y, z )  (   )(   )(   ) CO3 that . ( ,  , ) (a  b)(b  c)(c  a) (a) Compute an approximate value of 3.822  22.13 . 1/ 5 (b) A balloon is in the form of right circular cylinder of radius 1.5 m and 10 CO3 length 4m and is surmounted by hemi spherical ends. If the radius is increased by 0.01 m and length by.05 m. Find the percentage change in the volume of balloon. Name of Faculty: BBDNIIT 2024-25(Odd Semester) Page1