Page 1 Mechanical Paper Set-2 2016 Page 1 2016 paper set-II Q.1-Q.5 carry one mark each Q1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low s1 Correct option is (C) â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. Q2 The unruly crowd demanded that the accused be ______ without trial. (A) hanged (B) hanging (C) hankering (D) hung s1 Correct option is (A) â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. Q3 Choose the statement(s) where the underlined word is used correctly. (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only s1 Correct option is (D) â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Q4 Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below in NOT logically possible, based on the given fact? (A) If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) s1 Correct option is (C) Statements (i) and (ii) are not logically possible based on the given fact. Q5 A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m 2 is ______ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 s1 Correct option is (B) From the given data, the following window is possible The perimeter of the window x 5 = 6 = m x 5 6 = . 120 = m Area of the window = Area of square+Area of e l T .. . 12 12 4 3 12 2 ## =+ ^h .. 1440 623 =+ .m 206 2 = Q.6-Q.10 carry two marks each Q6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group, Q was 5. Assuming that the marks were distributed on a normal distribution which of the following statements will have the highest probability of being TRUE? (A) No students in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. Page 2 Mechanical Paper Set-2 2016 Page 1 2016 paper set-II Q.1-Q.5 carry one mark each Q1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low s1 Correct option is (C) â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. Q2 The unruly crowd demanded that the accused be ______ without trial. (A) hanged (B) hanging (C) hankering (D) hung s1 Correct option is (A) â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. Q3 Choose the statement(s) where the underlined word is used correctly. (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only s1 Correct option is (D) â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Q4 Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below in NOT logically possible, based on the given fact? (A) If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) s1 Correct option is (C) Statements (i) and (ii) are not logically possible based on the given fact. Q5 A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m 2 is ______ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 s1 Correct option is (B) From the given data, the following window is possible The perimeter of the window x 5 = 6 = m x 5 6 = . 120 = m Area of the window = Area of square+Area of e l T .. . 12 12 4 3 12 2 ## =+ ^h .. 1440 623 =+ .m 206 2 = Q.6-Q.10 carry two marks each Q6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group, Q was 5. Assuming that the marks were distributed on a normal distribution which of the following statements will have the highest probability of being TRUE? (A) No students in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. Page 2 Mechanical Paper Set-2 2016 (C) Most students of group Q scored marks in a narrow- er range than students in group P. (D) The median of the marks of group P is 100. s1 Correct option is (C) Mean µ ^h 105 = Standard deviation, 1 s ^h 25 = ` 68% within one standard deviation 1 µ 1 s = 105 25 =- 80 = 11 µs + 105 25 =+ 130 = Distribution of P Group Q Mean 2 µ ^h 85 = Standard deviation, 2 s ^h 5 = Pr x << µs µs -+ ^h . 0 6827 - ` 68% within one standard deviation 22 µs - 85 5 =- 80 = 22 µs + 85 5 =+ 90 = ` range of Q in one standard deviation is 80 to 90 68% within one standard deviation of Q is narrower ` 68% within one standard deviation of Q means most students of group Q. ` Most students of group Q [\ scored marks in a narrower range than students in group P [\. Q7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) All smart cities encourage the formation of surveillances states. (ii) Surveillances is an integral part of a smart city. (iii) Sustainability and surveillance go hand in hand in a smart city. (iv) There is a perception that smart cities promote surveillance. (A) (i) and (iv) only (B) (ii) and (iii) only (C) (iv) only (D) (i) only s1 Correct option is (B) Q8 Find the missing sequence in the letter series. B, FH, LNP, ______ (A) SUWY (B) TUVW (C) TVXZ (D) TWXZ s1 Correct option is (C) The following letter series is in the order of even letters series. Q9 The binary operation 4 is defined as ab ab ab 4 =+ + ^h , where a and b are any two real number. The value of the identity element of this operation, defined as the number x such that ax a 4 = , for any a, is. (A) 0 (B) 1 (C) 2 (D) 10 s1 Correct option is (A) The binary operation 4 is defined & ab 4 ab ab =+ + ^h ax 4 a = ` From the equation b [\ is the variable Option A: x 0 = ao 4 a a 0 0 # =+ + ^h aa 0 =+ = Option B: x 1 = a 1 4 aa 11 # =+ + ^h aa 1 =+ + a 21 =+ Option C: x 2 = a 2 4 aa 22 & # ++ ^h aa 22 =+ + a 32 =+ Option D: x 10 = a 10 4 aa 10 10 & # ++ ^h Page 3 Mechanical Paper Set-2 2016 Page 1 2016 paper set-II Q.1-Q.5 carry one mark each Q1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low s1 Correct option is (C) â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. Q2 The unruly crowd demanded that the accused be ______ without trial. (A) hanged (B) hanging (C) hankering (D) hung s1 Correct option is (A) â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. Q3 Choose the statement(s) where the underlined word is used correctly. (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only s1 Correct option is (D) â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Q4 Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below in NOT logically possible, based on the given fact? (A) If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) s1 Correct option is (C) Statements (i) and (ii) are not logically possible based on the given fact. Q5 A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m 2 is ______ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 s1 Correct option is (B) From the given data, the following window is possible The perimeter of the window x 5 = 6 = m x 5 6 = . 120 = m Area of the window = Area of square+Area of e l T .. . 12 12 4 3 12 2 ## =+ ^h .. 1440 623 =+ .m 206 2 = Q.6-Q.10 carry two marks each Q6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group, Q was 5. Assuming that the marks were distributed on a normal distribution which of the following statements will have the highest probability of being TRUE? (A) No students in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. Page 2 Mechanical Paper Set-2 2016 (C) Most students of group Q scored marks in a narrow- er range than students in group P. (D) The median of the marks of group P is 100. s1 Correct option is (C) Mean µ ^h 105 = Standard deviation, 1 s ^h 25 = ` 68% within one standard deviation 1 µ 1 s = 105 25 =- 80 = 11 µs + 105 25 =+ 130 = Distribution of P Group Q Mean 2 µ ^h 85 = Standard deviation, 2 s ^h 5 = Pr x << µs µs -+ ^h . 0 6827 - ` 68% within one standard deviation 22 µs - 85 5 =- 80 = 22 µs + 85 5 =+ 90 = ` range of Q in one standard deviation is 80 to 90 68% within one standard deviation of Q is narrower ` 68% within one standard deviation of Q means most students of group Q. ` Most students of group Q [\ scored marks in a narrower range than students in group P [\. Q7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) All smart cities encourage the formation of surveillances states. (ii) Surveillances is an integral part of a smart city. (iii) Sustainability and surveillance go hand in hand in a smart city. (iv) There is a perception that smart cities promote surveillance. (A) (i) and (iv) only (B) (ii) and (iii) only (C) (iv) only (D) (i) only s1 Correct option is (B) Q8 Find the missing sequence in the letter series. B, FH, LNP, ______ (A) SUWY (B) TUVW (C) TVXZ (D) TWXZ s1 Correct option is (C) The following letter series is in the order of even letters series. Q9 The binary operation 4 is defined as ab ab ab 4 =+ + ^h , where a and b are any two real number. The value of the identity element of this operation, defined as the number x such that ax a 4 = , for any a, is. (A) 0 (B) 1 (C) 2 (D) 10 s1 Correct option is (A) The binary operation 4 is defined & ab 4 ab ab =+ + ^h ax 4 a = ` From the equation b [\ is the variable Option A: x 0 = ao 4 a a 0 0 # =+ + ^h aa 0 =+ = Option B: x 1 = a 1 4 aa 11 # =+ + ^h aa 1 =+ + a 21 =+ Option C: x 2 = a 2 4 aa 22 & # ++ ^h aa 22 =+ + a 32 =+ Option D: x 10 = a 10 4 aa 10 10 & # ++ ^h Mechanical Paper Set-2 2016 Page 3 aa 10 10 =+ + a 11 10 =+ ` Option A only True. Q10 Which of the following curves represents the function ln ye sin x = _ ` ^ i j h for x 2 < p ? Here, x represents the abscissa and y represents the ordinate. s1 Correct option is (C) Q.11-Q.35 carry one mark each. Q11 The condition for which the eigen values of the matrix A k 2 1 1 = >H are positive, is (A) / k 12 > (B) k 2 >- (C) k 0 > (D) / k 12 <- s1 Correct option is (A) A k 2 1 1 = >H If , 12 ll are eigen values of A x 22 then A 12 ll = A k 21 =- , 12 ll 0 > k 21 - 0 > ` k 2 1 > Q12 The values of x for which the function fx xx xx 34 34 2 2 = +- -- ^h is NOT continuous are (A) 4 and 1 - (B) 4 and 1 (C) 4 - and 1 (D) 4 - and -1 s1 Correct option is (C) 4 - and 1 The function, fx ^h xx xx 34 34 2 2 = +- -- is not defined at x 1 = and x 4 =- ` The function fx ^h is not continuous at , x 41 =- . Q13 Laplace transform of cos t ? ^h is (A) s s 22 ? + (B) s 22 w w + (C) s s 22 ? - (D) s 22 w w - s1 Correct option is (A) cos Lt ? ^h #- s s 22 ? = + cos Lat sa s 22 ` = + ^ b h l #- Q14 A function f of the complex variable zx iy =+ , is given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and , vx yx y 22 =- ^h . The value of k, for which the function is analytic, is _____ s1 Correct answer is 1 - Given, u kxy 2 = & vx y 22 =- u x v y = & ky 2 y 2 =- ` k 1 =- Q15 Numerical integration using trapezoidal rule gives the best result for a single variable function, which is (A) linear (B) parabolic (C) logarithmic (D) hyperbolic s1 Correct option is (A) fx ^h is a linear function. Q16 A point mass having mass M is moving with a velocity V at an angle ? to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth walls and rebounds. The total change (final minus initial) in the momentum of the mass is Page 4 Mechanical Paper Set-2 2016 Page 1 2016 paper set-II Q.1-Q.5 carry one mark each Q1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low s1 Correct option is (C) â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. Q2 The unruly crowd demanded that the accused be ______ without trial. (A) hanged (B) hanging (C) hankering (D) hung s1 Correct option is (A) â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. Q3 Choose the statement(s) where the underlined word is used correctly. (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only s1 Correct option is (D) â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Q4 Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below in NOT logically possible, based on the given fact? (A) If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) s1 Correct option is (C) Statements (i) and (ii) are not logically possible based on the given fact. Q5 A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m 2 is ______ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 s1 Correct option is (B) From the given data, the following window is possible The perimeter of the window x 5 = 6 = m x 5 6 = . 120 = m Area of the window = Area of square+Area of e l T .. . 12 12 4 3 12 2 ## =+ ^h .. 1440 623 =+ .m 206 2 = Q.6-Q.10 carry two marks each Q6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group, Q was 5. Assuming that the marks were distributed on a normal distribution which of the following statements will have the highest probability of being TRUE? (A) No students in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. Page 2 Mechanical Paper Set-2 2016 (C) Most students of group Q scored marks in a narrow- er range than students in group P. (D) The median of the marks of group P is 100. s1 Correct option is (C) Mean µ ^h 105 = Standard deviation, 1 s ^h 25 = ` 68% within one standard deviation 1 µ 1 s = 105 25 =- 80 = 11 µs + 105 25 =+ 130 = Distribution of P Group Q Mean 2 µ ^h 85 = Standard deviation, 2 s ^h 5 = Pr x << µs µs -+ ^h . 0 6827 - ` 68% within one standard deviation 22 µs - 85 5 =- 80 = 22 µs + 85 5 =+ 90 = ` range of Q in one standard deviation is 80 to 90 68% within one standard deviation of Q is narrower ` 68% within one standard deviation of Q means most students of group Q. ` Most students of group Q [\ scored marks in a narrower range than students in group P [\. Q7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) All smart cities encourage the formation of surveillances states. (ii) Surveillances is an integral part of a smart city. (iii) Sustainability and surveillance go hand in hand in a smart city. (iv) There is a perception that smart cities promote surveillance. (A) (i) and (iv) only (B) (ii) and (iii) only (C) (iv) only (D) (i) only s1 Correct option is (B) Q8 Find the missing sequence in the letter series. B, FH, LNP, ______ (A) SUWY (B) TUVW (C) TVXZ (D) TWXZ s1 Correct option is (C) The following letter series is in the order of even letters series. Q9 The binary operation 4 is defined as ab ab ab 4 =+ + ^h , where a and b are any two real number. The value of the identity element of this operation, defined as the number x such that ax a 4 = , for any a, is. (A) 0 (B) 1 (C) 2 (D) 10 s1 Correct option is (A) The binary operation 4 is defined & ab 4 ab ab =+ + ^h ax 4 a = ` From the equation b [\ is the variable Option A: x 0 = ao 4 a a 0 0 # =+ + ^h aa 0 =+ = Option B: x 1 = a 1 4 aa 11 # =+ + ^h aa 1 =+ + a 21 =+ Option C: x 2 = a 2 4 aa 22 & # ++ ^h aa 22 =+ + a 32 =+ Option D: x 10 = a 10 4 aa 10 10 & # ++ ^h Mechanical Paper Set-2 2016 Page 3 aa 10 10 =+ + a 11 10 =+ ` Option A only True. Q10 Which of the following curves represents the function ln ye sin x = _ ` ^ i j h for x 2 < p ? Here, x represents the abscissa and y represents the ordinate. s1 Correct option is (C) Q.11-Q.35 carry one mark each. Q11 The condition for which the eigen values of the matrix A k 2 1 1 = >H are positive, is (A) / k 12 > (B) k 2 >- (C) k 0 > (D) / k 12 <- s1 Correct option is (A) A k 2 1 1 = >H If , 12 ll are eigen values of A x 22 then A 12 ll = A k 21 =- , 12 ll 0 > k 21 - 0 > ` k 2 1 > Q12 The values of x for which the function fx xx xx 34 34 2 2 = +- -- ^h is NOT continuous are (A) 4 and 1 - (B) 4 and 1 (C) 4 - and 1 (D) 4 - and -1 s1 Correct option is (C) 4 - and 1 The function, fx ^h xx xx 34 34 2 2 = +- -- is not defined at x 1 = and x 4 =- ` The function fx ^h is not continuous at , x 41 =- . Q13 Laplace transform of cos t ? ^h is (A) s s 22 ? + (B) s 22 w w + (C) s s 22 ? - (D) s 22 w w - s1 Correct option is (A) cos Lt ? ^h #- s s 22 ? = + cos Lat sa s 22 ` = + ^ b h l #- Q14 A function f of the complex variable zx iy =+ , is given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and , vx yx y 22 =- ^h . The value of k, for which the function is analytic, is _____ s1 Correct answer is 1 - Given, u kxy 2 = & vx y 22 =- u x v y = & ky 2 y 2 =- ` k 1 =- Q15 Numerical integration using trapezoidal rule gives the best result for a single variable function, which is (A) linear (B) parabolic (C) logarithmic (D) hyperbolic s1 Correct option is (A) fx ^h is a linear function. Q16 A point mass having mass M is moving with a velocity V at an angle ? to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth walls and rebounds. The total change (final minus initial) in the momentum of the mass is Page 4 Mechanical Paper Set-2 2016 (A) cos MV j 2 ? - t (B) sin MV j 2 ? t (C) cos MV j 2 ? t (D) sin MV j 2 ? - t s1 Correct option is (D) U v cossin Vi Vj qq =+ V v cossin Vi Vj qq =- mv T mV U =- ^h sin mV j 2 ? =- Q17 A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is (A) 2.0 (B) 1.0 (C) 0.5 (D) 0 s1 Correct option is (B) max 1 s t 1 = Q18 A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is (A) 0.25 (B) 0.50 (C) 1.0 (D) 2.0 s1 Correct option is (D) l h s s t pd t pd 4 2 = _ ^ i h 2 = Q19 The forces F 1 and F 2 in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is 0.25. The angle of wrap is 2 3p radians. It is given that R 1 = m and F21 = N. The torque (in N-m) exerted on the drum is ______ s1 Correct answer is 2.248 F F 2 1 e = µ? e ./ 0253 2 = # p . 3 248 = ` F 1 . 3 248 = N Torque, T FF r 12 # =- ^h . 3 248 1 1 # = - ^h . 2 248 = N-m Q20 A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among , mk and q is (A) qkm 2 = (B) qkm 2 = (C) q m k 2 = (D) q m k 2 = s1 Correct option is (B) Critical damping constant km 2 = q km 2 = Q21 A machine element XY , fixed at end X , is subjected to and axial load P, transverse load F, and a twisting moment T at its free and Y . The most critical point from the strength point of view is (A) a point on the circumference at location Y (B) a point at the center at location Y (C) a point on the circumference at location X Page 5 Mechanical Paper Set-2 2016 Page 1 2016 paper set-II Q.1-Q.5 carry one mark each Q1 The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low s1 Correct option is (C) â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. Q2 The unruly crowd demanded that the accused be ______ without trial. (A) hanged (B) hanging (C) hankering (D) hung s1 Correct option is (A) â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. Q3 Choose the statement(s) where the underlined word is used correctly. (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only s1 Correct option is (D) â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Q4 Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below in NOT logically possible, based on the given fact? (A) If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) s1 Correct option is (C) Statements (i) and (ii) are not logically possible based on the given fact. Q5 A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m 2 is ______ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 s1 Correct option is (B) From the given data, the following window is possible The perimeter of the window x 5 = 6 = m x 5 6 = . 120 = m Area of the window = Area of square+Area of e l T .. . 12 12 4 3 12 2 ## =+ ^h .. 1440 623 =+ .m 206 2 = Q.6-Q.10 carry two marks each Q6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group, Q was 5. Assuming that the marks were distributed on a normal distribution which of the following statements will have the highest probability of being TRUE? (A) No students in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. Page 2 Mechanical Paper Set-2 2016 (C) Most students of group Q scored marks in a narrow- er range than students in group P. (D) The median of the marks of group P is 100. s1 Correct option is (C) Mean µ ^h 105 = Standard deviation, 1 s ^h 25 = ` 68% within one standard deviation 1 µ 1 s = 105 25 =- 80 = 11 µs + 105 25 =+ 130 = Distribution of P Group Q Mean 2 µ ^h 85 = Standard deviation, 2 s ^h 5 = Pr x << µs µs -+ ^h . 0 6827 - ` 68% within one standard deviation 22 µs - 85 5 =- 80 = 22 µs + 85 5 =+ 90 = ` range of Q in one standard deviation is 80 to 90 68% within one standard deviation of Q is narrower ` 68% within one standard deviation of Q means most students of group Q. ` Most students of group Q [\ scored marks in a narrower range than students in group P [\. Q7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) All smart cities encourage the formation of surveillances states. (ii) Surveillances is an integral part of a smart city. (iii) Sustainability and surveillance go hand in hand in a smart city. (iv) There is a perception that smart cities promote surveillance. (A) (i) and (iv) only (B) (ii) and (iii) only (C) (iv) only (D) (i) only s1 Correct option is (B) Q8 Find the missing sequence in the letter series. B, FH, LNP, ______ (A) SUWY (B) TUVW (C) TVXZ (D) TWXZ s1 Correct option is (C) The following letter series is in the order of even letters series. Q9 The binary operation 4 is defined as ab ab ab 4 =+ + ^h , where a and b are any two real number. The value of the identity element of this operation, defined as the number x such that ax a 4 = , for any a, is. (A) 0 (B) 1 (C) 2 (D) 10 s1 Correct option is (A) The binary operation 4 is defined & ab 4 ab ab =+ + ^h ax 4 a = ` From the equation b [\ is the variable Option A: x 0 = ao 4 a a 0 0 # =+ + ^h aa 0 =+ = Option B: x 1 = a 1 4 aa 11 # =+ + ^h aa 1 =+ + a 21 =+ Option C: x 2 = a 2 4 aa 22 & # ++ ^h aa 22 =+ + a 32 =+ Option D: x 10 = a 10 4 aa 10 10 & # ++ ^h Mechanical Paper Set-2 2016 Page 3 aa 10 10 =+ + a 11 10 =+ ` Option A only True. Q10 Which of the following curves represents the function ln ye sin x = _ ` ^ i j h for x 2 < p ? Here, x represents the abscissa and y represents the ordinate. s1 Correct option is (C) Q.11-Q.35 carry one mark each. Q11 The condition for which the eigen values of the matrix A k 2 1 1 = >H are positive, is (A) / k 12 > (B) k 2 >- (C) k 0 > (D) / k 12 <- s1 Correct option is (A) A k 2 1 1 = >H If , 12 ll are eigen values of A x 22 then A 12 ll = A k 21 =- , 12 ll 0 > k 21 - 0 > ` k 2 1 > Q12 The values of x for which the function fx xx xx 34 34 2 2 = +- -- ^h is NOT continuous are (A) 4 and 1 - (B) 4 and 1 (C) 4 - and 1 (D) 4 - and -1 s1 Correct option is (C) 4 - and 1 The function, fx ^h xx xx 34 34 2 2 = +- -- is not defined at x 1 = and x 4 =- ` The function fx ^h is not continuous at , x 41 =- . Q13 Laplace transform of cos t ? ^h is (A) s s 22 ? + (B) s 22 w w + (C) s s 22 ? - (D) s 22 w w - s1 Correct option is (A) cos Lt ? ^h #- s s 22 ? = + cos Lat sa s 22 ` = + ^ b h l #- Q14 A function f of the complex variable zx iy =+ , is given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and , vx yx y 22 =- ^h . The value of k, for which the function is analytic, is _____ s1 Correct answer is 1 - Given, u kxy 2 = & vx y 22 =- u x v y = & ky 2 y 2 =- ` k 1 =- Q15 Numerical integration using trapezoidal rule gives the best result for a single variable function, which is (A) linear (B) parabolic (C) logarithmic (D) hyperbolic s1 Correct option is (A) fx ^h is a linear function. Q16 A point mass having mass M is moving with a velocity V at an angle ? to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth walls and rebounds. The total change (final minus initial) in the momentum of the mass is Page 4 Mechanical Paper Set-2 2016 (A) cos MV j 2 ? - t (B) sin MV j 2 ? t (C) cos MV j 2 ? t (D) sin MV j 2 ? - t s1 Correct option is (D) U v cossin Vi Vj qq =+ V v cossin Vi Vj qq =- mv T mV U =- ^h sin mV j 2 ? =- Q17 A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is (A) 2.0 (B) 1.0 (C) 0.5 (D) 0 s1 Correct option is (B) max 1 s t 1 = Q18 A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is (A) 0.25 (B) 0.50 (C) 1.0 (D) 2.0 s1 Correct option is (D) l h s s t pd t pd 4 2 = _ ^ i h 2 = Q19 The forces F 1 and F 2 in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is 0.25. The angle of wrap is 2 3p radians. It is given that R 1 = m and F21 = N. The torque (in N-m) exerted on the drum is ______ s1 Correct answer is 2.248 F F 2 1 e = µ? e ./ 0253 2 = # p . 3 248 = ` F 1 . 3 248 = N Torque, T FF r 12 # =- ^h . 3 248 1 1 # = - ^h . 2 248 = N-m Q20 A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among , mk and q is (A) qkm 2 = (B) qkm 2 = (C) q m k 2 = (D) q m k 2 = s1 Correct option is (B) Critical damping constant km 2 = q km 2 = Q21 A machine element XY , fixed at end X , is subjected to and axial load P, transverse load F, and a twisting moment T at its free and Y . The most critical point from the strength point of view is (A) a point on the circumference at location Y (B) a point at the center at location Y (C) a point on the circumference at location X Mechanical Paper Set-2 2016 Page 5 (D) a point at the center at location X s1 Correct option is (C) At centre b s 0 = and torsional shear stress are zero. Q22 For the brake shown in the figure, which one of the following is TRUE? (A) Self energizing for clockwise rotation of the drum (B) Self energizing for anti-clockwise rotation of the drum (C) Self energizing for rotation in either direction of the drum (D) Not of the self energizing type s1 Correct option is (A) For clockwise rotation M pivot / 0 = Fl Rx Ra NN ## # µ +- + 0 = When applied moment and frictional moment are in same direction is called self energizing brake. Q23 The volumetric flow rate (per unit depth) between two streamlines having stream functions 1 ? and 2 ? is (A) 12 yy (B) 12 yy (C) 2 1 y y (D) 12 yy - s1 Correct option is (D) Q24 Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is (A) linear (B) exponential (C) quadratic (D) cubic s1 Correct option is (A) Q25 A hollow cylinder has length L, inner radius r 1 , outer radius r 2 , and thermal conductivity k. The thermal resistance of the cylinder for radial conduction is (A) ln kL 2 r r 1 2 p ^h (B) ln kL 2 r r 2 1 p ^h (C) ln kL 2 r r 1 2 p ^h (D) ln kL 2 r r 2 1 p ^h s1 Correct option is (A) Q26 Consider the radiation heat exchange inside a annulus between two very long concentric cylinders. The radius of the outer cylinder is R o and that of the inner cylinder is R i . The radiation view factor of the outer cylinder onto itself is (A) R R 1 o i - (B) R R 1 o i - (C) R R 1 / o i 13 -cm (D) R R 1 o i - s1 Correct option is (D) F 11 0 = F 12 1 = F 21 A A F 2 1 12 # = RL RL 2 2 1 o i # p p = R R o i =Read More

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