SRM INSTITUTE OF SCIENCE AND TECHNOLOGY
Ramapuram Campus
FACULTY OF ENGINEERING AND TECHNOLOGY
Department of Mathematics
Odd Semester 2022 – 2023
Practice Questions for Toppers
21MAB101T – Calculus and Linear Algebra
Unit 2 – Functions of several variables
1. A window has the form of a rectangle surmounted by a semi-circle. If the
perimeter is 40 ft., find its dimensions so that the greatest amount of light may be
admitted.
2. A rectangular sheet of metal of length 6 metres and width 2 metres is given. Four
equal squares are removed from the corners. The sides of this sheet are now turned
up to form an open rectangular box. Find approximately, the height of the box,
such that the volume of the box is maximum.
3. The cost per hour of propelling a steamer is proportional to the cube of her speed
through water. Find the relative speed at which the steamer should be run against a
current of 5 km per hour to make a given trip at the least cost.
4. An open tank is to be constructed with a square base and vertical sides to hold a
given quantity of water. Find the ratio of its depth to the width so that the cost of
lining the tank with lead is least.
5. A corridor of width b runs perpendicular to a passageway of width a. Find the
longest beam which can be moved in a horizontal plane along the passageway into
the corridor?
6. Explain the applications of Maxima and Minima in engineering problems.
Staff incharge
HOD / Mathematics