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CAT 2007: Quantitative Questions a Day 51 to 100 - The Discussions

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Please carry the QQAD discussion for the next 50 problems here. Try getting each and every solution in the very 1st attempt itself. Avoid risky speed. Just in case you see any mod around, please request him to make this thread sticky. ... Read More »
hi , it's udit ....
pls help me in soving these....

*** when x + y + z = 6, x^2 + y^2 + z^2 = 8, x^3 + y^3 + z^3 = 5 then x^4 + y^4 + z^4 = ?? 0/1/9/ can not be det

*** how many natural numbers less than 100 can be expressed as a difference of two perfect squares in only one way ?? 25/28/35/38

*** when x^13 + x +90 is divided by x^2 x +n , remainder obtained is zero how many integral values of n is / are possible ?? 0/1/2/ infinite

cheers!!!!
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Hi,
Cheers
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Can anyone send me the link to get all the question and solution

For solutions of QQAD problems 51-100, refer post# 1961, pg 197 on this same thread. Posted by Deepan_Kapadia..
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Can anyone send me the link to get all the question and solution

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Hello,

I am not getting this post on my e-mail properly. Could owner of this can help me??

Please explain in detail as to what the issue is.
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Hello,

I am not getting this post on my e-mail properly. Could owner of this can help me??

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Hello,

I am not getting this post on my e-mail properly. Could owner of this can help me??
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1.48
2.80

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1.48
2.80
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plz help me

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Actually I M Not Getting Any Region Bounded By These Two Curves
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plz try to provide a diagram in he solutions to the geaometry and mensuration topics otherwise its real difficult to understand the sol
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ques# 105
solution for part A:
How many integral values of p are there for which the inequality 3 - x-p > x^2 is satisfied by at least one negative x?

"by atleast one negative x"
This implies whatever values of p we find for the solution x<0 (i.e -ve)

taking x as negative the inequality looks like

3-(x+P)>x^2
or x^2+x+p-3<0

solving this we will get 2 roots. Now we have to see how x^2+x+p-3 will behave between these roots and beyong these roots. At x=-1/2 we will get minimum value of x^2+x+p-3. Thus any value between the roots satisfy the inequality. now on sloving the equation x^2+x+p-3 the delta value is 13-4p. For real values of the solution 13-4p>=0.
=> p<=3.25
thus p can be any integral less than equal to 3. So the number of solutions will be infinite.
hence (e) non of the foregoing is the answer

check fallas. might be i m wrong
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Ques#105
Part B:

In the end of the question it says for all x in (1,2). This means x=1 for case 1and x=2 for case 2

case 1:
putting x=1 in the inequality we get
p^2+7*p+1<0

solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+7*p+1 will be less than zero (p= -7/2 will give ninimum value of the equation). Hence -6,-5,-4,-3,-2,-1 satisfy the inequality for x=1

case 2:
putting x=2 in the inequality we get
p^2+8*p+4<0

solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -7,-6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+8*p+4 will be less than zero (p= -4 will give ninimum value of the equation).
Hence -7,-6,-5,-4,-3,-2,-1 satisfy the inequality for x=1

The common integral values from case 1 and 2 are
-1,-2,-3,-4,-5,-6

thus, (d) 6 is the answer

Hope the solution is correct...have given major fundae:)
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