Page 1 ?CE-GATE-2014 PAPER-02| 1 Q. No. 1 – 5 Carry One Mark Each Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease __________ short-term memory loss. (A) experienced (B) unexperienced (C) is experiencing (D) experiences Answer: (D) Q2. Choose the most appropriate word from the options given below to complete the following sentence. __________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Answer: (A) Q3. Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries (D) Women of all countries have equal legal rights. Answer: (C) Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years. Answer: 25 to 25 Exp: 4 P 0.04 100 For 1 earth quake Reverse probability 100 P 1 earth quake 4 25 years ? = = ? ? ? ? ? = ? ? ? Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years Page 2 ?CE-GATE-2014 PAPER-02| 1 Q. No. 1 – 5 Carry One Mark Each Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease __________ short-term memory loss. (A) experienced (B) unexperienced (C) is experiencing (D) experiences Answer: (D) Q2. Choose the most appropriate word from the options given below to complete the following sentence. __________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Answer: (A) Q3. Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries (D) Women of all countries have equal legal rights. Answer: (C) Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years. Answer: 25 to 25 Exp: 4 P 0.04 100 For 1 earth quake Reverse probability 100 P 1 earth quake 4 25 years ? = = ? ? ? ? ? = ? ? ? Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years ?CE-GATE-2014 PAPER-02| 2 Answer: (A) Exp: 20 8 140 × After 1 year P = 6 2 years = 7.2 20 After 3 1.2 100 = × 8.65 = 20 After 4 years 8.65 100 = × 10 =˜ Time will be in between 3-4 years. Q. No. 6 – 10 Carry One Mark Each Q6. In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements : 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statement 1 and 2 are both required to determine the eldest child. (D) Statement 1 and 2 are not sufficient to determine the eldest child. Answer: (A) Q7. Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis Answer: (C) Page 3 ?CE-GATE-2014 PAPER-02| 1 Q. No. 1 – 5 Carry One Mark Each Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease __________ short-term memory loss. (A) experienced (B) unexperienced (C) is experiencing (D) experiences Answer: (D) Q2. Choose the most appropriate word from the options given below to complete the following sentence. __________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Answer: (A) Q3. Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries (D) Women of all countries have equal legal rights. Answer: (C) Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years. Answer: 25 to 25 Exp: 4 P 0.04 100 For 1 earth quake Reverse probability 100 P 1 earth quake 4 25 years ? = = ? ? ? ? ? = ? ? ? Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years ?CE-GATE-2014 PAPER-02| 2 Answer: (A) Exp: 20 8 140 × After 1 year P = 6 2 years = 7.2 20 After 3 1.2 100 = × 8.65 = 20 After 4 years 8.65 100 = × 10 =˜ Time will be in between 3-4 years. Q. No. 6 – 10 Carry One Mark Each Q6. In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements : 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statement 1 and 2 are both required to determine the eldest child. (D) Statement 1 and 2 are not sufficient to determine the eldest child. Answer: (A) Q7. Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis Answer: (C) ?CE-GATE-2014 PAPER-02| 3 Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item 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 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram? (A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1 Answer: (D) Exp: revenue generated through export of item 1 Kg ? ? ? ( ) Item 11 11 5 lakhs tows quantity 100 20 ? = × = ( ) revenue gen 12 30cr 6 250 C 20 Item1 100 11 ? × × × = × ? ? … (1) ( ) 6 Revenue gen Item 4 250. C 100 = × 15 cr 20 Lt. 22 = × … (2) 1 : 2 30 20 22 4 :1 11 15 20 × × = × Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? (A) 1 (B) 2 (C) 3 (D) 2 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 ?CE-GATE-2014 PAPER-02| 1 Q. No. 1 – 5 Carry One Mark Each Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease __________ short-term memory loss. (A) experienced (B) unexperienced (C) is experiencing (D) experiences Answer: (D) Q2. Choose the most appropriate word from the options given below to complete the following sentence. __________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Answer: (A) Q3. Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries (D) Women of all countries have equal legal rights. Answer: (C) Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years. Answer: 25 to 25 Exp: 4 P 0.04 100 For 1 earth quake Reverse probability 100 P 1 earth quake 4 25 years ? = = ? ? ? ? ? = ? ? ? Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years ?CE-GATE-2014 PAPER-02| 2 Answer: (A) Exp: 20 8 140 × After 1 year P = 6 2 years = 7.2 20 After 3 1.2 100 = × 8.65 = 20 After 4 years 8.65 100 = × 10 =˜ Time will be in between 3-4 years. Q. No. 6 – 10 Carry One Mark Each Q6. In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements : 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statement 1 and 2 are both required to determine the eldest child. (D) Statement 1 and 2 are not sufficient to determine the eldest child. Answer: (A) Q7. Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis Answer: (C) ?CE-GATE-2014 PAPER-02| 3 Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item 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 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram? (A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1 Answer: (D) Exp: revenue generated through export of item 1 Kg ? ? ? ( ) Item 11 11 5 lakhs tows quantity 100 20 ? = × = ( ) revenue gen 12 30cr 6 250 C 20 Item1 100 11 ? × × × = × ? ? … (1) ( ) 6 Revenue gen Item 4 250. C 100 = × 15 cr 20 Lt. 22 = × … (2) 1 : 2 30 20 22 4 :1 11 15 20 × × = × Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? (A) 1 (B) 2 (C) 3 (D) 2 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% ?CE-GATE-2014 PAPER-02| 4 Answer: (C) Exp: From the fig: zx 2. = [Pythagoras theorem] zQ = 1 Given ? Considering ZQX, which is right angle, is ? 2 2 2 Qx ZQ Zx = + 1 2 3 = + = Q.10 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV- individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is ______ Answer: 0.48 to 0.49 Exp: Let total population = 100 HIV + patients = 10 For the patient to be +Ve, should be either +Ve and test is showing +Ve or the patient should be – Ve but rest is showing +Ve 0.1 0.95 0.1 0.95 0.9 0.11 × ? × + × Q. No. 1 – 25 Carry One Mark Each Q.1 A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a 'Tail' when the coin is tossed again is (A) 0 (B) 1 2 (C) 4 5 (D) 1 5 Answer: (B) Exp. ( ) 1 P T 2 = Q.2 The determinant of matrix 0 1 2 3 1 0 3 0 2 3 0 1 3 0 1 2 ? ? ? ? ? ? ? ? ? ? ? ? is _________ Answer: 88 to 88 Exp. ( ) ( ) ( ) ( ) ( ) 0 1 2 3 1 2 3 0 1 3 1 0 3 0 1 3 0 1 3 2 3 1 2 3 0 1 0 1 2 3 0 2 3 0 1 2 1 0 1 2 6 0 3 3 0 3 0 1 4 3 3 0 9 88 = - - = ? - - - + - ? ? ? =- ? - - + - ? = ? ? W X P 1 1 1 1 Y Q 1 Z Page 5 ?CE-GATE-2014 PAPER-02| 1 Q. No. 1 – 5 Carry One Mark Each Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease __________ short-term memory loss. (A) experienced (B) unexperienced (C) is experiencing (D) experiences Answer: (D) Q2. Choose the most appropriate word from the options given below to complete the following sentence. __________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Answer: (A) Q3. Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries (D) Women of all countries have equal legal rights. Answer: (C) Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years. Answer: 25 to 25 Exp: 4 P 0.04 100 For 1 earth quake Reverse probability 100 P 1 earth quake 4 25 years ? = = ? ? ? ? ? = ? ? ? Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years ?CE-GATE-2014 PAPER-02| 2 Answer: (A) Exp: 20 8 140 × After 1 year P = 6 2 years = 7.2 20 After 3 1.2 100 = × 8.65 = 20 After 4 years 8.65 100 = × 10 =˜ Time will be in between 3-4 years. Q. No. 6 – 10 Carry One Mark Each Q6. In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements : 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statement 1 and 2 are both required to determine the eldest child. (D) Statement 1 and 2 are not sufficient to determine the eldest child. Answer: (A) Q7. Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis Answer: (C) ?CE-GATE-2014 PAPER-02| 3 Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item 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 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram? (A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1 Answer: (D) Exp: revenue generated through export of item 1 Kg ? ? ? ( ) Item 11 11 5 lakhs tows quantity 100 20 ? = × = ( ) revenue gen 12 30cr 6 250 C 20 Item1 100 11 ? × × × = × ? ? … (1) ( ) 6 Revenue gen Item 4 250. C 100 = × 15 cr 20 Lt. 22 = × … (2) 1 : 2 30 20 22 4 :1 11 15 20 × × = × Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? (A) 1 (B) 2 (C) 3 (D) 2 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% ?CE-GATE-2014 PAPER-02| 4 Answer: (C) Exp: From the fig: zx 2. = [Pythagoras theorem] zQ = 1 Given ? Considering ZQX, which is right angle, is ? 2 2 2 Qx ZQ Zx = + 1 2 3 = + = Q.10 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV- individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is ______ Answer: 0.48 to 0.49 Exp: Let total population = 100 HIV + patients = 10 For the patient to be +Ve, should be either +Ve and test is showing +Ve or the patient should be – Ve but rest is showing +Ve 0.1 0.95 0.1 0.95 0.9 0.11 × ? × + × Q. No. 1 – 25 Carry One Mark Each Q.1 A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a 'Tail' when the coin is tossed again is (A) 0 (B) 1 2 (C) 4 5 (D) 1 5 Answer: (B) Exp. ( ) 1 P T 2 = Q.2 The determinant of matrix 0 1 2 3 1 0 3 0 2 3 0 1 3 0 1 2 ? ? ? ? ? ? ? ? ? ? ? ? is _________ Answer: 88 to 88 Exp. ( ) ( ) ( ) ( ) ( ) 0 1 2 3 1 2 3 0 1 3 1 0 3 0 1 3 0 1 3 2 3 1 2 3 0 1 0 1 2 3 0 2 3 0 1 2 1 0 1 2 6 0 3 3 0 3 0 1 4 3 3 0 9 88 = - - = ? - - - + - ? ? ? =- ? - - + - ? = ? ? W X P 1 1 1 1 Y Q 1 Z ?CE-GATE-2014 PAPER-02| 5 Q.3 2 3i z 5 i - = - + can be expressed as (A) - 0.5 - 0.5i (B) - 0.5 + 0.5i (C) 0.5 - 0.5i (D) 0.5 + 0.5i Exp. 2 3i z 5 i - = - + ( ) 2 2 2 2 3i 5 i 5 i 5 i 10 2i 15i 3i 10 13i 3 5 i 25 1 i 1 13i 13 i 1 i i 13 0.5i 0.5. 26 26 2 2 2 - - - = × - + - - - - + + - + - = = - + - - - = = = = - = = Q.4 The integrating factor for the differential equation 1 k t 2 1 0 dP k P k L e is dt - + = (A) 1 k t e - (B) 2 k t e - (C) 1 k t e (D) 2 k t e Answer: (D) Exp. 1 K t 2 1 0 dP K P K L e dt - + = The standard form of Linear differential equations is ( ) 1 2 2 p dx K t 2 1 0 K dt K t dy py Q; I.F e dx dP K P K L e dt Integrating factor, I.F e e . - ? + = = ? + = ? = = Q.5 If {x} is a continuous, real valued random variable defined over the interval ( ) , -8 +8 and its occurrence is defined by the density function given as: ( ) 2 1 x a 2 b 1 f x e 2 * b - ? ? ? ? ? ? = p where ‘a’ and ‘b’ are the statistical attributes of the random variable {x}. The value of the integral 2 1 x a a 2 b 1 e dx is 2 * b - ? ? - ? ? ? ? -8 p ? (A) 1 (B) 0.5 (C) p (D) 2 p Answer: (B) Exp. We have ( ) ( ) ( ) ( ) a a a f x dx 1 f x dx f x dx 1 f x dx 0.5 8 -8 8 -8 -8 = ? + = ? = ? ? ? ? 0.5 0.5 ( ) x a d = µ -8 -8Read More

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