Page 1 Mechanical Paper Set-1 2016 Page 1 2016 paper set-I Q.1-Q.5 carry one mark each. Q1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ______. (A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world s1 Correct option is (A) Before superlative article ‘the’ has to be used. “one of” the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer. Q2 The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse s1 Correct option is (B) ‘lose’ is verb Q3 Despite the new medicine’s ______ in treating diabetes, it is not ______ widely. (A) effectiveness - prescribed (B) availability - used (C) prescription - available (D) acceptance - proscribed s1 Correct option is (A) ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word medicine’. Q4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples? (A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 s1 Correct option is (A) Total no. of fruits 5692000 = 100 45 100 15 5692000 ## = 384210 = Ripe type of apples 100 34 100 85 5692000 ## = 1644988 = ` Total no. of apples 384210 1644988 =+ 2029198 = Q5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place? (A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01 s1 Correct option is (C) From given data, the following diagram is possible I = I live AH = Ahmed lives M = Michael lives S = Susan lives A = Arun lives Q.6 to Q.10 carry two marks each. Q6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 s1 Correct option is (C) Page 2 Mechanical Paper Set-1 2016 Page 1 2016 paper set-I Q.1-Q.5 carry one mark each. Q1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ______. (A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world s1 Correct option is (A) Before superlative article ‘the’ has to be used. “one of” the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer. Q2 The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse s1 Correct option is (B) ‘lose’ is verb Q3 Despite the new medicine’s ______ in treating diabetes, it is not ______ widely. (A) effectiveness - prescribed (B) availability - used (C) prescription - available (D) acceptance - proscribed s1 Correct option is (A) ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word medicine’. Q4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples? (A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 s1 Correct option is (A) Total no. of fruits 5692000 = 100 45 100 15 5692000 ## = 384210 = Ripe type of apples 100 34 100 85 5692000 ## = 1644988 = ` Total no. of apples 384210 1644988 =+ 2029198 = Q5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place? (A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01 s1 Correct option is (C) From given data, the following diagram is possible I = I live AH = Ahmed lives M = Michael lives S = Susan lives A = Arun lives Q.6 to Q.10 carry two marks each. Q6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 s1 Correct option is (C) Page 2 Mechanical Paper Set-1 2016 100 70 100 50 # = 100 35 & 35 = % ` Option ‘C’ is correct. Q7 In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help him. (ii) He felt that when in need of help, his friends would let him down. (iii) He was sure that his friends would help him when in need. (iv) His friends did not help him last week. (A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only s1 Correct option is (B) The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements (iii) and (iv) as logically valid inferences. Q8 Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be True based on the above? (A) When Shiva plays chess with Leela and Pavithra, he often loses. (B) Leela is the oldest of the three. (C) Shiva is a better chess player than Pavithra. (D) Pavithra is the youngest of the three. s1 Correct option is (D) From given data, the following arrangement is possible. Shiva Leela Pavithra Among four alternatives, option (D) is TRUE. Q9 if q a r 1 = - and r b s 1 = - and S c q 1 = - , the value of abc is ______ (A) rqs 1 - ^h (B) 0 (C) 1 (D) rq s ++ s1 Correct option is (C) q a - r 1 = q 1 a & r 1 = q a & r = r b - S 1 = r 1 b & S 1 = S & r b = S c - q 1 = s 1 c & q 1 = S c & q = q a r = S c a & ^h r = S ac & r = S ac b ^h S = S abc & S 1 = ` abc 1 = ` Option (C) is correct. Q10 ,, PQ R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project? (A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20 s1 Correct option is (C) Q can finish the task 25 = days, 12 hrs/day 300 = hrs 1 & hr 300 1 = th R can finish the task 50 = days, 12 hrs/day 50 12 # = 600 = hrs 1 & hr 600 1 = th Q Working hours 72 12 & # - ^h 60 = hrs R Working hours 718 & # 126 = hrs After 7 days, the ratio of Work done by Q and R. Q : R Page 3 Mechanical Paper Set-1 2016 Page 1 2016 paper set-I Q.1-Q.5 carry one mark each. Q1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ______. (A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world s1 Correct option is (A) Before superlative article ‘the’ has to be used. “one of” the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer. Q2 The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse s1 Correct option is (B) ‘lose’ is verb Q3 Despite the new medicine’s ______ in treating diabetes, it is not ______ widely. (A) effectiveness - prescribed (B) availability - used (C) prescription - available (D) acceptance - proscribed s1 Correct option is (A) ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word medicine’. Q4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples? (A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 s1 Correct option is (A) Total no. of fruits 5692000 = 100 45 100 15 5692000 ## = 384210 = Ripe type of apples 100 34 100 85 5692000 ## = 1644988 = ` Total no. of apples 384210 1644988 =+ 2029198 = Q5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place? (A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01 s1 Correct option is (C) From given data, the following diagram is possible I = I live AH = Ahmed lives M = Michael lives S = Susan lives A = Arun lives Q.6 to Q.10 carry two marks each. Q6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 s1 Correct option is (C) Page 2 Mechanical Paper Set-1 2016 100 70 100 50 # = 100 35 & 35 = % ` Option ‘C’ is correct. Q7 In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help him. (ii) He felt that when in need of help, his friends would let him down. (iii) He was sure that his friends would help him when in need. (iv) His friends did not help him last week. (A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only s1 Correct option is (B) The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements (iii) and (iv) as logically valid inferences. Q8 Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be True based on the above? (A) When Shiva plays chess with Leela and Pavithra, he often loses. (B) Leela is the oldest of the three. (C) Shiva is a better chess player than Pavithra. (D) Pavithra is the youngest of the three. s1 Correct option is (D) From given data, the following arrangement is possible. Shiva Leela Pavithra Among four alternatives, option (D) is TRUE. Q9 if q a r 1 = - and r b s 1 = - and S c q 1 = - , the value of abc is ______ (A) rqs 1 - ^h (B) 0 (C) 1 (D) rq s ++ s1 Correct option is (C) q a - r 1 = q 1 a & r 1 = q a & r = r b - S 1 = r 1 b & S 1 = S & r b = S c - q 1 = s 1 c & q 1 = S c & q = q a r = S c a & ^h r = S ac & r = S ac b ^h S = S abc & S 1 = ` abc 1 = ` Option (C) is correct. Q10 ,, PQ R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project? (A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20 s1 Correct option is (C) Q can finish the task 25 = days, 12 hrs/day 300 = hrs 1 & hr 300 1 = th R can finish the task 50 = days, 12 hrs/day 50 12 # = 600 = hrs 1 & hr 600 1 = th Q Working hours 72 12 & # - ^h 60 = hrs R Working hours 718 & # 126 = hrs After 7 days, the ratio of Work done by Q and R. Q : R Mechanical Paper Set-1 2016 Page 3 300 60 : 600 126 20 : 21 Q.11-Q.35 carry one mark each. Q11 The solution to the system of equation is x y 2 4 5 3 - >H*4 2 30 = - )3 is (A) 6, 2 (B) , 62 - (C) , 62 -- (D) , 62 - s1 Correct option is (D) x 6 = , y 2 =- is the solution of equation xy 25 + 2 = and xy 43 -+ 30 =- Q12 If ft ^h is a function defined for all t 0 > , its Laplace transform Fs ^h is defined as (A) ef tdt st 0 3 ^h # (B) ef tdt st 0 3 - ^h # (C) ef tdt ist 0 3 ^h # (D) ef tdt ist 0 3 - ^h # s1 Correct option is (B) By the definition of Laplace transform of ft t 0 > 6 ^h , we have Fs _i Lf t = ^h #- ef tdt st 0 = 3 - ^h # Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of complex variable zx iy =+ where i 1 =- . If , ux y ^h xy 2 = , then , vx y ^h may be expressed as (A) xy 22 -+ + constant (B) xy 22 -+ constant (C) xy 22 ++ constant (D) xy 22 -+ + _i constant s1 Correct option is (A) Given u xy 2 = , ? v = The Cauchy-Riemann equation u x v y = & vu xy =- are satisfying with option (A) xy 22 -+ + constant. ` , Vx y ^h xy 22 =- ++ constant. Q14 Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is µ . The standard deviation for this distribution is given by (A) µ (B) 2 µ (C) µ (D) 1 µ s1 Correct option is (A) For Poisson distribution mean =variance Given mean µ = ` Variance µ = ` standard deviation µ = Q15 Solve the equation cos x x 10 = ^h using the Newton- Raphson method. The initial guess is x 4 = p . The value of the predicted root after the first iteration, up to second decimal, is ______ s1 Correct answer is 1.564 Let fx ^h cos xx 10 =- ^h & X 0 4 p = ak Then fx l^h sin x 110 =+ ^h x 1 x fx fx 0 0 0 =- ^ ^ h h 4 1 2 10 4 2 10 p =- + - p _ _ i i . . 4 8 0711 6 2857 & p + ^ ^ h h ` x 1 . 1 5641 = Q16 A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30c with the vertical. The magnitude of force F (in N) is ______ s1 Correct answer is 57.735 N By Lami’s theorem sin F 150c sin120 100 c = . 57 735 & N Page 4 Mechanical Paper Set-1 2016 Page 1 2016 paper set-I Q.1-Q.5 carry one mark each. Q1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ______. (A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world s1 Correct option is (A) Before superlative article ‘the’ has to be used. “one of” the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer. Q2 The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse s1 Correct option is (B) ‘lose’ is verb Q3 Despite the new medicine’s ______ in treating diabetes, it is not ______ widely. (A) effectiveness - prescribed (B) availability - used (C) prescription - available (D) acceptance - proscribed s1 Correct option is (A) ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word medicine’. Q4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples? (A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 s1 Correct option is (A) Total no. of fruits 5692000 = 100 45 100 15 5692000 ## = 384210 = Ripe type of apples 100 34 100 85 5692000 ## = 1644988 = ` Total no. of apples 384210 1644988 =+ 2029198 = Q5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place? (A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01 s1 Correct option is (C) From given data, the following diagram is possible I = I live AH = Ahmed lives M = Michael lives S = Susan lives A = Arun lives Q.6 to Q.10 carry two marks each. Q6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 s1 Correct option is (C) Page 2 Mechanical Paper Set-1 2016 100 70 100 50 # = 100 35 & 35 = % ` Option ‘C’ is correct. Q7 In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help him. (ii) He felt that when in need of help, his friends would let him down. (iii) He was sure that his friends would help him when in need. (iv) His friends did not help him last week. (A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only s1 Correct option is (B) The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements (iii) and (iv) as logically valid inferences. Q8 Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be True based on the above? (A) When Shiva plays chess with Leela and Pavithra, he often loses. (B) Leela is the oldest of the three. (C) Shiva is a better chess player than Pavithra. (D) Pavithra is the youngest of the three. s1 Correct option is (D) From given data, the following arrangement is possible. Shiva Leela Pavithra Among four alternatives, option (D) is TRUE. Q9 if q a r 1 = - and r b s 1 = - and S c q 1 = - , the value of abc is ______ (A) rqs 1 - ^h (B) 0 (C) 1 (D) rq s ++ s1 Correct option is (C) q a - r 1 = q 1 a & r 1 = q a & r = r b - S 1 = r 1 b & S 1 = S & r b = S c - q 1 = s 1 c & q 1 = S c & q = q a r = S c a & ^h r = S ac & r = S ac b ^h S = S abc & S 1 = ` abc 1 = ` Option (C) is correct. Q10 ,, PQ R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project? (A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20 s1 Correct option is (C) Q can finish the task 25 = days, 12 hrs/day 300 = hrs 1 & hr 300 1 = th R can finish the task 50 = days, 12 hrs/day 50 12 # = 600 = hrs 1 & hr 600 1 = th Q Working hours 72 12 & # - ^h 60 = hrs R Working hours 718 & # 126 = hrs After 7 days, the ratio of Work done by Q and R. Q : R Mechanical Paper Set-1 2016 Page 3 300 60 : 600 126 20 : 21 Q.11-Q.35 carry one mark each. Q11 The solution to the system of equation is x y 2 4 5 3 - >H*4 2 30 = - )3 is (A) 6, 2 (B) , 62 - (C) , 62 -- (D) , 62 - s1 Correct option is (D) x 6 = , y 2 =- is the solution of equation xy 25 + 2 = and xy 43 -+ 30 =- Q12 If ft ^h is a function defined for all t 0 > , its Laplace transform Fs ^h is defined as (A) ef tdt st 0 3 ^h # (B) ef tdt st 0 3 - ^h # (C) ef tdt ist 0 3 ^h # (D) ef tdt ist 0 3 - ^h # s1 Correct option is (B) By the definition of Laplace transform of ft t 0 > 6 ^h , we have Fs _i Lf t = ^h #- ef tdt st 0 = 3 - ^h # Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of complex variable zx iy =+ where i 1 =- . If , ux y ^h xy 2 = , then , vx y ^h may be expressed as (A) xy 22 -+ + constant (B) xy 22 -+ constant (C) xy 22 ++ constant (D) xy 22 -+ + _i constant s1 Correct option is (A) Given u xy 2 = , ? v = The Cauchy-Riemann equation u x v y = & vu xy =- are satisfying with option (A) xy 22 -+ + constant. ` , Vx y ^h xy 22 =- ++ constant. Q14 Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is µ . The standard deviation for this distribution is given by (A) µ (B) 2 µ (C) µ (D) 1 µ s1 Correct option is (A) For Poisson distribution mean =variance Given mean µ = ` Variance µ = ` standard deviation µ = Q15 Solve the equation cos x x 10 = ^h using the Newton- Raphson method. The initial guess is x 4 = p . The value of the predicted root after the first iteration, up to second decimal, is ______ s1 Correct answer is 1.564 Let fx ^h cos xx 10 =- ^h & X 0 4 p = ak Then fx l^h sin x 110 =+ ^h x 1 x fx fx 0 0 0 =- ^ ^ h h 4 1 2 10 4 2 10 p =- + - p _ _ i i . . 4 8 0711 6 2857 & p + ^ ^ h h ` x 1 . 1 5641 = Q16 A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30c with the vertical. The magnitude of force F (in N) is ______ s1 Correct answer is 57.735 N By Lami’s theorem sin F 150c sin120 100 c = . 57 735 & N Page 4 Mechanical Paper Set-1 2016 Q17 A point mass M is released from rest and slides down a spherical bowl (or radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is (A) gH (B) gR 2 (C) gH 2 (D) 0 s1 Correct option is (C) By Energy Conservation mgH mv 2 1 2 = V & gH 2 = Q18 The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that rr > 31 and rr > 42 , and that the areas of the cross-sections are the same. J 1 and J 2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J J 1 2 is (A) >1 (B) <0.5 (C) =1 (D) between 0.5 and 1 s1 Correct option is (A) Given, r 3 r > 1 , rr > 42 A 1 = Area of cross section of bar 1 - A 2 = Area of cross section of bar 2 - A 1 A 2 = rr 2 2 1 2 & - 6@ rr 4 2 3 2 p =- 7A ` rr 2 2 1 2 - rr 4 2 3 2 =- rr 3 2 1 2 & - rr 4 2 2 2 =- ` J J 1 2 rr rr 2 4 1 4 2 4 4 3 4 = - - p 7 7 A A rr rr rr rr 2 2 1 2 2 2 1 2 4 2 3 2 4 2 3 2 = +- +- ^^ ^^ hh hh rr rr 2 2 1 2 4 2 3 2 = + + rr rr 4 2 3 2 2 2 1 2 ` -=- 7A J J 1 2 1 > & rr rr >> 42 31 ` 6@ Q19 A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased by 19%, the tip deflection decrease approximately by (A) 19% (B) 29% (C) 41% (D) 50% s1 Correct option is (D) 1 d EI W 3 1 3 = 1 2 d d . a a 12 119 12 4 4 = _ ^ ^ i h h . 119 1 4 = ^h . 05 = 2 d . 05 1 d = ^h 2 d reduced by 50% Q20 A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is 10 kg-m 2 . The magnitude of the gyroscopic moment (in N-m) is ______ s1 Correct answer is 200 R 100 = m, v 20 = m/sec p ? R v = . sec rad 02 = s ? 100 = rad/sec I Kg m 10 2 - = Page 5 Mechanical Paper Set-1 2016 Page 1 2016 paper set-I Q.1-Q.5 carry one mark each. Q1 Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ______. (A) the highest peak in the world (B) highest peak in the world (C) one of highest peak in the world (D) one of the highest peak in the world s1 Correct option is (A) Before superlative article ‘the’ has to be used. “one of” the expression should take plural noun and so option ‘C’ and ‘D’ can’t be the answer. Q2 The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse s1 Correct option is (B) ‘lose’ is verb Q3 Despite the new medicine’s ______ in treating diabetes, it is not ______ widely. (A) effectiveness - prescribed (B) availability - used (C) prescription - available (D) acceptance - proscribed s1 Correct option is (A) ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word medicine’. Q4 In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples? (A) 2029198 (B) 2467482 (C) 2789080 (D) 3577422 s1 Correct option is (A) Total no. of fruits 5692000 = 100 45 100 15 5692000 ## = 384210 = Ripe type of apples 100 34 100 85 5692000 ## = 1644988 = ` Total no. of apples 384210 1644988 =+ 2029198 = Q5 Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place? (A) 3.00 (B) 4.99 (C) 6.02 (D) 7.01 s1 Correct option is (C) From given data, the following diagram is possible I = I live AH = Ahmed lives M = Michael lives S = Susan lives A = Arun lives Q.6 to Q.10 carry two marks each. Q6 A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 s1 Correct option is (C) Page 2 Mechanical Paper Set-1 2016 100 70 100 50 # = 100 35 & 35 = % ` Option ‘C’ is correct. Q7 In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help him. (ii) He felt that when in need of help, his friends would let him down. (iii) He was sure that his friends would help him when in need. (iv) His friends did not help him last week. (A) (i) and (ii) (B) (iii) and (iv) (C) (iii) only (D) (iv) only s1 Correct option is (B) The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements (iii) and (iv) as logically valid inferences. Q8 Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be True based on the above? (A) When Shiva plays chess with Leela and Pavithra, he often loses. (B) Leela is the oldest of the three. (C) Shiva is a better chess player than Pavithra. (D) Pavithra is the youngest of the three. s1 Correct option is (D) From given data, the following arrangement is possible. Shiva Leela Pavithra Among four alternatives, option (D) is TRUE. Q9 if q a r 1 = - and r b s 1 = - and S c q 1 = - , the value of abc is ______ (A) rqs 1 - ^h (B) 0 (C) 1 (D) rq s ++ s1 Correct option is (C) q a - r 1 = q 1 a & r 1 = q a & r = r b - S 1 = r 1 b & S 1 = S & r b = S c - q 1 = s 1 c & q 1 = S c & q = q a r = S c a & ^h r = S ac & r = S ac b ^h S = S abc & S 1 = ` abc 1 = ` Option (C) is correct. Q10 ,, PQ R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project? (A) 10:11 (B) 11:10 (C) 20:21 (D) 21:20 s1 Correct option is (C) Q can finish the task 25 = days, 12 hrs/day 300 = hrs 1 & hr 300 1 = th R can finish the task 50 = days, 12 hrs/day 50 12 # = 600 = hrs 1 & hr 600 1 = th Q Working hours 72 12 & # - ^h 60 = hrs R Working hours 718 & # 126 = hrs After 7 days, the ratio of Work done by Q and R. Q : R Mechanical Paper Set-1 2016 Page 3 300 60 : 600 126 20 : 21 Q.11-Q.35 carry one mark each. Q11 The solution to the system of equation is x y 2 4 5 3 - >H*4 2 30 = - )3 is (A) 6, 2 (B) , 62 - (C) , 62 -- (D) , 62 - s1 Correct option is (D) x 6 = , y 2 =- is the solution of equation xy 25 + 2 = and xy 43 -+ 30 =- Q12 If ft ^h is a function defined for all t 0 > , its Laplace transform Fs ^h is defined as (A) ef tdt st 0 3 ^h # (B) ef tdt st 0 3 - ^h # (C) ef tdt ist 0 3 ^h # (D) ef tdt ist 0 3 - ^h # s1 Correct option is (B) By the definition of Laplace transform of ft t 0 > 6 ^h , we have Fs _i Lf t = ^h #- ef tdt st 0 = 3 - ^h # Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of complex variable zx iy =+ where i 1 =- . If , ux y ^h xy 2 = , then , vx y ^h may be expressed as (A) xy 22 -+ + constant (B) xy 22 -+ constant (C) xy 22 ++ constant (D) xy 22 -+ + _i constant s1 Correct option is (A) Given u xy 2 = , ? v = The Cauchy-Riemann equation u x v y = & vu xy =- are satisfying with option (A) xy 22 -+ + constant. ` , Vx y ^h xy 22 =- ++ constant. Q14 Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is µ . The standard deviation for this distribution is given by (A) µ (B) 2 µ (C) µ (D) 1 µ s1 Correct option is (A) For Poisson distribution mean =variance Given mean µ = ` Variance µ = ` standard deviation µ = Q15 Solve the equation cos x x 10 = ^h using the Newton- Raphson method. The initial guess is x 4 = p . The value of the predicted root after the first iteration, up to second decimal, is ______ s1 Correct answer is 1.564 Let fx ^h cos xx 10 =- ^h & X 0 4 p = ak Then fx l^h sin x 110 =+ ^h x 1 x fx fx 0 0 0 =- ^ ^ h h 4 1 2 10 4 2 10 p =- + - p _ _ i i . . 4 8 0711 6 2857 & p + ^ ^ h h ` x 1 . 1 5641 = Q16 A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30c with the vertical. The magnitude of force F (in N) is ______ s1 Correct answer is 57.735 N By Lami’s theorem sin F 150c sin120 100 c = . 57 735 & N Page 4 Mechanical Paper Set-1 2016 Q17 A point mass M is released from rest and slides down a spherical bowl (or radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is (A) gH (B) gR 2 (C) gH 2 (D) 0 s1 Correct option is (C) By Energy Conservation mgH mv 2 1 2 = V & gH 2 = Q18 The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that rr > 31 and rr > 42 , and that the areas of the cross-sections are the same. J 1 and J 2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J J 1 2 is (A) >1 (B) <0.5 (C) =1 (D) between 0.5 and 1 s1 Correct option is (A) Given, r 3 r > 1 , rr > 42 A 1 = Area of cross section of bar 1 - A 2 = Area of cross section of bar 2 - A 1 A 2 = rr 2 2 1 2 & - 6@ rr 4 2 3 2 p =- 7A ` rr 2 2 1 2 - rr 4 2 3 2 =- rr 3 2 1 2 & - rr 4 2 2 2 =- ` J J 1 2 rr rr 2 4 1 4 2 4 4 3 4 = - - p 7 7 A A rr rr rr rr 2 2 1 2 2 2 1 2 4 2 3 2 4 2 3 2 = +- +- ^^ ^^ hh hh rr rr 2 2 1 2 4 2 3 2 = + + rr rr 4 2 3 2 2 2 1 2 ` -=- 7A J J 1 2 1 > & rr rr >> 42 31 ` 6@ Q19 A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased by 19%, the tip deflection decrease approximately by (A) 19% (B) 29% (C) 41% (D) 50% s1 Correct option is (D) 1 d EI W 3 1 3 = 1 2 d d . a a 12 119 12 4 4 = _ ^ ^ i h h . 119 1 4 = ^h . 05 = 2 d . 05 1 d = ^h 2 d reduced by 50% Q20 A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is 10 kg-m 2 . The magnitude of the gyroscopic moment (in N-m) is ______ s1 Correct answer is 200 R 100 = m, v 20 = m/sec p ? R v = . sec rad 02 = s ? 100 = rad/sec I Kg m 10 2 - = Mechanical Paper Set-1 2016 Page 5 Gyroscopic moment I sp ww . 10 02 100 ## = N-m 200 = N-m Q21 A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ______ mm. s1 Correct answer is 20 k 10 = kN/m F 0 100 = N ? . 025 = X 12 k F 2 2 2 nn 0 ? = -+ ? ? ? ? ^ _ ^ ^ h i h h n w w 1 = at resonance X k F 2 0 ? = . 2100 25 10 100 3 ## # = 20 = mm Q22 The spring constant of a helical compression spring DOES NOT depend on (A) coil diameter (B) material strength (C) number of active turns (D) wire diameter s1 Correct option is (B) Q23 The instantaneous stream-wise velocity of a turbulent flow is given as follows: ,, ,, , ux yz tu xy z ^^ hh ,, , ux yz t l^h The time-average of the fluctuating velocity ,, , ux yz t l^h is (A) u 2 l (B) u 2 - (C) zero (D) u 2 s1 Correct option is (C) Time average of fluctuating velocity is zero. Q24 For a floating body, buoyant force acts at the (A) centroid of the floating body (B) center of gravity of the body (C) centroid of the fluid vertically below the body (D) centroid of the displaced fluid. s1 Correct option is (D) For floating body Buoyancy force acts through the centre of buoyancy which is C.G. for displaced volume. Q25 A plastic sleeve of outer radius r 1 0 = mm covers a wire (radius . r 05 = mm) carrying electric current. Thermal conductivity of the plastic is 0.15 W/m-K. The heat transfer coefficient on the outer surface of the sleeve exposed to air is / Wm 25 2 -K. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will (A) increase (B) remain the same (C) decrease (D) be zero s1 Correct option is (A) r 0 1 = mm, k . 015 = W/m-K h / Wm 25 2 = -K r c h k 0 = for cylindrical shape . 25 015 1000 # = . 01540 # = 6 = mm ` rr > c 0 & The heat transfer from the wire to the ambient will increase. Q26 Which of the following statements are TRUE with respect to heat and work? (i) They are boundary phenomena (ii) They are exact differentials (iii) They are path functions (A) both (i) and (ii) (B) both (i) and (iii) (C) both (ii) and (iii) (D) only (iii) s1 Correct option is (B) Q27 Propane CH 38 ^h is burned in an oxygen atmosphere with 10% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of CO in the products is ______ s1 Correct answer is 14.29% CH O x 38 2 + CO HO ab 22 " + Carbon balance a 3 = Hydrogen balance:Read More

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