Page 1 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Q. No. 1 – 5 Carry One Mark Each 1. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Answer: (C) 3. Choose the word that is opposite in meaning to the word “coherent”. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91 Page 2 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Q. No. 1 – 5 Carry One Mark Each 1. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Answer: (C) 3. Choose the word that is opposite in meaning to the word “coherent”. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 Answer: (C) Exp: Total question 44×2=88 44×3=132 144 = 88 132 308 Total marks obtained= (21×2) + (15×3) + (23×2) =133 Total Number of students=44 Average 133 3.02 44 = = Q. No. 6 – 10 Carry One Mark Each 6. A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m. Answer: (B) 7. By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i), (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only Answer: (D) Page 3 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Q. No. 1 – 5 Carry One Mark Each 1. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Answer: (C) 3. Choose the word that is opposite in meaning to the word “coherent”. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 Answer: (C) Exp: Total question 44×2=88 44×3=132 144 = 88 132 308 Total marks obtained= (21×2) + (15×3) + (23×2) =133 Total Number of students=44 Average 133 3.02 44 = = Q. No. 6 – 10 Carry One Mark Each 6. A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m. Answer: (B) 7. By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i), (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only Answer: (D) ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 8. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012- 2013 (A) increased by 5 % (B) decreased by 13% (C) decreased by 20% (D) decreased by 11% Answer: (D) Exp: Per 100 Rs final value 107 Rs 100 Per Dollars 50 ? final value 107 60 for 100 dollars____? 100 50 107 89.16 100 60 × = × = Decreased by 11%. 9. he ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? (A) 1:1 (B) 2:1 (C) 1.5:1 (D) 2.5:1 Answer: (C) Exp: Take number of female students in 2011=100 ? Number of male in 2011=100 No. of female in 2012=100 No. of male in 2012=150 150 Ratio 100 = = 1.5: 1 10. Consider the equation: (7526) 8 - (Y) 8 = (4364) 8 , where (X) N stands for X to the base N. Find Y. (A) 1634 (B) 1737 (C) 3142 (D) 3162 Answer: (C) 3.5 3 2.5 2 1.5 1 0.5 0 2008 2009 2010 2011 2012 Ra tio of m ale to fe m ale stu de nts Page 4 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Q. No. 1 – 5 Carry One Mark Each 1. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Answer: (C) 3. Choose the word that is opposite in meaning to the word “coherent”. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 Answer: (C) Exp: Total question 44×2=88 44×3=132 144 = 88 132 308 Total marks obtained= (21×2) + (15×3) + (23×2) =133 Total Number of students=44 Average 133 3.02 44 = = Q. No. 6 – 10 Carry One Mark Each 6. A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m. Answer: (B) 7. By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i), (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only Answer: (D) ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 8. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012- 2013 (A) increased by 5 % (B) decreased by 13% (C) decreased by 20% (D) decreased by 11% Answer: (D) Exp: Per 100 Rs final value 107 Rs 100 Per Dollars 50 ? final value 107 60 for 100 dollars____? 100 50 107 89.16 100 60 × = × = Decreased by 11%. 9. he ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? (A) 1:1 (B) 2:1 (C) 1.5:1 (D) 2.5:1 Answer: (C) Exp: Take number of female students in 2011=100 ? Number of male in 2011=100 No. of female in 2012=100 No. of male in 2012=150 150 Ratio 100 = = 1.5: 1 10. Consider the equation: (7526) 8 - (Y) 8 = (4364) 8 , where (X) N stands for X to the base N. Find Y. (A) 1634 (B) 1737 (C) 3142 (D) 3162 Answer: (C) 3.5 3 2.5 2 1.5 1 0.5 0 2008 2009 2010 2011 2012 Ra tio of m ale to fe m ale stu de nts ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 Q. No. 1 – 25 Carry One Mark Each 1. Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? (A) Only L is TRUE. (B) Only M is TRUE. (C) Only N is TRUE. (D) L, M and N are TRUE. Answer: (D) Exp: ( ) [ ] ( ) g : mobile is good c : mobile is cheap P : Good mobile phones are not cheap g c g c a b a b Q : Cheap mobile phones are not good c g c g Both P and Q are equivalent which means P and Q imply each other ? ? ¬ ? ¬ ? ¬ ? = ¬ ? ? ? ¬ ? ¬ ? ¬ ? ? 2. Let X and Y be finite sets and f : X Y ? be a function. Which one of the following statements is TRUE? (A) For any subsets A and B of X, ( ) ( ) ( ) f A B f A f B ? = + (B) For any subsets A and B of X, ( ) ( ) ( ) f A B f A f B n = n (C) For any subsets A and B of X, ( ) ( ) ( ) { } f A B min f A , f B n = (D) For any subsets S and T of Y, ( ) ( ) ( ) 1 1 1 f S T f S f T - - - n = n Answer: (D) Exp: ( ) ( ) ( ) f : X Y defined by f a 1,f b 1,f c 2 where ? = = = { } { } { } { } ( ) ( ) ( ) ( ) { } ( ) { } ( ) { } ( ) ( ) { } ( ) X a,b,c Y 1,2 Let A a,c ,B b,c be subsets of X then f A B 2 ; f A 2 ; f B 2 f A B 2 ; f A 1,2 ;f B 1,2 f A f B 1,2 f A B 1 = = = = ? = = = n = = = n = n = ? Options (A), (B), (C) are not true Hence, option (D) is true Page 5 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Q. No. 1 – 5 Carry One Mark Each 1. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Answer: (C) 3. Choose the word that is opposite in meaning to the word “coherent”. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91 ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 Answer: (C) Exp: Total question 44×2=88 44×3=132 144 = 88 132 308 Total marks obtained= (21×2) + (15×3) + (23×2) =133 Total Number of students=44 Average 133 3.02 44 = = Q. No. 6 – 10 Carry One Mark Each 6. A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m. Answer: (B) 7. By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i), (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only Answer: (D) ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 8. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012- 2013 (A) increased by 5 % (B) decreased by 13% (C) decreased by 20% (D) decreased by 11% Answer: (D) Exp: Per 100 Rs final value 107 Rs 100 Per Dollars 50 ? final value 107 60 for 100 dollars____? 100 50 107 89.16 100 60 × = × = Decreased by 11%. 9. he ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? (A) 1:1 (B) 2:1 (C) 1.5:1 (D) 2.5:1 Answer: (C) Exp: Take number of female students in 2011=100 ? Number of male in 2011=100 No. of female in 2012=100 No. of male in 2012=150 150 Ratio 100 = = 1.5: 1 10. Consider the equation: (7526) 8 - (Y) 8 = (4364) 8 , where (X) N stands for X to the base N. Find Y. (A) 1634 (B) 1737 (C) 3142 (D) 3162 Answer: (C) 3.5 3 2.5 2 1.5 1 0.5 0 2008 2009 2010 2011 2012 Ra tio of m ale to fe m ale stu de nts ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 Q. No. 1 – 25 Carry One Mark Each 1. Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? (A) Only L is TRUE. (B) Only M is TRUE. (C) Only N is TRUE. (D) L, M and N are TRUE. Answer: (D) Exp: ( ) [ ] ( ) g : mobile is good c : mobile is cheap P : Good mobile phones are not cheap g c g c a b a b Q : Cheap mobile phones are not good c g c g Both P and Q are equivalent which means P and Q imply each other ? ? ¬ ? ¬ ? ¬ ? = ¬ ? ? ? ¬ ? ¬ ? ¬ ? ? 2. Let X and Y be finite sets and f : X Y ? be a function. Which one of the following statements is TRUE? (A) For any subsets A and B of X, ( ) ( ) ( ) f A B f A f B ? = + (B) For any subsets A and B of X, ( ) ( ) ( ) f A B f A f B n = n (C) For any subsets A and B of X, ( ) ( ) ( ) { } f A B min f A , f B n = (D) For any subsets S and T of Y, ( ) ( ) ( ) 1 1 1 f S T f S f T - - - n = n Answer: (D) Exp: ( ) ( ) ( ) f : X Y defined by f a 1,f b 1,f c 2 where ? = = = { } { } { } { } ( ) ( ) ( ) ( ) { } ( ) { } ( ) { } ( ) ( ) { } ( ) X a,b,c Y 1,2 Let A a,c ,B b,c be subsets of X then f A B 2 ; f A 2 ; f B 2 f A B 2 ; f A 1,2 ;f B 1,2 f A f B 1,2 f A B 1 = = = = ? = = = n = = = n = n = ? Options (A), (B), (C) are not true Hence, option (D) is true ?CS-GATE-2014 PAPER-03| www.gateforum.com India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 3. Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L G ? and that the size of L is at least 4. The size of L is _______. Answer: (5) Exp: Order of subgroup divides order of group (Lagrange’s theorem). 3, 5 and 15 can be the order of subgroup. As subgroup has atleast 4 elements and it is not equal to the given group, order of subgroup can’t be 3 and 15. Hence it is 5. 4. Which one of the following statements is TRUE about every n × n matrix with only real eigenvalues? (A) If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. (B) If the trace of the matrix is positive, all its eigenvalues are positive. (C) If the determinant of the matrix is positive, all its eigenvalues are positive. (D) If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive. Answer: (A) Exp: If the trace of the matrix is positive and the determinant of the matrix is negative then atleast one of its eigen values is negative. Since determinant = product of eigen values. 5. If V 1 and V 2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of 1 2 V V n is _______. Answer: (2) Exp: Let the basis of 6-dimensional vector space be {e1, e2, e3,e4, e5, e6}. In order for V1 n V2 to have smallest possible dimension V1 and V2 could be, say, {e1, e2, e3,e4} and {e3, e4, e5, e6} respectively. The basis of V1 n V2 would then be {e3, e4}. => Smallest possible dimension = 2. 6. If 2 0 xsin x p ? dx = kp, then the value of k is equal to _______. Answer: ( 4 ) Exp: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 0 0 2 0 sin x sin x xsin x dx K xsin x dx xsin x dx K x 2 x cos x 1 sin x x cos x sin x K cos sin 0 2 cos2 sin 2 cos sin K 0 2 0 0 K 4 K k 4 p p p p p p p ? ? =- = p? + - = p ? ? p< < p ? ? ? - - - - - + = p ? -p p + p - -? - p p+ p - -p p + p ? = p ? ? ? p + -?- p+ - p+ ? = p? p = p ? = ? ? ? ? ? ?Read More

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