mechanical engineering gate 2012 papers with solution pdf

! " ! # $ % & ' ! () * " "& !' - + + ! *+ +,+ 1+ " 2+ * ++, ++ /+ $ *3+ () ' ++ /+ ! */ + * +1 " *+ $ 3 () $ 56 () ! π * * = π = * * ' * × * * = ++ × /+ = */ 3* & ' ; & ' * , ! & < & ' % ;* − × ++ = ' ! 3*: ! , & ; ' *, & ! * ;* ; * < + " +/ $ + */ () " © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com / & , ' " , ' $ ' , ' () = & > ' 8* # ∆ 8* # ! 8* # " 8* > − $ ? () % & ! 0, , & & ' ' */ 3/ + +/ / + " /+ $ ++ () ' % =++ *+ , , *++ *+ ' ' , , @ 4A/ 1A+ " /2+ $ =+ () 56 () B5 = ' * * % * * # *+ × + * = = +3 − * * *π * × π × =++ = = = =* 24 =+ =+ %= B 5= * * × + × =* 24* = 1A+ @ A & ! C !D E ! EC* *5% ! % EC* 5% " *EC* 5% $ 3EC* 5% © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com () * 56 () 5% ' = E 6* , ' = E6 + " 5% , * E6 + " + "* * 5% ' & ! " = " = +, G '= + ' =+ F6 =+ ' =+ 6 +, E6* H *5% ' = EC* *5% , ! ! ! * " $ () " 56 () " ! " , 8 C* =3 * ( ) = 64 + 69+, " C* π*5% ! G 3π*5% & & ' $ () $ 56 ( ) ( ) = 64 + & +, , &' ' © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com * , 6* + '* + I* − , * , * + * * ,+ & & !' D * − * D " $ + D+ () 6* + '* + I* = 56 ( ) J & 6* + '* + I* − = + & * + * * D+ + = * + * * = & + * ,+ ,+ * + = + * * D * E " > $ * # $ " () % 8)3, >) , #)*, 8) , >)*, #)3, ! % $ " $ $ % () $ & )4 )4 & D " & 8)3, >) , #)4, $ 8) , >)4, #)*, , ! , / * * * * * D G , , )* )3 II & ' ' ,! ,! % ! ! ! ! ', ++ +3+ + I */ +++−+ + ++ +4+ I */ +++++ +*+ 3+ 4+ !' " *+ $ + © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com () " E I K I */ +3+)*/ +*+ 9*+µ = $ I , ! & " ! & $ () " *++ /++ 9+ +**/ I +* & 9A = , + * = " ** $ *4* 4= () + +**/ × /++ × 56 () G = * C; = * $ +* Π × + ** *×A ×+ L !' , * = = & ' (α) , ! & ' ( τ) & ' (ρ) L ρ+α+τ=+ α+ρ = τ " α+ρ = $ α+ρ =+ () " A ! & 4*/ + @ +A 9**/ A3 @ + B ! E ! ' / L 9*/A2 @ ' ' L ' & ' / & ' ! ( =/ 2A " A $ *1 + () 56 () = ã ì * = + ì 4*/ − **/ A3 + + A × */A2 − **/ A3 = 2A++ B@0 = A E *+ ( J %( 2+ J %%( ** /M % *+ 33+ *++ 4+M , A++ " 21/ $ 1*+ © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com () 56 ( ) ; ϕ = ϕ = ' * = * 2+ *+" 4+ = ** / * 33+ × + =*/ = A++ * I ' ω & α α ? ( α) * " + (ω) * * ω* $ () ** !D !' % : !' :, , + " +2 $ * +* () $ 56 () σ G ' ' ! $ ! & , L , * σ , ( )= = + * − =++ & = −+ + < ! , *4 σ = + +*, ∴ σ ! *: ! '96 ' = 6* ! 6)' = " $ * () 56 () & & '96 ' 6* & * , G & +, = = = (6 − ) * + 6* 64 − * = + * − + = L © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com *3 (6) 69+, " " " () " 56 () J & N 6N */ (6) = " ! ) ) ! − ! $ 9N 6N O 69+! ! ! 6 →+ & ) ≤6≤ * * " $ * () 56 () *= →+ * − = 6* * * 6* →+ " * =* I & ! I →+ * 6* ×3 * , = *× = ! ( ! # $ */ * + += + +/ " */ + ! *3 24 *3 2A 56 () () $ 9$ = */ − * × + += − + +/ = *3 24 *1 % K*6 − , + +4 $ */ ) + 3+ ! + ++= () " 56 () ∆G = $ ( − α= * +: " + +=* $ + =++ α) ∆G = $ − + ×2 + α = /1 α = /1 × π 2+ α = + +=* © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com *2 % ; $" = *+ + / , & ) ! & ; & ! / ; & /++ G 3++ , & ( 3/;, 3/+ 1/;, //+ " A/;, A/+ $ /+;, /++ () " 56 () ; = *+ + / =/ , ; = 3/ ; =1 , ; = // ; ;+ % % ; = ;+ − ;+ & % 3/ = ;+ − ;+ × /++ % // = ;+ − ;+ × 3++ % < & * ; = A/ & % = A/+ *A II ! , & ' * & ! , ( ρ * " * ρ + ρ ρ4 + ρ* ρ4 + ρ* * + ρ4 ρ + ρ* + ρ4 * ρ* ρ4 * * ( + * + ) 4 $ * ρ * ρ + ρ* + ρ4 + ρ* * + ρ4 * © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission ! www.EngineeringEBooksPdf.com () 56 () ' P L ;* + I+ = * + ρ4 * ρ4 , , ;** * I* + ? = ?* , ; = + F 8* = G ;* = * ρ4 * *8 ρ4 ;* = = ρ < + ρ* * + ρ4 ! ;* = * , + (" 4+ ρ ρ* + ρ* ρ4 @0 ⋅ B ) =3 +/ * +A * 2+M" (" 0 % = @0 ⋅ B ) 4+M" & + 2, CE $ M" 3+ *+ " + $ / () " 56 () ε= " " +2= * * − × + / 2+ − * × * +A × 2+ − 4+ = 3+ " − + /× * − × * = * − × 3+ = * +A × × * − 4+ = 1+ " θ = θ* = + " ∴ CE $ = + " ! ' !' ∆ α, % P &, P & ! − α (∆ ( )5 − *&) − *α ( ∆ ( )5 − *&) " − 4α ( ∆ ( )5 − *&) $ − α (∆ )5 ( − *&) © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission " www.EngineeringEBooksPdf.com () 4* ! L ! /+ % 3+E8 , *, ' ! = " *3 $ 4* () 56 () /+ Hτ K , ?8 π 3+E8 τ = *H ?8 = = ! = τ ! = 1+E8 = τ = = πτ = = × /+ × +4 π × 1+ = = ≈ / 42 44 = 3++ ! ' +/ ! ! 2+M % , ! ! + */, ! L , 3++ ++ = /3 " ** $ /1 () 56 () , ! F * ! = F µθ = + */×π =* ( − = 3++ A * * = 2* 41/ L = /3 43 * ) * − ! ! = ! ! ! ! ! *+ ' ! ! * ! ' ! " + $ * © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission # www.EngineeringEBooksPdf.com () $ # 56 () J & , = ! # ! ! ' ! ! ' ! ! ' # # # = / × × + A # = / × × + A #9 # = / × × + A ! & ! ! 9+/ * 4/ " ' (+ ) = + '( ' ' +6 − 3' = + 6* 6* L )= ! ' L π6 * 6* " π6 * $ π6 * −6 () 56 () * 6* ' * +6 ' − 3' = + ' (+ ) = + '( " )= 'P $ ' = 6* ' = *6 ' = −* ' ' = −* ' * ' 6* =* = − *6 −4 ' = − *6 −4 ' 6* 6* = +=6 −3 = +=6 −3 ( ) + ( −* ) − ( ) = + 6* = * * 3=+ * =3 = ±* ∴ " 6* + "* 6* + "* 6* L 6* G 4= ' + *' + I= *6 + ' + *I= / − ' + I= ! L % & ! 69 , '9 I9 69 , '9 ' " L I9 69*, '9 I9+ ! © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com $ ! () " 56 () & L −( + *' + I= ) − (* ) *6 + ' + *I= / − (4) + ' + I= '9 F * , & * F , & ) '9 ) / C / G & L 41 + / + / *+ + + + − + = & ' & A /+ , = +1 E8 E8 < & " *2 /* E ' , $ 3A () 56 () σ {( σ * L= , σ − σ** ) + ( σ L= } = /Hσ*4 = σ * =+ *1 24A E8 ' 42 * = +, σ** = *+, σ44 = − +Hσ ∴ σ − σ** ) + = σ** + σ**4 + σ*4 * σ τ' = L = = +1 E8 $ & " ! +3 < += # Q +M " */ E ' I */ ) + 12 × +/ + 11/3 × +/ © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com + +3 × +/ " $ 4A1 × +/ () " 56 () =+3 =+= α= + ;" = * / = */µ α φ= − α = + 3*44 α ;" 4A φ = ** A = (φ − α) × % * /× + * A × */ × +−= , ! $ & , /++ 2M 4/ + +3 × +/ / /+ +* 4* , * " * $ 4+ () C + = 56 () C = /+ + +" H = = /++ 3+ H" = H =+* = + /2/ β = /× * $ * & =* /A = / 4/ " ' % $ & & ', ! $* ! 7** & !' * $* − $ ? " $ $* $ − $ $* () $ 56 () 7** = − 7* = − = ! ! ' & I # ' & ' $ $* ' +++ % ! − ' ' !' , ! 3, ! © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com * " +/ $ + */ () " 56 () ' # α δ α ; % & !' (δ) ' α # ; ' !' 3* 4/ ' =1: ! +/ ++ */M" ' & */M" , //: " ' & ' J& & ' 24: $ : () $ 34 ) D !D + ! , ! & I A3E8 , & 4+ 7 33 () " 56 () A* = + 1+1 τ " A A4 $ ** = ! = + 1+1 × + × 4+ × A3 = 8= % AA41 A A43 E 33 & ' , I &! L L *C !' ! , ' ' ( * " $ * C C © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com () $ 3/ σ66 = 3+E8 Hσ'' = ++E8 E τ6' = 3+E8 P & 3+ /+ " E8 =+ $ ++ () 56 () σ66 = 3+ E8 H σ'' = # E 3= & ++ E8 , τ6' = 3+E8 P σ66 − σ'' * * + τ*6' = 4+* + 3+* = /+ E8 7( C ( )= ( )= − " )= ( ( )= + − ) & !' $ ( )= − − () $ 56 () C− ( C− 31 ) + − = − = − − = / , + + I & & * * − * " + − * + $ / * / () /−λ − λ% = + 56 () 4−λ λ* − 2λ + / − = + ( =+ (/ − λ ) ( − λ ) = = + λ* − 2λ + * = + λ = *, λ = = − *%) × - = + , λ=* 4 6* = + 6* = + + H + = 6* © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com G L * − & * $$ % ! * ++ D , & " !D ' !( " ", & I " 3/M =+M 32 ! ' ! $ / " ++E8 $ ** 4+ " () 56 ( ) C P , 7 = = +/ *+ 4/ = + 2A=/7 H7 = + 14* 7 ∴ + 2A=/7 = ++E8 ++ 3A % 7= = 7= = ++E8 /3 32 , /B & & B + =4 + 4* " *= $ 3= () # =7 & 4+ = + =447 = B ∴# = + =44B $$ % ! ' & ' #( *+ 2++ & #) 43 © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com & & L +* @0 ) #) 43 ( #) 43 8( ) M" *+ 2++ ( ) @0 ( ( @0 ⋅ B ) ( @0 ⋅ B ) )** 4* ** / *41 + +A4 + A/ A/ / *=1 + 4/3 +A #) 43 8( ) 2++ /+ M" ( 3+ *1= 3/ @0 ) ( @0 ⋅ B ) + A/ L / A3 24 " 1A $ 4A / () " 56 () * = L ( * − ) = + * × (*1= 3/ − *41 ) = A / *2 3* A @ " 43 $ 3= © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com () 56 () # ( = − ) = + * ( *41 − A/ /) = *2 ) $ * +, D , & & & ' ( ! ! &' $ ! ' ) " / $ ! * A J = G , /* * D )!) ) ) ) ) ) " ) )) $ )!) ) ) () " * 56 () = " / * = J A = G + $ ; J G− " JG − = $7 G − ∴ /4 / A ' ' ' H $7 G % &' A + ' , " D A ' " " " D ! D © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission ! www.EngineeringEBooksPdf.com $ " D ' () 56 () % &' D ) $ * ! ++ " II /3 + ' A +, ' , & ' II 4++ , /++B & ' 2+ ++2@ B & ( ' + % 2+ & * / =B /4*B " 323B $ 3=2B () " Q &* 0* 56 () * Q &** 0* &** )&* = − * =" − * 2+* − +* = ++2 × /++ − * * = 323B // * * * II A+ /= " 33 $ *A () $ 56 () ' ρ ; = ρ* × # * = ; = * L , ;* 8* × # * * ;* * = 8* * 4++ × 323 + × × 2+ = * A /++ × ++ 2+ × ; × ;* * # /= & !' /L* , L # /+ ! ! !' I / + " / $ */ ( 56 () = /+L− /L* © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission " www.EngineeringEBooksPdf.com L = /+ − +L H ∴ * L* , # & " 8, # $ #, ' T , *, 4, 3U ! ! ' =+: 3+: !D L ' -S ! ! , A=: ! ! ! ' ' !' + *22 + 443 ' ! ! ! L S ! ! ' ! ! , 1*: ! , " + ==1 ! ! ! ! ! ! , $ + 1*+ ( 56 () =+: A=: + /1= ' ! # & ∴ (6) = ' 3+: 1*: + *22 + *22 = + 443 + /1= + + *22 =/ ' ! & ' ' = *6 − + 6* L + " * ! $ ( 56 () ' = *6 − + 6* © All rights reserved by Gateforum Educational Services Pvt Ltd No part of this booklet may be reproduced or utilized in any form without the written permission www.EngineeringEBooksPdf.com ' = * − + *6 * '