Page 1 : 2 : Gate 2016 – ECE – Set 1 Q.1 – Q.5 Carry One Mark Each 01. 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 01. Ans: (A) Sol: 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. 02. The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse 02. Ans: (B) Sol: ‘lose’ is verb. 03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely (A) effectiveness --- prescribed (B) availability ---- used (B) prescription ---- available (D) acceptable--- proscribed 03. Ans: (A) Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’ 04. 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 04. Ans: (A) Sol: Total no. of fruits = 5692000 Unripe type of apples = 45% of 15% of 5692000 5692000 100 15 100 45 ? ? ? = 384210 Ripe type of apples 5692000 100 85 100 34 ? ? ? = 1644988 ?Total no. of apples = 384210 + 1644988 = 2029198 05. Michael lives 10 km way from where I live. Ahmed lives 5km 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 Page 2 : 2 : Gate 2016 – ECE – Set 1 Q.1 – Q.5 Carry One Mark Each 01. 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 01. Ans: (A) Sol: 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. 02. The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse 02. Ans: (B) Sol: ‘lose’ is verb. 03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely (A) effectiveness --- prescribed (B) availability ---- used (B) prescription ---- available (D) acceptable--- proscribed 03. Ans: (A) Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’ 04. 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 04. Ans: (A) Sol: Total no. of fruits = 5692000 Unripe type of apples = 45% of 15% of 5692000 5692000 100 15 100 45 ? ? ? = 384210 Ripe type of apples 5692000 100 85 100 34 ? ? ? = 1644988 ?Total no. of apples = 384210 + 1644988 = 2029198 05. Michael lives 10 km way from where I live. Ahmed lives 5km 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 : 3 : Questions & Solutions 05. Ans: (c) Sol: From given data, the following diagram is possible I = I live AH = Ahmed lives; M = Michael lives S = Susan lives; A= Arun lives ? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less than 7 km, from given alternatives, option ‘C’ only possible. Q.6 – Q.10 Carry two marks each 06. 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 shows symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 06. Ans: (C) Sol: = 100 50 100 70 ? = 100 35 = 35% 07. 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 interference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help them (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 07. Ans: (B) Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements iii and iv as logically valid inferences. I AH M A S 7 km 6.02 m 5 km 10 km Tuberculosic Afected 50% Infected 50% Does not Develop the disease 70% of 50% Develop the disease 30% of 50% Page 3 : 2 : Gate 2016 – ECE – Set 1 Q.1 – Q.5 Carry One Mark Each 01. 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 01. Ans: (A) Sol: 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. 02. The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse 02. Ans: (B) Sol: ‘lose’ is verb. 03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely (A) effectiveness --- prescribed (B) availability ---- used (B) prescription ---- available (D) acceptable--- proscribed 03. Ans: (A) Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’ 04. 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 04. Ans: (A) Sol: Total no. of fruits = 5692000 Unripe type of apples = 45% of 15% of 5692000 5692000 100 15 100 45 ? ? ? = 384210 Ripe type of apples 5692000 100 85 100 34 ? ? ? = 1644988 ?Total no. of apples = 384210 + 1644988 = 2029198 05. Michael lives 10 km way from where I live. Ahmed lives 5km 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 : 3 : Questions & Solutions 05. Ans: (c) Sol: From given data, the following diagram is possible I = I live AH = Ahmed lives; M = Michael lives S = Susan lives; A= Arun lives ? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less than 7 km, from given alternatives, option ‘C’ only possible. Q.6 – Q.10 Carry two marks each 06. 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 shows symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 06. Ans: (C) Sol: = 100 50 100 70 ? = 100 35 = 35% 07. 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 interference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help them (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 07. Ans: (B) Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements iii and iv as logically valid inferences. I AH M A S 7 km 6.02 m 5 km 10 km Tuberculosic Afected 50% Infected 50% Does not Develop the disease 70% of 50% Develop the disease 30% of 50% : 5 : Questions & Solutions 08. 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 palyer than Pavithra (D) Pavithra is the young of the three 08. Ans: (D) Sol: From given data, the following arrangement is possible Shiva Leela Pavithra Among four alternatives, option D is TRUE. 09. If q –a = r 1 and r –b = s 1 and S –C = q 1 , the value of abc is ____. (A) (rqs) –1 (B) 0 (C) 1 (D) r+q+s 09. Ans: (C) Sol: r 1 q a ? ? ? r 1 q 1 a ? ? q a = r b b b r s s 1 r 1 s 1 r ? ? ? ? ? ? q s q 1 s 1 q 1 s c c c ? ? ? ? ? ? ?? r s r s r q ac a c a ? ? ? ? ? (s ac ) b = s s abc = s ? ? abc = 1 10. P,Q,R and S are working on a project. Q can finish the taks 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 10. Ans: (C) Sol: Q can finish the task = 25 days, 12 hrs/day = 300 hrs, 1 hr th 300 1 ? R can finish the task = 50 days, 12 hrs/day Page 4 : 2 : Gate 2016 – ECE – Set 1 Q.1 – Q.5 Carry One Mark Each 01. 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 01. Ans: (A) Sol: 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. 02. The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse 02. Ans: (B) Sol: ‘lose’ is verb. 03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely (A) effectiveness --- prescribed (B) availability ---- used (B) prescription ---- available (D) acceptable--- proscribed 03. Ans: (A) Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’ 04. 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 04. Ans: (A) Sol: Total no. of fruits = 5692000 Unripe type of apples = 45% of 15% of 5692000 5692000 100 15 100 45 ? ? ? = 384210 Ripe type of apples 5692000 100 85 100 34 ? ? ? = 1644988 ?Total no. of apples = 384210 + 1644988 = 2029198 05. Michael lives 10 km way from where I live. Ahmed lives 5km 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 : 3 : Questions & Solutions 05. Ans: (c) Sol: From given data, the following diagram is possible I = I live AH = Ahmed lives; M = Michael lives S = Susan lives; A= Arun lives ? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less than 7 km, from given alternatives, option ‘C’ only possible. Q.6 – Q.10 Carry two marks each 06. 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 shows symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 06. Ans: (C) Sol: = 100 50 100 70 ? = 100 35 = 35% 07. 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 interference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help them (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 07. Ans: (B) Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements iii and iv as logically valid inferences. I AH M A S 7 km 6.02 m 5 km 10 km Tuberculosic Afected 50% Infected 50% Does not Develop the disease 70% of 50% Develop the disease 30% of 50% : 5 : Questions & Solutions 08. 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 palyer than Pavithra (D) Pavithra is the young of the three 08. Ans: (D) Sol: From given data, the following arrangement is possible Shiva Leela Pavithra Among four alternatives, option D is TRUE. 09. If q –a = r 1 and r –b = s 1 and S –C = q 1 , the value of abc is ____. (A) (rqs) –1 (B) 0 (C) 1 (D) r+q+s 09. Ans: (C) Sol: r 1 q a ? ? ? r 1 q 1 a ? ? q a = r b b b r s s 1 r 1 s 1 r ? ? ? ? ? ? q s q 1 s 1 q 1 s c c c ? ? ? ? ? ? ?? r s r s r q ac a c a ? ? ? ? ? (s ac ) b = s s abc = s ? ? abc = 1 10. P,Q,R and S are working on a project. Q can finish the taks 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 10. Ans: (C) Sol: Q can finish the task = 25 days, 12 hrs/day = 300 hrs, 1 hr th 300 1 ? R can finish the task = 50 days, 12 hrs/day : 6 : Gate 2016 – ECE – Set 1 = 50 × 12 = 600 hrs, th 600 1 hr 1 ? Q working hours ? (7 – 2) × 12 = 60 hrs R working hours ? 7 × 18 = 126 hrs After 7 days, the ratio of work done by Q and R Q : R 300 60 : 600 126 20 : 21 Page 5 : 2 : Gate 2016 – ECE – Set 1 Q.1 – Q.5 Carry One Mark Each 01. 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 01. Ans: (A) Sol: 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. 02. The policeman asked the victim of a theft, “What did you ______?” (A) loose (B) lose (C) loss (D) louse 02. Ans: (B) Sol: ‘lose’ is verb. 03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely (A) effectiveness --- prescribed (B) availability ---- used (B) prescription ---- available (D) acceptable--- proscribed 03. Ans: (A) Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word ‘medicine.’ 04. 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 04. Ans: (A) Sol: Total no. of fruits = 5692000 Unripe type of apples = 45% of 15% of 5692000 5692000 100 15 100 45 ? ? ? = 384210 Ripe type of apples 5692000 100 85 100 34 ? ? ? = 1644988 ?Total no. of apples = 384210 + 1644988 = 2029198 05. Michael lives 10 km way from where I live. Ahmed lives 5km 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 : 3 : Questions & Solutions 05. Ans: (c) Sol: From given data, the following diagram is possible I = I live AH = Ahmed lives; M = Michael lives S = Susan lives; A= Arun lives ? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less than 7 km, from given alternatives, option ‘C’ only possible. Q.6 – Q.10 Carry two marks each 06. 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 shows symptoms of disease? (A) 15 (B) 33 (C) 35 (D) 37 06. Ans: (C) Sol: = 100 50 100 70 ? = 100 35 = 35% 07. 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 interference(s) is/are logically valid and can be inferred from the above passage? (i) His friends were always asking him to help them (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 07. Ans: (B) Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to statements iii and iv as logically valid inferences. I AH M A S 7 km 6.02 m 5 km 10 km Tuberculosic Afected 50% Infected 50% Does not Develop the disease 70% of 50% Develop the disease 30% of 50% : 5 : Questions & Solutions 08. 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 palyer than Pavithra (D) Pavithra is the young of the three 08. Ans: (D) Sol: From given data, the following arrangement is possible Shiva Leela Pavithra Among four alternatives, option D is TRUE. 09. If q –a = r 1 and r –b = s 1 and S –C = q 1 , the value of abc is ____. (A) (rqs) –1 (B) 0 (C) 1 (D) r+q+s 09. Ans: (C) Sol: r 1 q a ? ? ? r 1 q 1 a ? ? q a = r b b b r s s 1 r 1 s 1 r ? ? ? ? ? ? q s q 1 s 1 q 1 s c c c ? ? ? ? ? ? ?? r s r s r q ac a c a ? ? ? ? ? (s ac ) b = s s abc = s ? ? abc = 1 10. P,Q,R and S are working on a project. Q can finish the taks 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 10. Ans: (C) Sol: Q can finish the task = 25 days, 12 hrs/day = 300 hrs, 1 hr th 300 1 ? R can finish the task = 50 days, 12 hrs/day : 6 : Gate 2016 – ECE – Set 1 = 50 × 12 = 600 hrs, th 600 1 hr 1 ? Q working hours ? (7 – 2) × 12 = 60 hrs R working hours ? 7 × 18 = 126 hrs After 7 days, the ratio of work done by Q and R Q : R 300 60 : 600 126 20 : 21 : 7 : Questions & Solutions Q.1 – Q.25 Carry one mark each. 01. Let M 4 = I (where I denotes the identity matrix)and M ? I, M 2 ? I and M 3 ? I. Then, for any natural number k, M –1 equals: (A) M 4k+1 (B) M 4k+2 (C) M 4k+3 (D) M 4k 01. Ans: (C) Sol: M 4 = I ? M 8 = M 4 = I ? M 7 = M ?1 ? M 12 = M 8 = I ? M 11 = M ?1 ? M 16 = M 12 = I ? M 15 = M ?1 ………………….. ? M ?1 = M 4K+ 3 , K is a natural number 02. The second moment of a Poisson-distributed random variables is 2. The mean of the random variable is _____. 02. Ans: ? = 1 Sol: E(x 2 ) = 2 V(X) = E (X 2 )- (E(X)) 2 Let mean of the poission random variable be x x = 2 ? x 2 x 2 + x ? 2 = 0 x = 1, ? 2 ? Mean is ? = 1 03. Given the following statements about a function f: R ?R, select the right option: P : If f(x) is continuous at x = x 0 , then it is also differentiable at x = x 0 Q : If f(x) is continuous at x = x 0 , then it may not be differentiable at x = x 0 R : If f(x) is continuous at x = x 0 , then it is also different at x = x 0 (A) P is true, Q is false, R is false (B) P is false, Q is true, R is true (C) P is false, Q is true, R is false (D) P is true, Q is false, R is true 03. Ans: (B) Sol: Since continuous function may not be differentiable. But differentiable function is always continuous. 04. Which one of the following is a property of the solutions to the Laplace equation : ? 2 f = 0? (A) The solution have neither maxima nor minima anywhere except at the boundaries (B) The solution are not separable in the coordinates (C) The solution are not continuous (D) The solution are not dependent on the boundary conditions 04. Ans: (A)Read More

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