Q1) The number of natural numbers n such that (n^2+1)^2/(n+1) is an integer?
Q2)Find the product of the factor of 316?
Q3)What is the remainder when 90^(91) is divided by 13?
Q4)If n^2 =123.4564321,which of the following is the value of n?
a) 11.1001 b) 11.1101 c) 11.1111 d) 11.1011
Q5)Find the remainder when 4^44 is divided by 15.
Q6)How many times the didgit 6 appear when we count from 11 to 400?
Q7)Remainder when 1714x1715x1717/12?
Q8)N^2=12345678987654321. Find N?
Q9)The smallest number which is a perfect squre and is of the form abbb is between.
a)3000-4000 b)4000-5000 c)2000-3000 d)1000-2000.
Q10)N=204x221x255x...x850.How many consecutive zeroes will be at the end of the number?
Q11) A number has exactly 15 composite factors,what can be the maximum number of prime factors of this number?
commented on: Fri, 2008-05-16 16:04
CAT@IIMs points: 259
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As i am nw wdout pencil nd
As i am nw wdout pencil nd paper...Dn try to solve easier ones....
Q1) The number of natural numbers n such that (n^2+1)^2/(n+1) is an integer?
Soln.As, (n^2+1)^2=[(n+1)^2-2n]^2
So dependin on 4n^2/(n+1) we will get integer
n=1,3 satisfies d condn, Cz all HCF(n,n+1)=1
Two no.s are possible....
Giv ur best to d world.
Nd d best will cm back to u....
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:07
CAT@IIMs points: 259
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Q3)What is the remainder
Q3)What is the remainder when 90^(91) is divided by 13?
Soln.:90^91=(91-1)^91
So,90^91=12(mod 13)
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:09
CAT@IIMs points: 259
Location:
Comments : 117
Q4)If n^2 =123.4564321,which
Q4)If n^2 =123.4564321,which of the following is the value of n?
a) 11.1001 b) 11.1101 c) 11.1111 d) 11.1011
Soln. I hp u knw d rule of ds kind of format..
So, n=11.1111
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:11
CAT@IIMs points: 259
Location:
Comments : 117
Q5)Find the remainder when
Q5)Find the remainder when 4^44 is divided by 15.
Soln.As 4^44=(15+1)^22
So, 4^44=1(mod 15)
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:14
CAT@IIMs points: 259
Location:
Comments : 117
Q6)How many times the didgit
Q6)How many times the didgit 6 appear when we count from 11 to 400?
Soln. For unit digit 9+10+10+10 =39 times.
For tens digit 10x4=40 times
Total=79 times...
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:18
CAT@IIMs points: 259
Location:
Comments : 117
Q7)Remainder when
Q7)Remainder when 1714x1715x1717/12?
Soln: Remainder of 1714x1715x1717/12
= R.O. 10x11x13/12=2
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....
commented on: Fri, 2008-05-16 16:21
CAT@IIMs points: 259
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Comments : 117
Q8)N^2=12345678987654321.
Q8)N^2=12345678987654321. Find N?
Soln. Same as Qs no.4
Answer is:111111111(Short Cut:No. of ones side by side till d highest no. present wdin dt digit..Here its 9)
Giv ur best to d world.
Nd d best wil cm back to u...
Regards,
Dipanjan...
commented on: Fri, 2008-05-16 16:32
CAT@IIMs points: 259
Location:
Comments : 117
Q11) A number has exactly 15
Q11) A number has exactly 15 composite factors,what can be the maximum number of prime factors of this number?
Soln:15=3x5
X^2 * Y^4 is d only form where X & Y are the primes...
Giv ur best to d world.
Nd d best will cm back to u...
Regards,
Dipanjan.....