ISI Maths - Important Questions

[Ridhika]

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

[Noel]

Answer for question 11 is A

[Akshay Jain]

[Akshay Jain]

[Noel]

B for question 19

[Bankelal]

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

[Ridhika]

@ 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?

[SINGHAM]

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.

[Ridhika]

Omg! Yup I got both.. thanks singham!

----- Reply message -----
From: "SINGHAM [via Discussion forum]" <ml-node+[hidden email]>
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.

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NAML

[The Villain]

Do we have to do all the questions ...topics on geometry and all??

[Ridhika]

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]" <ml-node+[hidden email]>
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??

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NAML

[Ridhika]

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

[Noel]

Is it C for question 82?

[Ridhika]

yes! but how? I just dont see the logic of this question!

[Noel]

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

[Noel]

[SoniaKapoor]

@Ridhika Are you solving the Bmath questions also which is give in the book?

[SINGHAM]

THANK YOU SO MUCH NOEL!

I was always afraid with mod expression! now it seems that I can handle some of them! Never got an online explession so detailed!

[Noel]

@singham..happy to help you :)