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<div dir="ltr" style="text-align: left;" trbidi="on"><br /><h1 align="center" class="LARGE">GATE question papers: Mechanical Engineering, 2011 (ME)<b> </b></h1><div><b><br /></b></div><div><div class="QuestionPaper"><b>1.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A streamline and an equipotential line in a flow field</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) are parallel to each other </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) are perpendicular to each other</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) intersect at an acute angle </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) are identical</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>2.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">If a mass of moist air in an airtight vessel is heated to a higher temperature, then</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) specific humidity of the air increases</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) specific humidity of the air decreases</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) relative humidity of the air increases</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) relative humidity of the air decreases</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>3.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">In a condenser of a power plant, the steam condenses at a temperature of 60<span style="font-family: Symbol;">°</span>C. The cooling water enters at 0 30<span style="font-family: Symbol;">°</span>C and leaves at 0 45<span style="font-family: Symbol;">°</span>C. The logarithmic mean temperature difference (LMTD) of the condenser is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 16.2 <span style="font-family: Symbol;">°</span>C </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 21.6 <span style="font-family: Symbol;">°</span>C </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 30 <span style="font-family: Symbol;">°</span>C  </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 37.5 <span style="font-family: Symbol;">°</span>C</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>4.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces R_P and R_Q at supports P and Q respectively are</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="125" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image001.gif" width="320" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 1 kN downward, 1 kN upward </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.5 kN upward, 0.5 kN downward</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0.5 kN downward, 0.5 kN upward </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1 kN upward, 1 kN upward</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>5.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="157" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image002.gif" width="318" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) <span style="font-family: Symbol;">-</span>1 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 2</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>6.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The maximum possible draft in cold rolling of sheet increases with the</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) increase in coefficient of friction </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) decrease in coefficient of friction</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) decrease in roll radius </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) increase in roll velocity</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>7.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The operation in which oil is permeated into the pores of a powder metallurgy product is known as</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) mixing </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) sintering </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) impregnation </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) infiltration</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>8.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A hole is dimension _{<img align="absmiddle" height="29" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image003.gif" width="47" />} mm. The corresponding shaft is of dimension _{<img align="absmiddle" height="29" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image004.gif" width="47" />}mm. The resulting assembly has</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) loose running fit </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) close running fit</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) transition fit </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) interference fit</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>9.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Heat and work are</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) intensive properties </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) extensive properties</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) point functions </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) path functions</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>10.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A column has a rectangular cross-section of 10mm <span style="font-family: Symbol;">´</span> 20mm and a length of 1m. The slenderness ratio of the column is close to</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 200 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 346 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 477 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1000</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>11.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A series expansion for the function sin <span style="font-family: Symbol;">q</span> is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="39" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image005.gif" width="101" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image006.gif" width="101" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image007.gif" width="132" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image008.gif" width="112" />}</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>12.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Green sand mould indicates that</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) polymeric mould has been cured </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) mould has been totally dried</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) mould is green in colour </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) mould contains moisture</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>13.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">What is _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image009.gif" width="55" />}equal to?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) <span style="font-family: Symbol;">q</span></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) sin <span style="font-family: Symbol;">q</span></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>14.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Eigenvalues of a real symmetric matrix are always</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) positive </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) negative </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) real </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) complex</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>15.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5 W/m² K. It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) The outer radius of the pipe is equal to the critical radius</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) The outer radius of the pipe is less than the critical radius</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Adding the insulation will reduce the heat loss</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) Adding the insulation will increase the heat loss</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>16.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The contents of a well-insulated tank are heated by a resistor of 23 <span style="font-family: Symbol;">W</span> in which 10 A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer to the system are positive. The rates of heat (Q), work (W) and change in internal energy (<span style="font-family: Symbol;">D</span>U) during the process in kW are</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) Q = 0, W = −2.3, <span style="font-family: Symbol;">D</span>U = +2.3 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Q = +2.3, W = 0, <span style="font-family: Symbol;">D</span>U = +2.3</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Q = −2.3, W = 0, <span style="font-family: Symbol;">D</span>U = −2.3  </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) Q = 0, W = +2.3, <span style="font-family: Symbol;">D</span>U = −2.3</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>17.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Match the following criteria of material failure, under biaxial stresses <span style="font-family: Symbol;">s</span>₁and <span style="font-family: Symbol;">s</span>₂and yield stress <span style="font-family: Symbol;">s</span>_y, with their corresponding graphic representations :</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="301" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image010.jpg" width="477" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) P-M, Q-L, R-N </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) P-N, Q-M, R-L </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) P-M, Q-N, R-L </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) P-N, Q-L,R-M</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>18.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The product of two complex numbers 1 + i and 2 <span style="font-family: Symbol;">-</span> 5i is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 7 <span style="font-family: Symbol;">-</span> 3i </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) <span style="font-family: Symbol;">-</span> 3 <span style="font-family: Symbol;">-</span> 4i </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C)  <span style="font-family: Symbol;">-</span> 3 <span style="font-family: Symbol;">-</span> 4i </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 7 + 3i</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>19.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 10 minutes</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 20 minutes</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 25 minutes</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 50 minutes</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>20.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The word <b>kanban</b> is most appropriately associated with</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) economic order quantity </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) just–in–time production</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) capacity planning </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) product design</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>21.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">If f(x) is an even function and a is a positive real number, then  _{<img align="absmiddle" height="49" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image011.gif" width="53" />}equals</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) a </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 2a </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="49" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image012.gif" width="59" />} </div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>22.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The coefficient of restitution of a perfectly plastic impact is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 1</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 2</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) <span style="font-family: Symbol;">¥</span></div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>23.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A thin cylinder of inner radius 500mm and thickness 10mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress in MPa is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 100</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 250</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 500</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1000</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>24.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Which one among the following welding processes uses non-consumable electrode?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) Gas metal arc welding</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Submerged arc welding</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Gas tungsten arc welding</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) Flux coated arc welding</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>25.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The crystal structure of austenite is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) Body centered cubic </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Face centered cubic</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Hexagonal closed packed </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) Body centered tetragonal</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>26.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist <span style="font-family: Symbol;">q</span> at the free end is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="145" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image013.gif" width="410" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="51" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image014.gif" width="59" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="51" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image015.gif" width="57" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="51" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image016.gif" width="59" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="51" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image017.gif" width="52" />}</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>27.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Figure shows the schematic for the measurement of velocity of air (density = 1.2kg /m³) through a constant-area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg /m³) in the two columns of the manometer is 10mm. Take acceleration due to gravity as 2 9.8m/ s². The velocity of air in m/s is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="267" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image018.jpg" width="251" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 6.4</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 9.0</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 12.8</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 25.6</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>28.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800kJ/kg and 1800kJ/kg respectively. Neglecting pump work, the specific steam consumption in kg/kW-hour is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 3.60</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.36</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0.06</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 0.01</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>29.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The integral _{<img align="absmiddle" height="49" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image019.gif" width="41" />}, when evaluated by using Simpson's 1/3 rule on two equal subintervals each of length 1, equals</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 1.000</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 1.098</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1.111</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1.120</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>30.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Two identical ball bearings P and Q are operating at loads 30 kN and 45 kN respectively. The ratio of the life of bearing P to the life of bearing Q is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 81/16</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 27/8</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 9/4</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 3/2</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>31.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="195" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image020.gif" width="281" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 3 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 3/2</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 2/3</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>32.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force F_x (in N) exerted by the rubber band as a function of distance x (in m) is given by <br /> F_x = 300x². If the stone is displaced by 0.1m from the un-stretched position <br /> (x = 0) of the rubber band, the energy stored in the rubber band is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="254" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image021.gif" width="344" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0.01 J </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.1 J </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1 J </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 10 J</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>33.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Consider the differential equation _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image022.gif" width="23" />}= (1 + y²) x. The general solution with constant c is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) y = _{<img align="absmiddle" height="39" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image023.gif" width="85" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) y = _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image024.gif" width="76" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) y = _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image025.gif" width="76" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) y = _{<img align="absmiddle" height="47" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image026.gif" width="83" />}</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>34.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image027.gif" width="21" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image028.gif" width="21" />} </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image029.gif" width="21" />} </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image030.gif" width="21" />}</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>35.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="165" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image031.gif" width="343" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 32 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 23 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 16 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 11</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>36.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The shear strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100 mm diameter from a 1.5 mm thick sheet is close to</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 45 kN</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 70 kN</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 141 kN</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 3500 kN</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>37.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are _{<img align="absmiddle" height="36" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image032.gif" width="15" />}and 2 respectively. The Reynolds number based on the plate length for both the flows is 10⁴. The Prandtl and Nusselt numbers for P are _{<img align="absmiddle" height="37" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image033.gif" width="15" />}and 35 respectively. The Prandtl and Nusselt numbers for Q are respectively</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 8 and 140 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 8 and 70 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 4 and 70 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 4 and 35</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>38.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The crank radius of a single-cylinder I. C. engine is 60 mm and the diameter of the cylinder is 80 mm. The swept volume of the cylinder in 3 cm is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 48 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 96 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 302 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 603</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>39.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of the liquid as 990 3 kg /m³. The isentropic specific work done by the pump in kJ/kg is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0.10 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.30 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 2.50 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 2.93</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>40.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300K. The heat transfer coefficient between the steel ball and the surrounding is 5 W/m² K. The thermal conductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of the steel ball is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) large because conduction resistance is far higher than the convective resistance</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) large because conduction resistance is far less than the convective resistance</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) small because conduction resistance is far higher than the convective resistance</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) small because conduction resistance is far less than the convective resistance</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>41.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300 K and 1500 K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures in Kelvin at the end of the compression and expansion processes are respectively</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 500 and 900 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 900 and 500</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 500 and 500 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 900 and 900</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>42.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of  vibration of the system is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="136" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image034.gif" width="315" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image035.gif" width="48" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image036.gif" width="52" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image037.gif" width="55" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image038.gif" width="55" />}</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>43.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A 1 kg block is resting on a surface with coefficient of friction μ = 0.1. A force of 0.8 N is applied to the block as shown in figure. The friction force is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="91" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image039.gif" width="371" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.8 N </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0.98 N </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 1.2 N</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>44.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Consider the following system of equations:</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">2x₁ + x₂ + x₃ = 0,</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">x₂ <span style="font-family: Symbol;">-</span> x₃ = 0,</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">x₁ + x₂ = 0.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">This system has</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) a unique solution </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) no solution</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) infinite number of solutions </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) five solutions</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>45.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A single-point cutting tool with 12<span style="font-family: Symbol;">°</span> rake angle is used to machine a steel work-piece. The depth of cut, i.e. uncut thickness is 0.81 mm. The chip thickness under orthogonal machining condition is 1.8mm. The shear angle is approximately</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 22<span style="font-family: Symbol;">°</span> </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 26<span style="font-family: Symbol;">°</span> </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 56<span style="font-family: Symbol;">°</span> </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 76<span style="font-family: Symbol;">°</span></div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>46.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Match the following non-traditional machining processes with the corresponding material removal mechanisms :</div><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none;"> <tbody><tr> <td style="border: solid windowtext 1.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 169.85pt;" valign="top" width="226"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Machining process</div></td> <td style="border-left: none; border: solid windowtext 1.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" valign="top" width="222"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Mechanism of material removal</div></td> </tr><tr> <td style="border-top: none; border: solid windowtext 1.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 169.85pt;" valign="top" width="226"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">P. Chemical machining</div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" valign="top" width="222"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">1. Erosion</div></td> </tr><tr> <td style="border-top: none; border: solid windowtext 1.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 169.85pt;" valign="top" width="226"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Q. Electro-chemical machining</div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" valign="top" width="222"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">2. Corrosive reaction</div></td> </tr><tr style="height: 10.75pt;"> <td style="border-top: none; border: solid windowtext 1.0pt; height: 10.75pt; padding: 0in 5.4pt 0in 5.4pt; width: 169.85pt;" valign="top" width="226"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">R. Electro-discharge machining</div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 10.75pt; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" valign="top" width="222"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">3. Ion displacement</div></td> </tr><tr> <td style="border-top: none; border: solid windowtext 1.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 169.85pt;" valign="top" width="226"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">S. Ultrasonic machining</div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" valign="top" width="222"> <div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">4. Fusion and vaporization</div></td> </tr></tbody></table><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) P-2, Q-3, R-4, S-1 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) P-2, Q-4, R-3, S-1</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) P-3, Q-2, R-4, S-1</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) P-2, Q-3, R-1, S-4</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>47.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A cubic casting of 50 mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 48.32 mm </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 49.90 mm </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 49.94 mm </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 49.96 mm</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Common Data Questions</b></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Common Data Questions: 48 & 49</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300K.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The following are the properties and relations pertaining to air:</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Specific heat at constant pressure, c_p = 1.005 kJ/kgK;</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Specific heat at constant volume, c_v = 0.718 kJ/kgK;</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Characteristic gas constant, R = 0.287 kJ/kgK.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Enthalpy, h = c_pT.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Internal energy, u = c_v T.</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>48.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">If the air has to flow from station P to station Q, the maximum possible value of</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">pressure in kPa at station Q is close to</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 50</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 87</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 128</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 150</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>49.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">If the pressure at station Q is 50 kPa, the change in entropy (s_Q <span style="font-family: Symbol;">-</span> s_P ) in kJ/kgK is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) <span style="font-family: Symbol;">-</span>0.155</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0.160</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 0.355</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Common Data Questions: 50 and 51</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">One unit of product P₁requires 3 kg of resource R₁ and 1 kg of resource R₂. One unit of product P₂ requires 2 kg of resource R₁and 2 kg of resource R₂. The profits per unit by selling product P₁ and P₂ are Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource R₁ and 100kg of resource R₂.</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>50.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The unit worth of resource R₂, i.e., dual price of resource R₂ in Rs. Per kg is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 1350</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1500</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 2000</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>51.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The manufacturer can make a maximum profit of Rs.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 60000</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 135000</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 150000</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 200000</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Linked Answer Questions</b></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b><span style="color: green;">Statement for Linked Answer Questions: 52 & 53</span></b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A triangular-shaped cantilever beam of uniform–thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam</div><div class="QuestionPaper"> </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="201" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image040.gif" width="315" /></div><br /> <div class="QuestionPaper"><b>52.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="40" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image041.gif" width="35" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="39" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image042.gif" width="35" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="39" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image043.gif" width="35" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="39" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image044.gif" width="28" />}</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>53.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The maximum deflection of the beam is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image045.gif" width="40" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image046.gif" width="39" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image047.gif" width="35" />}</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) _{<img align="absmiddle" height="41" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image048.gif" width="35" />}</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Statement for Linked Answer Questions: 54 & 55</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m² is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="207" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image049.gif" width="393" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><br /></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>54.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The density of air in kg/m³ at the nozzle exit is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 0.560 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 0.600 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 0.727 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 0.800</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>55.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The mass flow rate of air through the nozzle in kg/s is</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 1.30 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 1.77 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 1.85 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 2.06</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>General Aptitude (GA) Questions</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Q. No. 56 – 60 Carry One Mark Each</b></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>56.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Choose the word from the options given below that is most nearly opposite in meaning to the given word: </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Amalgamate</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) merge </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) split </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) collect </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) separate</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>57.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Which of the following options is the closest in the meaning to the word below:</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Inexplicable</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) Incomprehensible </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Indelible</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Inextricable </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) Infallible</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>58.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) P² = Q³ R² </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Q² = PR </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) Q² = R³ P </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) R = P² Q²</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><b>59.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Choose the most appropriate word(s) from the options given below to complete the following sentence.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">I contemplated ______ Singapore for my vacation but decided against it.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) to visit </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) having to visit </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) visiting </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) for a visit</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>60.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Choose the most appropriate word from the options given below to complete the following sentence.</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or______.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) hyperbolic </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) restrained</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) argumentative </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) indifferent</div><div class="QuestionPaper">Answer: (B)</div><div class="QuestionPaper"><br /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Q. 61 to Q. 65 carry two marks each</b></div><div class="QuestionPaper"><br /></div><div class="QuestionPaper"><b>61.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 7.58 litres </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 7.84 litres </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 7 litres </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 7.29 litres</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>62.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><b>Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.</b> </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">Based on the above passage which topic would not be included in a unit on bereavement?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) how to write a letter of condolence</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) what emotional stages are passed through in the healing process</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) what the leading causes of death are</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) how to give support to a grieving friend</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><b>63.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;"><img height="296" src="http://www.questionpapers.net.in/gate_question_papers/mechanical_engineering/gate-mechanical-engineering-2011_files/image050.jpg" width="457" /></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) P  </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) Q </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) R </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) S</div><div class="QuestionPaper">Answer: (D)</div><div class="QuestionPaper"><b>64.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 5 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 4 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 7 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 6</div><div class="QuestionPaper">Answer: (A)</div><div class="QuestionPaper"><b>65.</b></div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?</div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(A) 4  </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(B) 5 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(C) 6 </div><div class="QuestionPaper" style="margin-left: 0in; text-indent: 0in;">(D) 7</div><div class="QuestionPaper">Answer: (C)</div><div class="QuestionPaper"><br /></div><div align="center" class="QuestionPaper" style="margin-left: 0in; text-align: center; text-indent: 0in;"><b>End of Question Paper</b></div><div class="QuestionPaper"><br /></div></div></div>

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GATE question papers: Mechanical Engineering, 2011 (ME)   1. A streamline and an equipotential line in a flow field (A) are parallel to ...

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