1. UˡÊÊ ÈÁSÃ Ê apple ß Îc U U Êfl ÿ Áflfl UáÊ UˡÊÊ ˇÊ apple éœ. 2. ß UˡÊÊ ÈÁSÃ Ê apple ÃËŸ ʪ Ò - ʪ I, ʪ II fl ʪ III.

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1 This booklet contains 3+4 printed pages. ß ÈÁSÃ Ê apple 3+4 ÈÁŒ à Îc Ò FRM No. : PAPER - : MATHEMATICS & APTITUDE TEST Ÿ òê - : ªÁáÊà ÃÕÊ Á L Áø UˡÊáÊ Do not open this Test Booklet until you are asked to do so. ß ËˇÊÊ ÈÁSÃ Ê Êapple à à Ÿ πêapple apple Ã Ê Ÿ Ê Read carefully the Instructions on the Back Cover of this Test Booklet. ß ËˇÊÊ ÈÁSÃ Ê apple Á apple Êfl áê ÁŒ ª ÁŸŒapple ÊÊapple Êapple äÿêÿ apple apple Important Instructions : ûfl ÍáÊ ÁŸŒapple Ê 1. Immediately fill in the particulars on this page of the Test Booklet with Black Ball Point Pen provided in the examination hall.. This Test Booklet consists of three parts - Part I, Part II and Part III. Part I has 30 objective type questions of Mathematics consisting of FOUR marks for each correct response. Part II Aptitude Test has 50 objective type questions consisting of FOUR marks for each correct response. Mark your answers for these questions in the appropriate space against the number corresponding to the question in the Answer Sheet placed inside this Test Booklet. Use the Black Ball Point Pen provided in the examination hall for writing particulars/marking responses on Side-1 and Side- of the Answer Sheet. Part III consists of questions carrying 70 marks which are to be attempted on a separate Drawing Sheet which is also placed inside the Test Booklet. Marks allotted to each question are written against each question. Use colour pencils or crayons only on the Drawing Sheet. Do not use water colours. For each incorrect response in Part I and Part II, ¼ (one fourth) marks of the total marks allotted to the question (i.e. 1 mark) would be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 3. There is only one correct response for each question in Part I and Part II. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction above. 4. The test is of 3 hours duration. The maximum marks are On completion of the test, the candidates must hand over the Answer Sheet of Mathematics and Aptitude Test-Part I & II and the Drawing Sheet of Aptitude Test-Part III alongwith Test Booklet for Part III to the Invigilator in the Room/Hall. Candidates are allowed to take away with them the Test Booklet of Mathematics and Aptitude Test-Part I & II. 6. The CODE for this Booklet is R. Make sure that the CODE printed on Side- of the Answer Sheet and on the Drawing Sheet (Part III) is the same as that on this booklet. Also tally the Serial Number of the Test Booklet, Answer Sheet and Drawing Sheet and ensure that they are same. In case of discrepancy in Code or Serial Number, the candidate should immediately report the matter to the Invigilator for replacement of the Test Booklet, Answer Sheet and the Drawing Sheet. 7. Do not fold or make any stray mark on the Answer Sheet. Name of the Candidate (in Capitals) : èÿõë Ê ŸÊ ( «apple ˇÊ Êapple apple ) Roll Number : in figures ŸÈ Ê Êapple apple : in words ÊéŒÊapple apple Examination Centre Number : ˡÊÊ apple 㜠Ÿê U Centre of Examination (in Capitals) : UˡÊÊ apple 㜠( «apple ˇÊ UÊapple apple ) Candidate s Signature : Invigilator s Signature : èÿõë apple SÃÊˇÊ ÁŸ ËˇÊ apple SÃÊˇÊ Invigilator s Signature () : ÁŸ ËˇÊ apple SÃÊˇÊ () Test Booklet Code ˡÊÊ ÈÁSÃ Ê apple à R 1. UˡÊÊ ÈÁSÃ Ê apple ß Îc U U Êfl ÿ Áflfl UáÊ UˡÊÊ ˇÊ apple éœ UÊÿapple ª apple fl Ê apple ÊÚ ÊÚßZ U appleÿ apple Ãà Ê apple. ß UˡÊÊ ÈÁSÃ Ê apple ÃËŸ ʪ Ò - ʪ I, ʪ II fl ʪ III. ÈÁSÃ Ê apple ʪ I apple ªÁáÊà apple 30 flsãèáÿd Ÿ Ò Á apple àÿapple Ÿ apple Ë ûê U apple Á ÿapple øê U ÁŸœÊ Á Uà Á ÿapple ªÿapple Ò Êª II Á L Áø UˡÊáÊ apple 50 flsãèáÿd Ÿ Ò Á Ÿ apple àÿapple Ë ûê U apple Á øê U Ò ßŸ ŸÊapple Ê ûê U ß UˡÊÊ ÈÁSÃ Ê apple Uπapple ûê U òê apple ªÃ ÅÿÊ apple ªÊapple apple apple ª UÊ ÁŸ ÊÊŸ ªÊ U ŒËÁ ûê U òê apple ÎD-1 fl ÎD- U flê Á Uà Áflfl UáÊ Á πÿapple fl ûê U Á à UŸapple appleãè UˡÊÊ ˇÊ apple éœ UÊÿapple ª apple fl Ê apple ÊÚ ÊÚßZ appleÿ Ê Ë ÿêappleª apple U ÈÁSÃ Ê apple ʪ III apple Ÿ Ò Á Ÿ apple Á 70 ÁŸœÊ Á UÃ Ò ÿ Ÿ ß Ë UˡÊÊ ÈÁSÃ Ê apple 㜠U UπË «ŲÊß ª ÊË U U UŸapple Ò àÿapple Ÿ appleãè ÁŸœÊ Á Uà Ÿ apple ê Èπ Á Ã Ò «ŲÊß ª ÊË U U apple fl UªËŸ apple Á ÕflÊ apple ÿêappleÿ Ê Ë ÿêappleª apple U ÊŸË apple UªÊapple Ê ÿêappleª Ÿ apple U ʪ I ÊÒ U ʪ II apple àÿapple ª à ûê U apple Á Ÿ apple Á ÁŸœÊ Á UÃ È Êapple apple apple ¼ ( -øêòõêß ) ʪ ( ÕÊ Ã 1 ) È ÿêappleª apple apple Ê U Á Ê ªapple ÿᜠûê U òê apple Á Ë Ÿ Ê Êappleß ûê U Ÿ Ë ÁŒÿÊ ªÿÊ Ò, ÃÊapple È ÿêappleª apple apple Êappleß Ÿ Ë Ê appleu Ê ªapple 3. ß UˡÊÊ ÈÁSÃ Ê apple ʪ I ÊÒ U ʪ II apple àÿapple Ÿ Ê apple fl Ë Ë ûê U Ò apple Áœ ûê U ŒappleŸapple U apple ª à ûê U ÊŸÊ ÊÿappleªÊ ÊÒ U UÊappleÄà ÁŸŒapple Ê apple ŸÈ Ê U Ê U Á ÿapple Êÿapple ªapple 4. UˡÊÊ Ë flᜠ3 ÉÊ appleu Ò Áœ à 390 Ò 5. UˡÊÊ Ê# ÊappleŸapple U, èÿõë ªÁáÊà fl Á L Áø UˡÊáÊ- ʪ I fl II Ê ûê U òê fl Á L Áø UˡÊáÊ- ʪ III Ë «UÊß ª ÊË U fl UˡÊÊ ÈÁSÃ Ê Êª III Ê / ˇÊ ÁŸ UËˇÊ Êapple ÊÒ U Ë UˡÊÊ Ê / ˇÊ UÊapple«apple èÿõë ªÁáÊà fl Á L Áø UˡÊáÊ- ʪ I fl II Ë UˡÊÊ ÈÁSÃ Ê Ÿapple ÊÕ apple Ê Ãapple Ò 6. ß ÈÁSÃ Ê Ê apple à R Ò ÿ ÈÁŸÁ øã U apple Á ß ÈÁSÃ Ê Ê apple Ã, ûê U òê apple ÎD- fl «UÊß ª ÊË U ( ʪ-III) U U apple apple à apple Á ÃÊ Ò ÿ Ë ÈÁŸÁ øã U apple Á UˡÊÊ ÈÁSà Ê, ûê U òê fl «ŲUÊß ª ÊË U U ÅÿÊ Á ÃË Ò ª U apple à ÿê ÅÿÊ Á ÛÊ Êapple, ÃÊapple èÿáõ ÿêapple Êapple ÁŸ UËˇÊ apple ŒÍ UË UˡÊÊ ÈÁSà Ê, ûê U òê fl «ŲÊß ª ÊË U appleÿapple apple Á ã apple ÃÈ UãÃ ß òêèá U apple flªã UÊ 7. ûê U òê Êapple Ÿ Êapple«apple fl Ÿ Ë U ãÿ ÁŸ ÊÊŸ ªÊ

2 1. If f (x)+ f (1 x)=x +1, x R, then the range of f is : Part I / ʪ I Mathematics / ªÁáÊà 1. ÿᜠf (x)+ f (1 x)=x +1, Ë x R apple Á, ÃÊapple f Ê Á U U Ò 1, 3 1, 3 () 1, 3 () 1, 3 1 1, , 3 3 1, 3 1, 3. Let A={z C : z =5} and B={z C : z+5+1i =4}. Then the minimum value of z ω, for z A and ω B, is : 6 () ÊŸÊ A={z C : z =5} ÃÕÊ B={z C : z+5+1i =4} Ò, ÃÊapple z A ÃÕÊ ω B apple Á z ω Ê ãÿíÿã ÊŸ Ò 6 () If the product of the roots of the equation, x 5kx+e log e k 1=0 is 49, then the sum of the squares of the roots of the equation is : 55 () ÿáœ Ë UáÊ x 5kx+e log e k 1=0 apple Í Êapple Ê ªÈáÊŸ» 49 Ò, ÃÊapple Ë UáÊ apple Í Êapple apple flªêapplez Ê ÿêappleª Ò 55 () R/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

3 If A = , then the determinant of the matrix adj(a) is equal to : 4. ÿᜠ5 15 A = Ò, ÃÊapple Ê ÿí adj(a) Ê Ê UÁáÊ (Determinant) UÊ U Ò () 56 () Let S be the set of all real values of λ for which the system of linear equations 5. ÊŸÊ λ apple Ë flêsãáfl ÊŸÊapple Ê ÈìÊÿ S Ò Á Ÿ apple Á ÒUÁπ Ë UáÊ ÁŸ Êÿ λx+y+z=5λ λx+y+z=5λ λx+y z=1 λx+y z=1 3y+z=9 has infinitely many solutions. Then, S : equals R. () is a singleton. contains exactly two elements. is an empty set. 3y+z=9 apple Ÿ à Ò, ÃÊapple S R apple UÊ U Ò () ÈìÊÿ (singleton) Ò apple ÊòÊ ŒÊapple flÿfl Ò Á UÄà ÈìÊÿ Ò R/Page 3 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

4 6. In order to get through in an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails. The number of ways in which he can fail, in this examination, is : 6. 9 Ÿ òêêapple Ë UˡÊÊ Ê UŸapple apple Á, UˡÊÊÕË Êapple Ÿ Ÿ òêêapple Ë ÅÿÊ Á apple fl Ê Ÿ Ë Ò, apple Áœ Ÿ òêêapple apple Ê ÊappleŸÊ Êfl ÿ Ò ß UˡÊÊ apple ŸÈûÊËáÊ ÊappleŸapple apple à UË Êapple Ë ÅÿÊ Ò () 55 () (8)! 9 (8)! 7. Let T r denote the r th term in the binomial expansion of (a+1) 50. If 7. (a+1) 50 apple Ám Œ Ê U apple ÊŸÊ r flê Œ T r Ò ÿᜠT 5 +T 7 = 15 5 T 6 then the sum of all the values of a is : T 5 +T 7 = 15 5 T 6 Ò, ÃÊapple a apple Ë ÊŸÊapple Ê ÿêappleª Ò 1 1 () 3 () R/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

5 8. In an ordered set of four numbers, the first 3 are in A.P. and the last 3 are in G.P., whose common ratio is 7/4. If the product of the first and fourth of these numbers is 49, then the product of the second and third of these is : 8. øê U ÅÿÊ Êapple apple Á à ÈìÊÿ apple Õ 3 Ê Ã U üêapple Ë apple Ò ÃÕÊ Áà 3 ªÈáÊÊappleûÊ U üêapple Ë apple Ò Á Ê Êfl ŸÈ Êà 7/4 Ò ÿᜠߟ apple apple Õ ÃÕÊ øêòõë ÅÿÊ Êapple Ê ªÈáÊŸ» 49 Ò, ÃÊapple ŒÍ UË ÃÕÊ ÃË UË ÅÿÊ Êapple Ê ªÈáÊŸ» Ò () 11 () If (sin x+ sin 4 x+ sin 6 x ad inf.)loge e 9. ÿᜠ(sin x+ sin 4 x+ sin 6 x loge e Ÿ à à ) π 0 < x < satisfies the equation, y sinx 5y+4=0, then is equal cosx sinx to : π 0 < x < ÃÈc U UÃÊ Ò, ÃÊapple Ë UáÊ y 5y+4=0 Êapple sinx cosx sinx UÊ U Ò ( + ) ( + ) () ( + 1) () ( + 1) R/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

6 10. Let 1 f ( x) = x x for all x ( 0) R, where for each t R, [t] denotes the greatest integer less than or equal to t. Then : 10. ÊŸÊ Ë x ( 0) R apple Á 1 f ( x) = x x, Ê àÿapple t R apple Á [t] apple «Ê ÍáÊÊZ Œ ÊÊ ÃÊ Ò Êapple t apple UÊ U ÕflÊ t apple UÊapple UÊ Ò lim f ( x) = 0 x + 0 lim f ( x) = 0 x + 0 lim () f ( x) = 1 x lim f ( x) = 1 x 1 lim () f ( x) = 1 x lim f ( x) = 1 x 1 lim f ( x) = 1 x lim f ( x) = 1 x x x x If f ( x) =, x 0 1+ cosx k loge loge 3, x= 0 is a continuous function in the interval [0, π), then k is equal to : 4 () x x x ÿᜠf ( x) =, x 0 1+ cosx k loge loge 3, x= 0 à UÊ [0, π) apple Ãû Ÿ Ò, ÃÊapple k UÊ U Ò 4 () If y=y(x) is an implicit function of x given by ycosx+xcosy=π ; then y (0) is equal to : π () π 0 π 1. ÿᜠy=y(x), x apple S c U (implicit)» Ÿ Ò Êapple ycosx+xcosy=π mê UÊ ŒûÊ Ò, ÃÊapple y (0) UÊ U Ò π () π 0 π R/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

7 13. For each x R, let f (x)= x 1, g(x)=cosx and ϕ(x)=f (g( sinx)) g( f (x)). Then, ϕ is : differentiable at each point of R. () not differentiable at 0. not differentiable at 1. differentiable only in π π,. 13. Ë x R apple Á ÊŸÊ f (x)= x 1, g(x)=cosx ÃÕÊ ϕ(x)=f (g( sinx)) g( f (x)) Ò, ÃÊapple ϕ R apple àÿapple Á ŒÈ U fl ŸËÿ Ò () 0 U fl ŸËÿ Ÿ Ë Ò 1 U fl ŸËÿ Ÿ Ë Ò π π apple fl, apple fl ŸËÿ Ò 14. If f (x)= x 16 for all x R, then the total number of points of R at which f : R R attains local extreme values, is : 1 () Let x x e e I= d x, J= dx 4x x 4x x e+ e+ 1 e + e + 1 then, J I equals : 14. ÿáœ Ë x R apple Á f (x)= x 16 Ò, ÃÊapple R apple Ÿ Á ŒÈ Êapple Ë ÅÿÊ Ê f : R R, SÕÊŸËÿ U (extreme) ÊŸ appleãê Ò, Ò 1 () ÊŸÊ x x e e I= d x, J= dx 4x x 4x x e+ e+ 1 e + e + 1 Ò, ÃÊapple J I UÊ U Ò 4x x 1 e e+ 1 log e 4 C x x + e+ e+ 1 4x x 1 e e+ 1 log e 4 C x x + e+ e+ 1 () x x 1 e++ e 1 log e C x x + e + e 1 () x x 1 e++ e 1 log e C x x + e + e 1 x x 1 e + e 1 log e C x x + e++ e 1 x x 1 e + e 1 log e C x x + e++ e 1 4x x 1 e+ e+ 1 log e 4 C x x + e e+ 1 (where C is a constant of integration) 4x x 1 e+ e+ 1 log e 4 C x x + e e+ 1 ( Ê C Ê Ÿ ø U Ò) R/Page 7 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

8 16. If x x d x = mπ+ n 1 x 0 ordered pair (m, n) is equal to :, then the 16. ÿᜠx x d x = mπ+ n 1 x 0 ÿèç (m, n) UÊ U Ò Ò, ÃÊapple Á à 1 1, , 3 8 () 1, 8 3 () 1, , , , , The area (in sq. units) of the region bounded by the curve, 1y=36 x and the tangents drawn to it at the points, where the curve intersects the x-axis, is : 1 () Let y=y(x) be the solution of the differential equation : dy x log ex y 3 x log x, ( x > 1) d e x +=. If y(e)=0, then y(e ) is equal to : e 17. fl 1y=36 x ÃÕÊ U Ÿ Á ŒÈ Êapple, Ê fl x- ˇÊ Ê ÁÃë appleuœ UÃË Ò, U πë øë ªß S Ê appleuπê Êapple apple Ëø ÁÉÊ appleu ˇÊappleòÊ Ê ˇÊappleòÊ» (flª ß ÊßÿÊapple apple ) Ò 1 () ÊŸÊ y=y(x) fl Ë UáÊ dy x log ex y 3 x log ex, ( x > 1) dx += Ê Ò ÿᜠy(e)=0 Ò, ÃÊapple y(e ) UÊ U Ò e () 1 e () 1 e 3 e 3e 3 e 3e R/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

9 19. Let the straight lines, 5x 3y+15=0 and 5x+3y 15=0 form a triangle with the x-axis. Then the radius of the circle circumscribing this triangle is : 19. ÊŸÊ appleuπê 5x 3y+15=0 ÃÕÊ 5x+3y 15=0 ÃÕÊ x- ˇÊ apple ÊÕ ÁòÊ È ŸÊÃapple Ò, ÃÊapple ÁòÊ È apple Á UflÎûÊ Ë ÁòÊíÿÊ Ò () 17 5 () The mirror image of the circle x +y 10x 10y=0 in the line x+y+5=0 is a circle passing through the point : ( 3, 7) () ( 9, 7) ( 3, 11) ( 9, 11) 0. flîûê x +y 10x 10y=0 Ê appleuπê x+y+5=0 apple Œ áê ÁÃÁ flîûê Ò Êapple Á Á ŒÈ apple Êapple U ÊÃÊ Ò, fl Ò ( 3, 7) () ( 9, 7) ( 3, 11) ( 9, 11) 1. Let S be the focus of the parabola, x +8y=0 and Q be any point on it. If P divides the line segment SQ in the ratio 1 :, then the locus of P is : 9x +4y+3=0 () 9y +4x+3=0 3x +7y+36=0 3y +7x+36=0 1. ÊŸÊ Ufl ÿ x +8y=0 Ë ŸÊÁ S Ò ÃÕÊ Q U Êappleß Á ŒÈ Ò ÿᜠÁ ŒÈ P, appleuπêπ «U SQ Êapple 1 : apple ŸÈ Êà apple Ê UÃÊ Ò, ÃÊapple P Ê Á ŒÈ Õ Ò 9x +4y+3=0 () 9y +4x+3=0 3x +7y+36=0 3y +7x+36=0 R/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

10 . Let π θ 0,. If the eccentricity of the hyperbola x cos θ y =6cos θ is 3 times the eccentricity of the ellipse x +y cos θ=30cos θ then θ is equal to : π. ÊŸÊ θ 0, ÿᜠÁà Ufl ÿ x cos θ y =6cos θ Ë à apple 㜠ÃÊ, ŒËÉÊ flîûê x +y cos θ=30cos θ Ë à apple 㜠ÃÊ Ê 3 ªÈŸË Ò, ÃÊapple θ UÊ U Ò π 6 π 6 () π 4 () π 4 cos cos π 3 π 3 x 1 y+ 3 z If the line = = lies in the 4 1 plane x+ly+mz=16, then l +m is equal to : 3. ÿᜠappleuπê x 1 y+ 3 z+ 5 = = 4 1, à x+ly+mz=16 apple ÁSÕà Ò, ÃÊapple l +m UÊ U Ò () 0 () R/Page 10 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

11 4. The equation of the plane passing through the line of intersection of the planes ( i j+ k) = and ( i j ) r r + 4= 0 and perpendicular to the plane ( i j k) r + 4= 0, is : ( i j k) r + 4 = 3 () ( i j k) r + 4 = 5 ( i j k) r + 5 = 3 ( i j k) r + 5 = 5 4. Ã Ê Ë UáÊ, Êapple à Êapple ( i j+ k) = ÃÕÊ ( i j ) r r + 4= 0 Ë ÁÃë appleuœë appleuπê apple Êapple U ÊÃÊ Ò, ÃÕÊ Ã ( i j k) r = apple flã Ò, Ò ( i j k) r + 4 = 3 () ( i j k) r + 4 = 5 ( i j k) r + 5 = 3 ( i j k) r + 5 = 5 5. If a, b, c be three unit vectors, b and c are non-parallel, such that ( ) b c + a b c =, then the angle between a and b is : 5. ÿᜠa, b, c ÃËŸ ÁŒ Ê Ò, b ÃÕÊ c Ê Ã U Ÿ Ë Ò, apple apple Á ( ) b c + a b c = Ò, ÃÊapple a ÃÕÊ b apple Ëø Ê ÊappleáÊ Ò π 6 π 6 () π 3 () π 3 π 4 π 4 3π 4 3π 4 R/Page 11 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

12 6. A box contains 6 red balls and black balls. Two balls are drawn, at random, from it without replacement. If X denotes the number of red balls drawn, then E(X) is equal to : 6. Ä apple apple 6 Ê ªapple Œapple Ò ÃÕÊ Ê Ë ªapple Œapple Ò Ä apple apple apple ŒÊapple ªapple Œapple ÿêœîë UÿÊ, Á ŸÊ ÁÃSÕÊ ŸÊ apple, ÁŸ Ê Ë ÊÃË Ò ÿᜠX ÁŸ Ê Ë ªß Ê ªapple ŒÊapple Ë ÅÿÊ Œ ÊÊ ÃÊ Ò, ÃÊapple E(X) UÊ U Ò 3 3 () 1 () A six faced die is so biased that it is thrice likely to show an even number than an odd number, when thrown. If the die is thrown twice, the probability that sum of the numbers on the die is even, is : 7. «U» Ëÿ Ê apple Êapple ß Ê U Á ŸÃ (biased) ŸÊÿÊ ªÿÊ Ò Á ß apple»apple Ÿapple U ÅÿÊ ÊŸapple Ë ÊflŸÊ, Áfl ÅÿÊ apple ÊŸapple Ë ÊflŸÊ Ë ÃËŸ ªÈŸË Ò ÿáœ Ê Ê ŒÊapple Ê U UÊ Ê ªÿÊ, ÃÊapple Ê apple U Êapple Ê ÿêappleª ÅÿÊ ÊŸapple Ë ÊÁÿ ÃÊ Ò () 5 8 () R/Page 1 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

13 8. The total number of x [0, π] which satisfy the equation 4(cos 10 x+sin x)=4+sin 6 x sin (x), is : () x [0, π] apple ÁSÕà apple Ë È ÅÿÊ Êapple Ë UáÊ 4(cos 10 x+sin x)=4+sin 6 x sin (x) Êapple ÃÈc U UÃË Ò, Ë ÅÿÊ Ò () tan sin cos is equal 9. tan sin cos UÊ U Ò to : () 3 () The Boolean expression (p q) ((~ q) p) is equivalent to : ~ p q () ~ q p p q (~ p) (~ q) 30. Í Ëÿ (Boolean) ÿ (p q) ((~ q) p) apple ÃÈÀÿ Ò ~ p q () ~ q p p q (~ p) (~ q) R/Page 13 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

14 Part II / ʪ II Aptitude Test / Á L Áø UˡÊáÊ Directions : (For Q. No. 31 to 34). ÁŸŒapple Ê (. 31 apple 34 apple Á ) Problem Figure / Ÿ Ê Î Áà For the elevation given in the problem figure identify the correct 3-D figure from amongst the answer figures. ŒË ªÿË Ÿ Ê Î Áà apple ê Èπ ŒÎ ÿ Êapple Ë 3-D ûê U Ê Î ÁÃÿÊapple apple apple øêáÿÿapple Answer Figures / ûê U Ê Î ÁÃÿÊ 31. () 3. () 33. () 34. () R/Page 14 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

15 Directions : (For Q. No. 35 to 37). The 3-D figure shows the view of an object. Identify the correct top view from amongst the answer figures. ÁŸŒapple Ê (. 35 apple 37 apple Á ) 3-D Ÿ Ê Î Áà apple flsãè apple ŒÎ ÿ Êapple ÁŒπÊÿÊ ªÿÊ Ò ß Ê Ë UË ŒÎ ÿ, ûê U Ê Î ÁÃÿÊapple apple apple øêáÿÿapple Problem Figure / Answer Figures / ûê U Ê Î ÁÃÿÊ Ÿ Ê Î Áà 35. () 36. () 37. () Directions : (For Q. No. 38 to 41). ÁŸŒapple Ê (. 38 apple 41 apple Á ) Find the odd figure out of the problem figures given below. ŸËøapple ŒË ªÿË Ÿ Ê Î ÁÃÿÊapple apple apple Áfl Ê Î Áà øêáÿÿapple 38. () R/Page 15 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

16 39. () 40. () 41. () Directions : (For Q. No. 4 to 47). ÁŸŒapple Ê (. 4 apple 47 apple Á ) Which one of the answer figures will complete the sequence of the three problem figures? ûê U Ê Î ÁÃÿÊapple apple apple ÊÒŸ- Ë Ê Î Áà Êapple ÃËŸ Ÿ Ê Î ÁÃÿÊapple apple ªÊŸapple apple ŸÈ (sequence) Í UÊ Êapple ÊÿappleªÊ? Problem Figures / Ÿ Ê Î ÁÃÿÊ Answer Figures / ûê U Ê Î ÁÃÿÊ 4. () R/Page 16 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

17 Problem Figures / Ÿ Ê Î ÁÃÿÊ Answer Figures / ûê U Ê Î ÁÃÿÊ 43. () 44. () 45. () 46. () 47. () R/Page 17 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

18 Directions : (For Q. No. 48 to 53). ÁŸŒapple Ê (. 48 apple 53 apple Á ) Which one of the answer figures shows the correct view of the 3 D problem figure after the problem figure is opened up? 3 D Ÿ Ê Î Áà Êapple πêapple Ÿapple U, ûê U Ê Î ÁÃÿÊapple apple apple Ë ŒÎ ÿ ÊÒŸ- Ê Ò? Problem Figure / Ÿ Ê Î Áà Answer Figures / ûê U Ê Î ÁÃÿÊ 48. () 49. () 50. () R/Page 18 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

19 Problem Figure / Ÿ Ê Î ÁÃ Answer Figures / ûê U Ê Î ÁÃÿÊ 51. () 5. () 53. () R/Page 19 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

20 Directions : (For Q. No. 54 to 57). The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures. ÁŸŒapple Ê (. 54 apple 57 apple Á ) Ÿ Ê Î Áà apple flsãè Êapple Ê UË ŒÎ ÿ ÁŒπÊÿÊ ªÿÊ Ò ÃË U Ë ÁŒ ÊÊ apple ŒappleπÃapple È ûê U Ê Î ÁÃÿÊapple apple apple Ë ê Èπ ŒÎ ÿ øêáÿÿapple Problem Figure / Ÿ Ê Î Áà Answer Figures / ûê U Ê Î ÁÃÿÊ 54. () 55. () 56. () 57. () R/Page 0 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

21 Directions : (For Q. No. 58 to 61). ÁŸŒapple Ê (. 58 apple 61 apple Á ) Which one of the answer figures is the correct mirror image of the problem figure with respect to X - X? ûê U Ê Î ÁÃÿÊapple apple apple ÊÒŸ- Ë Ê Î Áà ŒË ªÿË Ÿ Ê Î ÁÃ Ê X - X apple ê ÁœÃ Ë Œ áê ÁÃÁ ê Ò? Problem Figure / Ÿ Ê Î Áà Answer Figures / ûê U Ê Î ÁÃÿÊ 58. () 59. () 60. () 61. () R/Page 1 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

22 Directions : (For Q. No. 6 to 65). ÁŸŒapple Ê (. 6 apple 65 apple Á ) The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures. Ÿ Ê Î Áà apple flsãè Êapple Ê UË ŒÎ ÿ ÁŒπÊÿÊ ªÿÊ Ò ÃË U Ë ÁŒ ÊÊ apple ŒappleπÃapple È ûê U Ê Î ÁÃÿÊapple apple apple Ë ê Èπ ŒÎ ÿ øêáÿÿapple Problem Figure / Ÿ Ê Î Áà Answer Figures / ûê U Ê Î ÁÃÿÊ 6. () 63. () 64. () 65. () R/Page SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

23 66. Which out of the following is the country called the Roof of the World? Japan () Tibet Mongolia Uzbekistan 66. ÁŸêŸÁ Áπà apple apple ÊÒŸ Ê Œapple Ê M» ÊÚ» Œ flà«u ÊÃÊ Ò? Ê ÊŸ () ÁÃé à ªÊappleÁ ÿê ï appleá SÃÊŸ 67. Which one of the following has a better insulation value? A concrete wall () A brick wall A cavity wall A stone wall 67. ÁŸêŸ apple apple ÊÒŸ Ê apple à U ßã È apple ÊŸ ÊŸ Ò? Ë U Ë ŒËflÊ U () ßZ U Ë ŒËflÊ U ªÈ Ê ŒËflÊ U àõ U Ë ŒËflÊ U 68. Which one of the following is a renewable source of energy? Coal () Natural Gas Ocean waves Oil 68. ÁŸêŸÁ Áπà apple apple ÊÒŸ- Ë Ê Ê ˇÊÿ dêappleã Ò? Êappleÿ Ê () Ê Î Áà ªÒ Ê Êª U apple U Ãapple 69. Charles Correa was which of the following? A British Architect () An Indian Architect An American Architect A Brazilian Architect 69. øêà ÊappleÁ UÿÊ ÁŸêŸÁ Áπà apple apple ÊÒŸ ÕÊ? Á Á U Ê flêsãè Ê U () Ê UÃËÿ flêsãè Ê U appleá U Ë flêsãè Ê U Ê Ë Ë flêsãè Ê U R/Page 3 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

24 70. Who amongst the following is not a qualified architect? Remo Fernandes () Arundhati Roy Satish Gujral B.V. Doshi 70. ÁŸêŸÁ Áπà apple apple ÊÒŸ ÿêappleçÿ flêsãè Ê U Ÿ Ë Ò? appleu Êapple» ŸÊZ«UË () L œáã UÊÿ ÃË Ê ªÈ UÊ Ë.flË. ŒÊapple ÊË 71. Ellora group of temples represent which of the following? Hindu Religion () Buddhist Religion Jain Religion All of the above 71. Êapple UÊ Í Ê ÁŒ U ÁŸêŸ apple apple Á Ê ÁÃÁŸÁœàfl UÃÊ Ò? Á ŒÍ œ () ÊÒh œ ÒŸ œ UÊappleÄÃ Ë 7. Parthenon is located in which country? Romania () Russia Greece Japan 7. ÊÕapple ŸŸ Á Œapple Ê apple ÁSÕà Ò? UÊapple ÊÁŸÿÊ () M ª Ë Ê ÊŸ 73. Which of the following is equivalent to the Nobel Prize in architecture? Academy Award () Padma Shree Pritzker Prize Star of Architecture 73. ÁŸêŸÁ Áπà apple apple ÊÒŸ Ê flêsãè Ê apple ŸÊapple apple È US Ê U apple UÊ U Ò? ÊŒ Ë È US Ê U () k üêë Á ï U È US Ê U ÊÁ appleäø U apple S UÊ U R/Page 4 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

25 74. An escalator looks like which one of the following? Ladder () Staircase Ramp Lift 74. S apple apple U U ÁŸêŸÁ Áπà apple apple Á apple Ò Ê ÁŒπÃÊ Ò? Ë Ë () Ë Ë (S appleu U apple ) Ò U Á ç U 75. Who amongst the following is an architect? Vikram Seth () Lauri Baker Khushwant Singh Ruskin Bond 75. ÁŸêŸÁ Áπà apple apple flêsãè Ê U ÊÒŸ Ò? Áfl apple U () ÊÒ UË apple U πè Êfl à Á UÁS Ÿ ÊÚã«U 76. Burj Khalifa is located in which one of the following countries? Saudi Arabia () Dubai Turkey Afghanistan 76. È π Ë» Ê Á Œapple Ê apple ÁSÕà Ò? ŒË U () ŒÈ ß ÃÈ Ë» ªÊÁŸSÃÊŸ 77. Which of the following is the most striking feature of the Sydney Opera House? Entrance Hall () Interior Design Sail shaped roof Location 77. ÁŸêŸ apple apple ÊÒŸ Ë Á «UŸË Êapple apple UÊ Ê Ë apple àfl ÍáÊ Áfl Êapple ÃÊ Ò? flapple Ê ÊÚ () Ê ÃÁ U Á«U Êߟ Ê Ê Ê U Ë Uà SÕÊŸ R/Page 5 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

26 78. Which one of the following is an odd combination? Forts and Jaipur () Lakes and Udaipur Temples and Madurai Rain and Kutch 78. ÁŸêŸ apple apple ÊÒŸ Ê Ë ÿêapple Ÿ Ò? Á apple ÊÒ U ÿ È U () ÊË apple ÊÒ U Œÿ È U ÁŒ U ÊÒ U ŒÈ Ò fl Ê ÊÒ U ë U 79. Tsunami is a result of which of the following? Sea storms () Earthquakes in coastal areas Earthquakes in the sea bed Strong ocean waves 79. ÈŸÊ Ë Êapple ÁŸêŸ apple apple Á Ê Á UáÊÊ Ò? ʪ U ÃÍ» ÊŸ () à UËÿ ß Ê Êapple apple Í ÈŒ à apple Í ÊÄÃ Ê Êª U apple U 80. Chandigarh was planned by an architect who was which of the following? American () French German Australian 80. ø «U˪ Êapple flêsãè Ê U mê UÊ ÁŸÿÊappleÁ à Á ÿê ªÿÊ ÕÊ Êapple ÁŸêŸÁ Áπà apple apple ÕÊ appleá U Ë ()» apple ø Ÿ ÊÚS apple UÁ ÿêß - o 0 o - - o 0 o - SPACE FOR ROUGH WORK / U» Êÿ apple Á ª R/Page 6 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

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28 Space For Rough Work /» Êÿ apple Á ª R/Page 8 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

29 Space For Rough Work /» Êÿ apple Á ª R/Page 9 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

30 Space For Rough Work /» Êÿ apple Á ª R/Page 30 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

31 Space For Rough Work /» Êÿ apple Á ª R/Page 31 SPACE FOR ROUGH WORK / U» Êÿ apple Á ª

32 Read the following instructions carefully : 1. Part I has 30 objective type questions of Mathematics consisting of FOUR marks each for each correct response. Part II (Aptitude Test) has 50 objective type questions consisting of FOUR marks for each correct response. Part III consists of questions carrying 70 marks which are to be attempted on a separate Drawing Sheet which is also placed inside this Test Booklet. Marks allotted to each question are written against each question. For each incorrect response in Part I and Part II, ¼ (one fourth) marks of the total marks allotted to the question (i.e. 1 mark) would be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet.. Handle the Test Booklet, Answer Sheet and Drawing Sheet with care, as under no circumstances (except for discrepancy in Test Booklet Code and Answer Sheet Code), another set will be provided. 3. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/ writing work are to be done on the space provided for this purpose in the Test Booklet itself, marked Space for Rough Work. This space is given at the bottom of each page and in five pages (Page 7-31) at the end of the booklet. 4. Each candidate must show on demand his/her Admit Card to the Invigilator. 5. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat. 6. On completion of the test, the candidates should not leave the examination hall without handing over their Answer Sheet of Mathematics and Aptitude Test - Part I & II and Drawing Sheet of Aptitude Test-Part III to the Invigilator on duty and sign the Attendance Sheet at the time of handing over the same. Cases where a candidate has not signed the Attendance Sheet the second time will be deemed not have handed over these documents and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet. However, the candidates are allowed to take away with them the Test Booklet of Mathematics and Aptitude Test - Part I & II. 7. Use of Electronic/Manual Calculator or drawing instruments (such as scale, compass etc.) are not allowed. 8. The candidates are governed by all Rules and Regulations of the Examination body with regard to their conduct in the Examination Hall. All cases of unfair means will be dealt with as per the Rules and Regulations of the Examination body. 9. No part of the Test Booklet, Answer Sheet and Drawing Sheet shall be detached/folded or defaced under any circumstances. 10. The candidates will write the Test Booklet Number as given in the Test Booklet, Answer Sheet and Drawing Sheet in the Attendance Sheet also. 11. Candidates are not allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material except the Admit Card inside the examination room/hall. R/Page 3 ÁŸêŸÁ Áπà ÁŸŒapple Ê äÿêÿ apple apple 1. ÈÁSÃ Ê apple ʪ I apple ªÁáÊà apple 30 flsãèáÿd Ÿ Ò Á apple àÿapple Ÿ apple Ë ûê U apple Á øê U ÁŸœÊ Á Uà Á ÿapple ªÿapple Ò Êª II ( Á L Áø UˡÊáÊ) apple 50 flsãèáÿd Ÿ Ò Á Ÿ apple àÿapple Ë ûê U apple Á øê U Ò ÈÁSÃ Ê apple ʪ III apple Ÿ Ò Á Ÿ apple Á 70 ÁŸœÊ Á UÃ Ò ÿ Ÿ ß Ë UˡÊÊ ÈÁSÃ Ê apple 㜠U UπË «UÊß ª ÊË U U UŸapple Ò àÿapple Ÿ appleãè ÁŸœÊ Á Uà Ÿ apple ê Èπ Á Ã Ò Êª I ÊÒ U ʪ II apple àÿapple ª à ûê U apple Á Ÿ apple Á ÁŸœÊ Á UÃ È Êapple apple apple ¼ ( -øêòõêß ) ʪ ( ÕÊ Ã 1 ) È ÿêappleª apple apple Ê U Á Ê ªapple ÿᜠûê U òê apple Á Ë Ÿ Ê Êappleß ûê U Ÿ Ë ÁŒÿÊ ªÿÊ Ò, ÃÊapple È ÿêappleª apple apple Êappleß Ÿ Ë Ê appleu Ê ªapple. UˡÊÊ ÈÁSà Ê, ûê U òê fl «UÊß ª ÊË U Ê äÿêÿ Ífl ÿêappleª apple U, ÄÿÊapple Á Á Ë Ë Á UÁSÕÁà apple ( apple fl UˡÊÊ ÈÁSÃ Ê fl ûê U òê apple Êapple«U apple Á ÛÊÃÊ Ë ÁSÕÁà Êapple UÊapple«U) ŒÍ UË UˡÊÊ ÈÁSÃ Ê éœ Ÿ Ë UÊÿË Ê ªË 3. èÿáõ ÿêapple Êapple ûê U òê U Êappleß Ë U» Êÿ ÿê Á πêß Ê Ê UŸapple Ë ŸÈ Áà Ÿ Ë Ò Ë ªáÊŸÊ fl Á πêß Ê Ê, UˡÊÊ ÈÁSÃ Ê apple ÁŸœÊ Á Uà ª Êapple Á U» Êÿ apple Á ª mê UÊ ŸÊ Ê Á à Ò, U Ë Á ÿê ÊÿappleªÊ ÿ ª àÿapple Îc U U ŸËøapple Ë Êapple U ÃÕÊ ÈÁSÃ Ê apple à apple Ê ø Îc UÊapple ( Îc U 7-31) U ŒË ªß Ò 4. Ê ªapple ÊŸapple U àÿapple èÿõë ÁŸ UËˇÊ Êapple ŸÊ flapple Ê Ê«U ÁŒπÊ 5. œëˇê ÿê ÁŸ UËˇÊ Ë Áfl Êapple ŸÈ Áà apple Á ŸÊ Êappleß èÿõë ŸÊ SÕÊŸ Ÿ UÊapple«apple 6. UˡÊÊ Ê# ÊappleŸapple U, èÿõë ÁŸ UËˇÊ Êapple Êapple Ÿapple ªÁáÊà - ʪ I fl Á L Áø UˡÊáÊ - ʪ II Ê ûê U òê fl Á L Áø UˡÊáÊ- ʪ III Ë «UÊß ª ÊË U ŒappleŸapple ÊÒ U ÁSÕÁà òê U Ÿapple SÃÊˇÊ U ŒÊapple Ê UÊ UŸapple apple øêã Ë UˡÊÊ Ê UÊapple«apple apple Ê Ÿ UŸapple U ÿ ÊŸÊ ÊÿappleªÊ Á ûê U òê fl «UÊß ª ÊË U Ÿ Ë ÊÒ UÊ ª Ò Á apple ŸÈÁøà ʜŸ ÿêappleª Ë üêappleáêë apple ÊŸÊ ÊÿappleªÊ èÿõë Ÿapple Êÿapple ÊÕ apple ªÍ appleu Ê ÁŸ ÊÊŸ ÁSÕÁà òê apple ÁŒ ª SÕÊŸ U fl ÿ ªÊ ÃÕÊÁ, èÿõë ŸË ªÁáÊà fl Á L Áø UˡÊáÊ - ʪ I fl II Ë UˡÊÊ ÈÁSÃ Ê Êapple apple Ê Ãapple Ò 7. ß appleä UÊÚÁŸ / SÃøÊÁ à Á U ÿê «UÊß ª UáÊ ( Ò apple Á S apple, Ê ßàÿÊÁŒ) Ê ÿêappleª flá Ã Ò 8. UˡÊÊ Ê apple Êø UáÊ apple Á èÿõë UˡÊÊ ÁŸ Êÿ apple ÁŸÿ Êapple fl ÁflÁŸÿ Êapple mê UÊ ÁŸÿÁ à Êapple ªapple ŸÈÁøà ʜŸ ÿêappleª apple Ë Ê Êapple Ê»Ò Ê UˡÊÊ ÁŸ Êÿ apple ÁŸÿ Êapple fl ÁflÁŸÿ Êapple apple ŸÈ Ê U ÊappleªÊ 9. Á Ë Ë ÁSÕÁà apple UˡÊÊ ÈÁSà Ê, ûê U òê fl «UÊß ª ÊË U Ê Êappleß Ë Êª Ÿ ÃÊapple ª Á ÿê Ê ªÊ ÊÒ U Ÿ Ë Êapple«Ê ÊÿappleªÊ ÕflÊ Á ªÊ«Ê ÊÿappleªÊ 10. UˡÊÊ ÈÁSà Ê, ûê U òê fl «UÊß ª ÊË U apple ŒË ªß UˡÊÊ ÈÁSÃ Ê ÅÿÊ Êapple èÿõë Ë Ã UË apple apple ÊÁ$ UË òê apple Ë Á πapple 11. èÿõë mê UÊ UˡÊÊ ˇÊ/ ÊÚ apple flapple Ê Ê«U apple ÊflÊ Á Ë Ê U Ë Ê Uÿ Ê ª Ë, ÈÁŒ à ÿê SÃÁ ÁπÃ, ʪ Ë Áø ÿê, apple U, Êapple Êß» ÊappleŸ, ß appleä UÊÚÁŸ UáÊ ÿê Á Ë ãÿ Ê U Ë Ê ª Ë Êapple apple ÊŸapple ÿê ÿêappleª UŸapple Ë ŸÈ Áà Ÿ Ë Ò