# ISI Maths - Important Questions

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## ISI Maths - Important Questions

 Hi guys, I was reccomended to solve the book published by ISI - Mathematics a the 10+2 level so that one can tackle the 1st portion of the ISI paper with ease. Those who are also solving this book or are aspiring for ISI please join this discussion - where we can all keep posting the most difficult questions from it. Anybody who has any idea how to tackle them, please enlighten the rest of us :) Q11) The digit in the unit position of the integer 1!+2!+..+99! is ? A)3 B)0 C)1 D)7 Q16) The expression (1+q)(1+q^2)(1+q^4)(1+q^8)(1+q^16)(1+q^32)(1+q^64) where q ne 1 equals A)(1+q^128)/1-q B)(1+q^64)/1-q C){1+q^2^(1+2+..+6)}/1-q D) none of the above Q19) 2 contestants runa 3km race along a circular track of length 300m. If their speeds are in the ratio 4:3, how ofen and where would the winner pass the other? (initial start off is not counted as passing) A) 4 times at starting B) twice at starting C) Twice at dist of 225m from starting D)Twice; once at dist of 75m and then 225m from starting Q51) 60 students appeared in a test consisting of 3 papers I, II and III. 25 passed in Paper I. 20 in PI. 8 in PIII. 42 passed in at least one of PI and PII, 30 in at least one of PI and PIII, 25 in at least one of Papers II and III. one 1 student passed in all 3 papers. The the num of students who failed in all the papers is: A)15 B) 17 C) 45 D)33 Q52) A student studying the weather for d days observed: (i) it rained of 7 days, morning or afternoon (ii) when it rained in the afternoon, it was clear in the morning (iii) there were 5 clear afternoons (iv) there were 6 clear mornings. the d equals: A) 7 B) 11 C) 10 D)9
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## Re: ISI Maths - Important Questions

 Answer for question 11 is A
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## Re: ISI Maths - Important Questions

 Akshay Jain Masters in Economics Delhi School of Economics 2013-15
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## Re: ISI Maths - Important Questions

 In reply to this post by Ridhika Akshay Jain Masters in Economics Delhi School of Economics 2013-15
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 In reply to this post by Ridhika B for question 19
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## Re: ISI Maths - Important Questions

 In reply to this post by Ridhika 16. Its coming out to be D  (1 - q^128)/1-q as when you multiply the denominator and numerator by (1-q) (1-q)(1+q)=(1-q^2) (1-q^2)(1+q^2) = (1-q^4) ... and it becomes (1-q^64)(1+q^64) = (1-q^128) 51. 15 days 52. student studied d(morning and evening) days. Thus total of 2d mornings + afternoons (d days -> d mornings + d afternoons) and it rained for 7 days ( evenings or mornings.) with 5 clear afternoons and 6 clear afternoons so eqn becomes 7 + 5 + 6 = 2d or d=9 days "Woh mara papad wale ko!"
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## Re: ISI Maths - Important Questions

 @ Akshay, thank u! @ Aditya - the answer for q16 is (A) - I just dont know how.. You are spot on for q52..! thanks :) Ans 51 is 15 students.. can you tell me how you got that?
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## Re: ISI Maths - Important Questions

 Q 16 is pretty easy! Just multiply the given expression in question with 1-q and you end up with 1+q^128 .But that's not the final answer as you multiplied the expression with 1-q, so to get the final answer, undo your trick by dividing 1+q^128  by 1-q, so (1+q)(1+q^2)(1+q^4)(1+q^8)(1+q^16)(1+q^32)(1+q^64)=(1+q^128)/1-q . Q 51 Draw venn diagram, focus on the intersections. Then it is very easy to come up with answer within a minute. Note that students who are failed in all papers are the same who could not even at least pass one paper.
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## Re: ISI Maths - Important Questions

 Omg! Yup I got both.. thanks singham! ----- Reply message ----- From: "SINGHAM [via Discussion forum]" To: "Ridhika" <[hidden email]> Subject: ISI Maths - Important Questions Date: Tue, Apr 1, 2014 9:26 AM Q 16 is pretty easy! Just multiply the given expression in question with 1-q and you end up with 1+q^128 .But that's not the final answer as you multiplied the expression with 1-q, so to get the final answer, undo your trick by dividing 1+q^128  by 1-q, so (1+q)(1+q^2)(1+q^4)(1+q^8)(1+q^16)(1+q^32)(1+q^64)=(1+q^128)/1-q . Q 51 Draw venn diagram, focus on the intersections. Then it is very easy to come up with answer within a minute. Note that students who are failed in all papers are the same who could not even at least pass one paper. If you reply to this email, your message will be added to the discussion below: http://discussion-forum.2150183.n2.nabble.com/ISI-Maths-Important-Questions-tp7585806p7585871.html To unsubscribe from ISI Maths - Important Questions, click here. NAML
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 In reply to this post by Ridhika Do we have to do all the questions ...topics on geometry and all??
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## Re: ISI Maths - Important Questions

 So I'm skipping the trigo and geometry questions.. I don't think it gets asked.. havent seen it any of the papers so far.. ----- Reply message ----- From: "Ron [via Discussion forum]" To: "Ridhika" <[hidden email]> Subject: ISI Maths - Important Questions Date: Wed, Apr 2, 2014 7:27 PM Do we have to do all the questions ...topics on geometry and all?? If you reply to this email, your message will be added to the discussion below: http://discussion-forum.2150183.n2.nabble.com/ISI-Maths-Important-Questions-tp7585806p7585979.html To unsubscribe from ISI Maths - Important Questions, click here. NAML
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## Re: ISI Maths - Important Questions

 In reply to this post by The Villain Okay so the next set of questions is: 72 - 76 82) Let x1, x2,..,x100 be 100 integers such that the sum of any 5 of them is 20. Then, A) the largest xi = 5 B) smallest xi = 3 C) x17=x83 D) none of the above 87) The remainder when 3^37 is divided by 79 is? A) 78 B) 1 C) 2 D) 35
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## Re: ISI Maths - Important Questions

 Is it C for question 82?
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## Re: ISI Maths - Important Questions

 yes! but how? I just dont see the logic of this question!
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## Re: ISI Maths - Important Questions

 The way i see it..there is only one possible case where adding any arbitrary five elements out of the hundred gives you a sum of 20..its by considering every xi to be equal to 4..hence option C
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 In reply to this post by Ridhika
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 In reply to this post by Ridhika @Ridhika Are you solving the Bmath questions also which is give in the book? MA Economics DSE 2014-16