Indian Institute of Technology Madras (IIT-M) 2003 M.Tech Mechanical Engineering mechanical engg-gate - Question Paper

GATE ME - 2003
Duration: three Hours Maximum Marks: 150
learn the subsequent instructions carefully:
1. This ques. paper contains 90 objective ques.. Q.1 to Q.30 carry 1 mark every and
Q.31 to Q.90 carry 2 marks every.
2. ans all the ques..
3. ques. must be answered on special machine gradable Objective Response Sheet (ORS)
by darkening the improper bubble (marked A, B, C, D) against the ques. number on the
left hand side of the ORS, using HB pencil. every ques. has only 1 accurate ans. In case
you wish to change an answer, erase the old ans completely using a good soft eraser.
4. There will be NEGATIVE marking. In Q.1 to Q.30, 0.25 mark will be deducted for every
wrong ans and in Q.31 to Q.90, 0.5 mark will be deducted for every wrong ans. More
than 1 ans marked against a ques. will be deemed as an incorrect response and will
be negatively marked.
5. Write your registration number, name and name of the Centre at the specified locations on
the right half of the ORS.
6. Using HB pencil, darken the improper bu—ufr every digit of your registration number and
the letters corresponding to your paper code.
7. No charts or tables are given in the exam hall.
8. Use the blank pages provided at the end of the ques. paper for rough work.
9. select the nearest numerical ans among the option provided.
10. Please check all pages and report, if there is any discrepancy.
Q.1 - Q.30 Carry 1 Mark every
sin2 x
1. Lt is equal to
x—O X
(a) 0
(b) -1
(C) 1
(d) none
2. The accuracy of Simpson’s rule quadrature for a step size h is
(a) 0(h2)
(b) 0(h3)
(c) 0(h4)
(d) 0(h5)
3. For the matrix four one the eigen vaues are
14
(a) three and -3
(b) -3 and -5
(c) three and 5
(d) five and 0
4. The 2nd moment of a circular area about the diameter is provided by (D is the diameter).
5. A concentrated load of P acts on a simply supported beam of span L at a distance
•-from the left support. The bending moment at the point of application of the
load is provided by
PL 2PL PL 2PL

6. 2 identical circular rods of identical diameter and identical length are subjected to identical
magnitude of axial tensile force. 1 of the rods is made out of mild steel having the modulus
of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity
of 100 Gpa. presume both the materials to be homogeneous and isotropic and the axial force
causes the identical amount of uniform stress in both the rods. The stresses developed are within
the proportional limit of the respective materials. Which of the subsequent observations is

Earning:   Approval pending.