Page 1 ?ECGATE2014 PAPER02 1 Q. No. 1 – 5 Carry One Mark Each 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways. (A) each (B) both (C) all (D) either Answer: (B) 2. Which of the options given below best completes the following sentence? She will feel much better if she ________________. (A) will get some rest (B) gets some rest (C) will be getting some rest (D) is getting some rest Answer: (B) 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing Answer: (C) 4. A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1? 0.167; 2? 0.167; 3? 0.152; 4? 0.166; 5? 0.168; 6 ? 0.180. We call this die (A) irregular (B) biased (C) Gaussian (D) insufficient Answer: (B) Exp: For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised. 5. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630 Answer: 45 Exp: 2nd number is in increa sin g order as shown above 1st number 2 3 6 15 45 157.5 630 1.5 2 2.5 3 3.5 4 Page 2 ?ECGATE2014 PAPER02 1 Q. No. 1 – 5 Carry One Mark Each 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways. (A) each (B) both (C) all (D) either Answer: (B) 2. Which of the options given below best completes the following sentence? She will feel much better if she ________________. (A) will get some rest (B) gets some rest (C) will be getting some rest (D) is getting some rest Answer: (B) 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing Answer: (C) 4. A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1? 0.167; 2? 0.167; 3? 0.152; 4? 0.166; 5? 0.168; 6 ? 0.180. We call this die (A) irregular (B) biased (C) Gaussian (D) insufficient Answer: (B) Exp: For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised. 5. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630 Answer: 45 Exp: 2nd number is in increa sin g order as shown above 1st number 2 3 6 15 45 157.5 630 1.5 2 2.5 3 3.5 4 ?ECGATE2014 PAPER02 2 Q. No. 6 – 10 Carry One Mark Each 6. Find the odd one in the following group Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X (A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X Answer: (C) Exp: 7. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? (A) The number of red lights is equal to the number of blue lights (B) The number of green lights is equal to the number of yellow lights (C) The sum of the red and green lights is equal to the sum of the yellow and blue lights (D) The sum of the red and blue lights is equal to the sum of the green and yellow lights Answer: (D) 8. The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? Answer: 163 Exp: Eight consecutive odd number =656 a6, a1, a2, a ,a+2 ,a+4, a+6 a+8=656 a=81 Smallest m=75 … (1) Average consecutive even numbers a 2 a a 2 a 4 87 4 a 86  + + + + + ? = ? = Second largest number =88 1+2=163 9. The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? a W Z B 6 3 2 17 23 26 2 B H K N 6 3 2 M S V X 6 3 2 W C G J 6 4 3 Page 3 ?ECGATE2014 PAPER02 1 Q. No. 1 – 5 Carry One Mark Each 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways. (A) each (B) both (C) all (D) either Answer: (B) 2. Which of the options given below best completes the following sentence? She will feel much better if she ________________. (A) will get some rest (B) gets some rest (C) will be getting some rest (D) is getting some rest Answer: (B) 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing Answer: (C) 4. A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1? 0.167; 2? 0.167; 3? 0.152; 4? 0.166; 5? 0.168; 6 ? 0.180. We call this die (A) irregular (B) biased (C) Gaussian (D) insufficient Answer: (B) Exp: For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised. 5. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630 Answer: 45 Exp: 2nd number is in increa sin g order as shown above 1st number 2 3 6 15 45 157.5 630 1.5 2 2.5 3 3.5 4 ?ECGATE2014 PAPER02 2 Q. No. 6 – 10 Carry One Mark Each 6. Find the odd one in the following group Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X (A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X Answer: (C) Exp: 7. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? (A) The number of red lights is equal to the number of blue lights (B) The number of green lights is equal to the number of yellow lights (C) The sum of the red and green lights is equal to the sum of the yellow and blue lights (D) The sum of the red and blue lights is equal to the sum of the green and yellow lights Answer: (D) 8. The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? Answer: 163 Exp: Eight consecutive odd number =656 a6, a1, a2, a ,a+2 ,a+4, a+6 a+8=656 a=81 Smallest m=75 … (1) Average consecutive even numbers a 2 a a 2 a 4 87 4 a 86  + + + + + ? = ? = Second largest number =88 1+2=163 9. The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? a W Z B 6 3 2 17 23 26 2 B H K N 6 3 2 M S V X 6 3 2 W C G J 6 4 3 ?ECGATE2014 PAPER02 3 (A) Item 2 (B) Item 3 (C) Item 6 (D) Item 5 Answer: (D) Exp: Item:2 Item:3 7 3 4 3 20 250 10 100 20 500 10 100 0.5 10 5 10 1 Item 2 × × × × × = × = 7 3 23 250 10 19 500 10 1.2 Item3 × × × × = Item: 6 Item:5 19 1.18 Item 6 16 = = 20 5 1.6 1.6 Item 5 12 3 = = ? = 10. It takes 30 minutes to empty a halffull tank by draining it at a constant rate. It is decided to simultaneously pump water into the halffull tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes? (A) 4 times the draining rate (B) 3 times the draining rate (C) 2.5 times the draining rate (D) 2 times the draining rate Answer: (A) Exp: half V 30(s) drawing rate s = = Total volume =60 S tank 1 1 1 (s )(10) (s)10 30s s (s) s 3s s1 4s s 4drawing rate  =  = = = Item 6 16% Item 1 11% Item5 12% Item4 22% Item3 19% Item2 20% Exports Item 6 19% Item 1 12% Item 5 20% Item3 23% Item 2 20% Revenues Item 4 6% Page 4 ?ECGATE2014 PAPER02 1 Q. No. 1 – 5 Carry One Mark Each 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways. (A) each (B) both (C) all (D) either Answer: (B) 2. Which of the options given below best completes the following sentence? She will feel much better if she ________________. (A) will get some rest (B) gets some rest (C) will be getting some rest (D) is getting some rest Answer: (B) 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing Answer: (C) 4. A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1? 0.167; 2? 0.167; 3? 0.152; 4? 0.166; 5? 0.168; 6 ? 0.180. We call this die (A) irregular (B) biased (C) Gaussian (D) insufficient Answer: (B) Exp: For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised. 5. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630 Answer: 45 Exp: 2nd number is in increa sin g order as shown above 1st number 2 3 6 15 45 157.5 630 1.5 2 2.5 3 3.5 4 ?ECGATE2014 PAPER02 2 Q. No. 6 – 10 Carry One Mark Each 6. Find the odd one in the following group Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X (A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X Answer: (C) Exp: 7. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? (A) The number of red lights is equal to the number of blue lights (B) The number of green lights is equal to the number of yellow lights (C) The sum of the red and green lights is equal to the sum of the yellow and blue lights (D) The sum of the red and blue lights is equal to the sum of the green and yellow lights Answer: (D) 8. The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? Answer: 163 Exp: Eight consecutive odd number =656 a6, a1, a2, a ,a+2 ,a+4, a+6 a+8=656 a=81 Smallest m=75 … (1) Average consecutive even numbers a 2 a a 2 a 4 87 4 a 86  + + + + + ? = ? = Second largest number =88 1+2=163 9. The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? a W Z B 6 3 2 17 23 26 2 B H K N 6 3 2 M S V X 6 3 2 W C G J 6 4 3 ?ECGATE2014 PAPER02 3 (A) Item 2 (B) Item 3 (C) Item 6 (D) Item 5 Answer: (D) Exp: Item:2 Item:3 7 3 4 3 20 250 10 100 20 500 10 100 0.5 10 5 10 1 Item 2 × × × × × = × = 7 3 23 250 10 19 500 10 1.2 Item3 × × × × = Item: 6 Item:5 19 1.18 Item 6 16 = = 20 5 1.6 1.6 Item 5 12 3 = = ? = 10. It takes 30 minutes to empty a halffull tank by draining it at a constant rate. It is decided to simultaneously pump water into the halffull tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes? (A) 4 times the draining rate (B) 3 times the draining rate (C) 2.5 times the draining rate (D) 2 times the draining rate Answer: (A) Exp: half V 30(s) drawing rate s = = Total volume =60 S tank 1 1 1 (s )(10) (s)10 30s s (s) s 3s s1 4s s 4drawing rate  =  = = = Item 6 16% Item 1 11% Item5 12% Item4 22% Item3 19% Item2 20% Exports Item 6 19% Item 1 12% Item 5 20% Item3 23% Item 2 20% Revenues Item 4 6% ?ECGATE2014 PAPER02 4 Q. No. 1 – 25 Carry One Mark Each 1. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is ________. Answer: 200 Exp: ( ) ( ) AB A . B 5 . 40 200 = = = 2. Let X be a random variable which is uniformly chosen from the set of positive odd numbers less than 100. The expectation E[X]is __________. Answer:50 Exp: ( ) X 1,3,5,....,99 n 50 number of observations = ? = ( ) [ ] ( ) n 2 i i 1 1 1 1 E x x 1 3 5 .... 99 50 50 n 50 50 = ? = = + + + + = = ? 3. For 0 t , = <8 the maximum value of the function ( ) t 2t f t e 2e   =  occurs at (A) t = log e 4 (B) t = log e 2 (C) t = 0 (D) t = log e 8 Answer: (A) Exp: ( ) ' t 2t f t e 4e 0   = + = ( ) t t t 4 e '' 4 e 1 e 4e 1 e t log 4 and f t 0 at t log    ? ? ?  ? = ? = ? ? < = 4. The value of x x 1 lim 1 x ?8 ? ? + ? ? ? ? is (A) ln2 (B) 1.0 (C) e (D) 8 Answer: (C) Exp: ( ) x x 1 lim 1 e standard limit x ?8 ? ? + = ? ? ? ? 5. If the characteristic equation of the differential equation 2 2 d y dy 2 y 0 dx dx + a + = has two equal roots, then the values of a are ( ) A 1 ± ( ) B 0,0 ( ) C j ± ( ) D 1/ 2 ± Answer: (A) Exp: 2 For equal roots, Discriminant B 4AC 0  = 2 4 4 0 1 ? a  = ?a=± Page 5 ?ECGATE2014 PAPER02 1 Q. No. 1 – 5 Carry One Mark Each 1. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways. (A) each (B) both (C) all (D) either Answer: (B) 2. Which of the options given below best completes the following sentence? She will feel much better if she ________________. (A) will get some rest (B) gets some rest (C) will be getting some rest (D) is getting some rest Answer: (B) 3. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. (A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing Answer: (C) 4. A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence: 1? 0.167; 2? 0.167; 3? 0.152; 4? 0.166; 5? 0.168; 6 ? 0.180. We call this die (A) irregular (B) biased (C) Gaussian (D) insufficient Answer: (B) Exp: For a very large number of throws, the frequency should be same for unbiased throw. As it not same, then the die is baised. 5. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630 Answer: 45 Exp: 2nd number is in increa sin g order as shown above 1st number 2 3 6 15 45 157.5 630 1.5 2 2.5 3 3.5 4 ?ECGATE2014 PAPER02 2 Q. No. 6 – 10 Carry One Mark Each 6. Find the odd one in the following group Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X (A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X Answer: (C) Exp: 7. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct? (A) The number of red lights is equal to the number of blue lights (B) The number of green lights is equal to the number of yellow lights (C) The sum of the red and green lights is equal to the sum of the yellow and blue lights (D) The sum of the red and blue lights is equal to the sum of the green and yellow lights Answer: (D) 8. The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number? Answer: 163 Exp: Eight consecutive odd number =656 a6, a1, a2, a ,a+2 ,a+4, a+6 a+8=656 a=81 Smallest m=75 … (1) Average consecutive even numbers a 2 a a 2 a 4 87 4 a 86  + + + + + ? = ? = Second largest number =88 1+2=163 9. The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg? a W Z B 6 3 2 17 23 26 2 B H K N 6 3 2 M S V X 6 3 2 W C G J 6 4 3 ?ECGATE2014 PAPER02 3 (A) Item 2 (B) Item 3 (C) Item 6 (D) Item 5 Answer: (D) Exp: Item:2 Item:3 7 3 4 3 20 250 10 100 20 500 10 100 0.5 10 5 10 1 Item 2 × × × × × = × = 7 3 23 250 10 19 500 10 1.2 Item3 × × × × = Item: 6 Item:5 19 1.18 Item 6 16 = = 20 5 1.6 1.6 Item 5 12 3 = = ? = 10. It takes 30 minutes to empty a halffull tank by draining it at a constant rate. It is decided to simultaneously pump water into the halffull tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes? (A) 4 times the draining rate (B) 3 times the draining rate (C) 2.5 times the draining rate (D) 2 times the draining rate Answer: (A) Exp: half V 30(s) drawing rate s = = Total volume =60 S tank 1 1 1 (s )(10) (s)10 30s s (s) s 3s s1 4s s 4drawing rate  =  = = = Item 6 16% Item 1 11% Item5 12% Item4 22% Item3 19% Item2 20% Exports Item 6 19% Item 1 12% Item 5 20% Item3 23% Item 2 20% Revenues Item 4 6% ?ECGATE2014 PAPER02 4 Q. No. 1 – 25 Carry One Mark Each 1. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is ________. Answer: 200 Exp: ( ) ( ) AB A . B 5 . 40 200 = = = 2. Let X be a random variable which is uniformly chosen from the set of positive odd numbers less than 100. The expectation E[X]is __________. Answer:50 Exp: ( ) X 1,3,5,....,99 n 50 number of observations = ? = ( ) [ ] ( ) n 2 i i 1 1 1 1 E x x 1 3 5 .... 99 50 50 n 50 50 = ? = = + + + + = = ? 3. For 0 t , = <8 the maximum value of the function ( ) t 2t f t e 2e   =  occurs at (A) t = log e 4 (B) t = log e 2 (C) t = 0 (D) t = log e 8 Answer: (A) Exp: ( ) ' t 2t f t e 4e 0   = + = ( ) t t t 4 e '' 4 e 1 e 4e 1 e t log 4 and f t 0 at t log    ? ? ?  ? = ? = ? ? < = 4. The value of x x 1 lim 1 x ?8 ? ? + ? ? ? ? is (A) ln2 (B) 1.0 (C) e (D) 8 Answer: (C) Exp: ( ) x x 1 lim 1 e standard limit x ?8 ? ? + = ? ? ? ? 5. If the characteristic equation of the differential equation 2 2 d y dy 2 y 0 dx dx + a + = has two equal roots, then the values of a are ( ) A 1 ± ( ) B 0,0 ( ) C j ± ( ) D 1/ 2 ± Answer: (A) Exp: 2 For equal roots, Discriminant B 4AC 0  = 2 4 4 0 1 ? a  = ?a=± ?ECGATE2014 PAPER02 5 6. Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance (A) in series with a current source (B) in parallel with a voltage source (C) in series with a voltage source (D) in parallel with a current source Answer: (D) Exp: Norton’s theorem 7. In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then the magnitude of the current (in mA) through the 4kO resistor at t = 0 + is _______. Answer: 1.2 mA Exp: For t = o+ ( ) ( ) 10 i o 1.11mA 9K i o 1.2mA + = ? + 8. A silicon bar is doped with donor impurities N D = 2.25 x 10 15 atoms / cm 3 . Given the intrinsic carrier concentration of silicon at T = 300 K is n i = 1.5 x 10 10 cm 3 . Assuming complete impurity ionization, the equilibrium electron and hole concentrations are (A) n 0 = 1.5 x 10 16 cm 3 , p 0 = 1.5 x 10 5 cm 3 (B) n 0 = 1.5 x 10 10 cm 3 , p 0 = 1.5 x 10 15 cm 3 (C) n 0 = 2.25 x 10 15 cm 3 , p 0 = 1.5 x 10 10 cm 3 (D) n 0 = 2.25 x 10 15 cm 3 , p 0 = 1 x 10 5 cm 3 Answer: (D) Exp: 15 3 D 10 3 i N 2.25 10 Atom / cm h 1.5 10 / cm = × = × Since complete ionization taken place, ( ) 15 3 0 D 2 10 2 5 3 i 0 15 0 h N 2.25 10 / cm 1.5 10 n P 1 10 / cm n 2.25 10 = = × × = = = × × 5kO 4 kO 1kO 1mH t 0 = 10 F µ 10 V +  i equ Z Load N I 5 kO 4 kO ( ) i 0+ 10V +  • •Read More
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