Page 1 ?CH-GATE-2014 PAPER| 1 Q.No-1-5 Carry One Mark Each 1. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2. Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) choices (D) strength Answer: (B) 3. Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 4. If y = 5x 2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of -1 Answer: (C) Exp: 2 x 0, y 3 dy y 5x 3, 10x dx dy Slope of tan gent 10 0 0 dx = = = + = ? ? = = × = ? ? ? ? Slope = 0 ? tangent is parallel to x-axis. 5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost = Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800×100 = 130,000 So, cost of production per tonne of daily production 130,000 Rs.1300. 100 = = Page 2 ?CH-GATE-2014 PAPER| 1 Q.No-1-5 Carry One Mark Each 1. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2. Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) choices (D) strength Answer: (B) 3. Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 4. If y = 5x 2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of -1 Answer: (C) Exp: 2 x 0, y 3 dy y 5x 3, 10x dx dy Slope of tan gent 10 0 0 dx = = = + = ? ? = = × = ? ? ? ? Slope = 0 ? tangent is parallel to x-axis. 5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost = Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800×100 = 130,000 So, cost of production per tonne of daily production 130,000 Rs.1300. 100 = = ?CH-GATE-2014 PAPER| 2 Q.No-6-10 Carry Two Marks Each 6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK Answer: (D) Exp: ALRVX?only one vowel EPVZB?only one vowel ITZDF?only one vowel OYEIK?three vowels 7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5 Answer: (B) Exp: (a) Anuj: Even numbered floor (2,4,6) (b) Bhola: Even numbered floor (2,4,6) (c) Chandan lives on the floor above that of Faisal. (d) Dilip: not on 2 nd floor. (e) Eswar: does not live immediately above or immediately below Bhola From the options its clear, that only option (B) satisfies condition (e). So, correct Ans is (B). 8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Answer: 180 to 180 Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x So, 3x+4x+5x+6x = 360 x = 20 Smallest angle of quadrilateral = 3×20 = 60° Smallest angle of triangle = 2 60 40 3 × °= ° Largest angle of triangle = 2×40° = 60° Three angles of triangle are 40°, 60°, 80° Largest angle of quadrilateral is 120° Sum (2 nd largest angle of triangle + largest angle of quadrilateral) = 60°+120°=180°. Page 3 ?CH-GATE-2014 PAPER| 1 Q.No-1-5 Carry One Mark Each 1. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2. Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) choices (D) strength Answer: (B) 3. Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 4. If y = 5x 2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of -1 Answer: (C) Exp: 2 x 0, y 3 dy y 5x 3, 10x dx dy Slope of tan gent 10 0 0 dx = = = + = ? ? = = × = ? ? ? ? Slope = 0 ? tangent is parallel to x-axis. 5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost = Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800×100 = 130,000 So, cost of production per tonne of daily production 130,000 Rs.1300. 100 = = ?CH-GATE-2014 PAPER| 2 Q.No-6-10 Carry Two Marks Each 6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK Answer: (D) Exp: ALRVX?only one vowel EPVZB?only one vowel ITZDF?only one vowel OYEIK?three vowels 7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5 Answer: (B) Exp: (a) Anuj: Even numbered floor (2,4,6) (b) Bhola: Even numbered floor (2,4,6) (c) Chandan lives on the floor above that of Faisal. (d) Dilip: not on 2 nd floor. (e) Eswar: does not live immediately above or immediately below Bhola From the options its clear, that only option (B) satisfies condition (e). So, correct Ans is (B). 8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Answer: 180 to 180 Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x So, 3x+4x+5x+6x = 360 x = 20 Smallest angle of quadrilateral = 3×20 = 60° Smallest angle of triangle = 2 60 40 3 × °= ° Largest angle of triangle = 2×40° = 60° Three angles of triangle are 40°, 60°, 80° Largest angle of quadrilateral is 120° Sum (2 nd largest angle of triangle + largest angle of quadrilateral) = 60°+120°=180°. ?CH-GATE-2014 PAPER| 3 9. One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft? (A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25 Answer: (D) Exp: Let number of people in country y = 100 So, number of people in country x = 300 Total number of people taller than 6ft in both the countries 1 2 300 100 5 100 100 = × + × = % of people taller than 6ft in both the countries 5 100 1.25%. 400 = × = 10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value) (i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv) Answer: (B) Exp: In the question the monthly average rainfall chart for 50 years has been given. Let us check the options. (i) On average, it rains more in July than in December ? correct. (ii) Every year, the amount of rainfall in August is more than that in January. ? may not be correct because average rainfall is given in the question. (iii) July rainfall can be estimated with better confidence than February rainfall. ? From chart it is clear the gap between 5 percentile and 95 percentile from average is higher in February than that in July ? correct. (iv) In August at least 500 mm rainfall ? May not be correct, because its 50 year average. So correct option (B) (i) and (iii). 800 700 600 500 400 300 200 100 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average 5 percentile 95 percentile Page 4 ?CH-GATE-2014 PAPER| 1 Q.No-1-5 Carry One Mark Each 1. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2. Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) choices (D) strength Answer: (B) 3. Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 4. If y = 5x 2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of -1 Answer: (C) Exp: 2 x 0, y 3 dy y 5x 3, 10x dx dy Slope of tan gent 10 0 0 dx = = = + = ? ? = = × = ? ? ? ? Slope = 0 ? tangent is parallel to x-axis. 5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost = Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800×100 = 130,000 So, cost of production per tonne of daily production 130,000 Rs.1300. 100 = = ?CH-GATE-2014 PAPER| 2 Q.No-6-10 Carry Two Marks Each 6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK Answer: (D) Exp: ALRVX?only one vowel EPVZB?only one vowel ITZDF?only one vowel OYEIK?three vowels 7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5 Answer: (B) Exp: (a) Anuj: Even numbered floor (2,4,6) (b) Bhola: Even numbered floor (2,4,6) (c) Chandan lives on the floor above that of Faisal. (d) Dilip: not on 2 nd floor. (e) Eswar: does not live immediately above or immediately below Bhola From the options its clear, that only option (B) satisfies condition (e). So, correct Ans is (B). 8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Answer: 180 to 180 Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x So, 3x+4x+5x+6x = 360 x = 20 Smallest angle of quadrilateral = 3×20 = 60° Smallest angle of triangle = 2 60 40 3 × °= ° Largest angle of triangle = 2×40° = 60° Three angles of triangle are 40°, 60°, 80° Largest angle of quadrilateral is 120° Sum (2 nd largest angle of triangle + largest angle of quadrilateral) = 60°+120°=180°. ?CH-GATE-2014 PAPER| 3 9. One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft? (A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25 Answer: (D) Exp: Let number of people in country y = 100 So, number of people in country x = 300 Total number of people taller than 6ft in both the countries 1 2 300 100 5 100 100 = × + × = % of people taller than 6ft in both the countries 5 100 1.25%. 400 = × = 10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value) (i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv) Answer: (B) Exp: In the question the monthly average rainfall chart for 50 years has been given. Let us check the options. (i) On average, it rains more in July than in December ? correct. (ii) Every year, the amount of rainfall in August is more than that in January. ? may not be correct because average rainfall is given in the question. (iii) July rainfall can be estimated with better confidence than February rainfall. ? From chart it is clear the gap between 5 percentile and 95 percentile from average is higher in February than that in July ? correct. (iv) In August at least 500 mm rainfall ? May not be correct, because its 50 year average. So correct option (B) (i) and (iii). 800 700 600 500 400 300 200 100 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average 5 percentile 95 percentile ?CH-GATE-2014 PAPER| 4 Q.No-1-25 Carry One Mark Each 1. Gradient of a scalar variable is always (A) a vector (B) a scalar (C) a dot product (D) zero Answer: (A) Exp. Gradient i j k x y z If f is a scalar point function f f f f grad f i j k is a vector. x y z ? ? ? ?= + + ? ? ? ? ? ? ? = = + + ? ? ? 2. For the time domain function, f(t) = t 2 ,which ONE of the following is the Laplace transform of ( ) t 0 f t dt ? ? ( ) 4 3 A s ( ) 2 1 B 4s ( ) 3 2 C s ( ) 4 2 D s Answer: (D) Exp. We have ( ) ( ) ( ) ( ) t 0 t 2 2 3 4 3 0 F s L f t dt where F s L f t s 2 2 2 L t dt 3 L t s s s ? ? = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. If f*(x) is the complex conjugate of f(x) = cos(x) + i sin(x), then for real a and b, ( ) ( ) b a f * x f x dx is ALWAYS ? ( ) A positive ( ) B negative ( ) C real ( ) D imaginary Answer: (C) Exp. ( ) ( ) ( ) f x cos x isin x = + ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) b b a a b b ix ix a a f * x cos x isin x f * x .f x dx cos x isin x cos isin x dx e .e dx 1.dx b a R a, b, R Real for real a & b. - = - = - + = = = - ? ? ? ? ? ? ? ? 4. If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about its minima will NEVER have a term containing (A) first derivative (B) second derivative (C) third derivative (D) any higher derivative Answer: (A) Page 5 ?CH-GATE-2014 PAPER| 1 Q.No-1-5 Carry One Mark Each 1. A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2. Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) choices (D) strength Answer: (B) 3. Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 4. If y = 5x 2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of -1 Answer: (C) Exp: 2 x 0, y 3 dy y 5x 3, 10x dx dy Slope of tan gent 10 0 0 dx = = = + = ? ? = = × = ? ? ? ? Slope = 0 ? tangent is parallel to x-axis. 5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost = Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800×100 = 130,000 So, cost of production per tonne of daily production 130,000 Rs.1300. 100 = = ?CH-GATE-2014 PAPER| 2 Q.No-6-10 Carry Two Marks Each 6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK Answer: (D) Exp: ALRVX?only one vowel EPVZB?only one vowel ITZDF?only one vowel OYEIK?three vowels 7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5 Answer: (B) Exp: (a) Anuj: Even numbered floor (2,4,6) (b) Bhola: Even numbered floor (2,4,6) (c) Chandan lives on the floor above that of Faisal. (d) Dilip: not on 2 nd floor. (e) Eswar: does not live immediately above or immediately below Bhola From the options its clear, that only option (B) satisfies condition (e). So, correct Ans is (B). 8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Answer: 180 to 180 Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x So, 3x+4x+5x+6x = 360 x = 20 Smallest angle of quadrilateral = 3×20 = 60° Smallest angle of triangle = 2 60 40 3 × °= ° Largest angle of triangle = 2×40° = 60° Three angles of triangle are 40°, 60°, 80° Largest angle of quadrilateral is 120° Sum (2 nd largest angle of triangle + largest angle of quadrilateral) = 60°+120°=180°. ?CH-GATE-2014 PAPER| 3 9. One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft? (A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25 Answer: (D) Exp: Let number of people in country y = 100 So, number of people in country x = 300 Total number of people taller than 6ft in both the countries 1 2 300 100 5 100 100 = × + × = % of people taller than 6ft in both the countries 5 100 1.25%. 400 = × = 10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value) (i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv) Answer: (B) Exp: In the question the monthly average rainfall chart for 50 years has been given. Let us check the options. (i) On average, it rains more in July than in December ? correct. (ii) Every year, the amount of rainfall in August is more than that in January. ? may not be correct because average rainfall is given in the question. (iii) July rainfall can be estimated with better confidence than February rainfall. ? From chart it is clear the gap between 5 percentile and 95 percentile from average is higher in February than that in July ? correct. (iv) In August at least 500 mm rainfall ? May not be correct, because its 50 year average. So correct option (B) (i) and (iii). 800 700 600 500 400 300 200 100 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average 5 percentile 95 percentile ?CH-GATE-2014 PAPER| 4 Q.No-1-25 Carry One Mark Each 1. Gradient of a scalar variable is always (A) a vector (B) a scalar (C) a dot product (D) zero Answer: (A) Exp. Gradient i j k x y z If f is a scalar point function f f f f grad f i j k is a vector. x y z ? ? ? ?= + + ? ? ? ? ? ? ? = = + + ? ? ? 2. For the time domain function, f(t) = t 2 ,which ONE of the following is the Laplace transform of ( ) t 0 f t dt ? ? ( ) 4 3 A s ( ) 2 1 B 4s ( ) 3 2 C s ( ) 4 2 D s Answer: (D) Exp. We have ( ) ( ) ( ) ( ) t 0 t 2 2 3 4 3 0 F s L f t dt where F s L f t s 2 2 2 L t dt 3 L t s s s ? ? = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = = = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. If f*(x) is the complex conjugate of f(x) = cos(x) + i sin(x), then for real a and b, ( ) ( ) b a f * x f x dx is ALWAYS ? ( ) A positive ( ) B negative ( ) C real ( ) D imaginary Answer: (C) Exp. ( ) ( ) ( ) f x cos x isin x = + ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) b b a a b b ix ix a a f * x cos x isin x f * x .f x dx cos x isin x cos isin x dx e .e dx 1.dx b a R a, b, R Real for real a & b. - = - = - + = = = - ? ? ? ? ? ? ? ? 4. If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about its minima will NEVER have a term containing (A) first derivative (B) second derivative (C) third derivative (D) any higher derivative Answer: (A) ?CH-GATE-2014 PAPER| 5 Exp. For a real valued function y = f(x) Taylor series expansion about ‘a’ ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 x a f x f a x a f ' a f '' a ..... 2! For min ima at x a, f ' a 0. - = + - + + = = So, Taylor series expansion of f(x) about ‘a’ will never contain first derivative term. 5. From the following list, identify the properties which are equal in both vapour and liquid phases at equilibrium P. Density Temperature R. Chemical potential S. Enthalpy (A) P and Q only (B) Q and R only (C) R and S only (D) P and S only Answer: (B) Exp. For phase equilibrium ( ) g l g l g l Temperature; T T Pr essure; P P correct Ans is B . Chemical potential; ? = ? = ? ? µ =µ ? 6. In a closed system, the isentropic expansion of an ideal gas with constant specific heats is represented by Answer: (D) Exp. For isentropic expansion, PV cons tan t Taking log on both sides ln P ln V 0 ln P negative ln V ? = +? = =-?= is positive slope of lnP vs ln V is negative. ? ? ( ) A P V ( ) B P V ( ) D ( ) ln P ( ) ln V ( ) C ( ) ln P ( ) ln VRead More

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