Engineering Mathematics-I Past Paper 2023 PDF

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE Regular & Supplementary Winter Examination-2023 Course: B. Tech Branch: All Semester: I Course Code & Name: Engineering Mathematics-I (BTBS...

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE Regular & Supplementary Winter Examination-2023 Course: B. Tech Branch: All Semester: I Course Code & Name: Engineering Mathematics-I (BTBS101) Max Marks: 60 Date:01-01-24 Duration: 3 Hr. Instructions to the Students: 1. All the questions are compulsory. 2. The level of question/expected answer as per OBE or the Course Outcome (CO) on which the question is based is mentioned in ( ) in front of the question. 3. Use of non-programmable scientific calculators is allowed. 4. Assume suitable data wherever necessary and mention it clearly. (Level/CO) Marks Q. 1 Solve Any Two of the following. 12 A) Find the rank of matrix by converting it into Normal Form [ ] Understand 6 (CO1) Find eigen values & eigen vector for largest eigen value for the matrix [ ] Understand 6 B) (CO1) Check the consistency and solve: 6 Understand C) (CO1) Q.2 Solve Any Two of the following. 12 A) If ( ) , show that ( ) ( ) Understand 6 (CO2) Understand B) If ( ), prove that 6 (CO2) Understand C) If ( ) then find the value of 6 (CO2) Q. 3 Solve Any Two of the following. 12 ( ) A) If , , then evaluate ( ) at 1, 1,0 Understand 6 (CO3) Discuss the maxima and minima for the function ( ) and hence B) find the extreme value of the function. Understand (CO3) 6 Using Lagrange’s undetermined multipliers find the maximum value of Understand C) 6 when (CO3) Q.4 Solve Any Two of the following. 12 A) ( ) dx Understand Evaluate ∫ 6 (CO4) Trace the curve ( ). Understand B) 6 (CO4) Understand C) Trace the curve ( ), ( ). 6 (CO4) Q. 5 Solve Any Two of the following. 12 1 z z–x 2 2 Understand A) Evaluate    xz dx dy dz 6 0 0 0 (CO5) 2 Understand B) Find the area bounded by y = 4x and 2x – 3y = – 4. 6 (CO5)  Understand – (x2+ y2) C) Change to polar and evaluate   e dx dy. 6 (CO5) 0 0