Number System - Questions & Discussions

is the answer 750???????

spaniel Says
is the answer 750???????


Spaniel,

Yes, the answer is 750. How did you get it ?? Kindly share the approach ..

Thank you.

Kindly help,

How many integers between 1 and 1000, both inclusive, can be expressed as the difference of the squares of two non negative integers ??

Thank you.



The answer is nothing but all odd numbers -> 499.
and all multiples of 4 -> 249.
=> Total = 499 + 249 = 748. .
The answer is nothing but all odd numbers -> 499.
and all multiples of 4 -> 249.
=> Total = 499 + 249 = 748. .


Enceladus,

Why all odd numbers and the multiples of 4.. What is the logic behind this ??

Thank you.

What is the remainder when 21^3+23^3+25^3+27^3 divided by 96?

1) 0
2) 72
3) 12
4) 48
5) 24

for the above question,
1) 0

What is the remainder when 21^3+23^3+25^3+27^3 divided by 96?

1) 0
2) 72
3) 12
4) 48
5) 24



0...
use a^3+b^3.

Q (1):There exists a 10 digit number such that the 1st digit from left represents the number of 0's in the number, the 2nd digit from left represents the number of 1's occurring in the number and so on until the 10th digit represents the number of 9's in the number.

1. The sum of the digits of the number is:
1. 8 2. 9 3. 10 4. 19

2. The number of 0s in the number is:
1. 9 2. 8 3. 7 4. 6

3. The number of 1s occurring in the number is:
1. 0 2. 1 3. 2 4. 3

Q(2)Rahul intends to draw one rectangle of integer sides with a pencil which can last for a maximum possible length of 100 units only. Let R denote the set of all possible distinct rectangles from which rahul can choose to draw one such rectangle.

1. The number of rectangles in set R is
1. 636 2. 601 3. 613 4. 625

2. All the rectangles in R are formed in to groups such that all the rectangles of same perimeter are in the same group. What is maximum number of groups that is possible?
1. 99 2. 96 3. 49 4. 51

plzz help::
the remainder wen 10^10+10^100+10^1000+.....+10^10000000000 is divided by 7 is
0
1
2
5

plzz help::
the remainder wen 10^10+10^100+10^1000+.....+10^10000000000 is divided by 7 is
0
1
2
5

The answer is 5...
solution -
(10^10)/7 = (3^10)/7.
Now (3^6)/7 gives 1 remainder ( Fermat's th.)
(3^10)/7 = (3^4)/7 = 81/7 which gives 4 remainder.

Similarly, all other expressions will also give remainder 4.
there r total 10 expp..
so it reduces to 40/7 which gives 5 remainder..

plzz help::
the remainder wen 10^10+10^100+10^1000+.....+10^10000000000 is divided by 7 is
0
1
2
5


The answer is 5...
solution -
(10^10)/7 = (3^10)/7.
Now (3^6)/7 gives 1 remainder ( Fermat's th.)
(3^10)/7 = (3^4)/7 = 81/7 which gives 4 remainder.

Similarly, all other expressions will also give remainder 4.
there r total 10 expp..
so it reduces to 40/7 which gives 5 remainder..
plzz help::
the remainder wen 10^10+10^100+10^1000+.....+10^10000000000 is divided by 7 is
0
1
2
5


It should be 5.

E(7) = 6.
10 mod 6 = 4.
100 mod 6 = 4.
1000 mod 6 = 4.
and so on....
So this expression reduced to 10*3^4.
=> 10*3^4 mod 7 = 5.

Can anyone plz explain how the remainder problems are to be done when the dividend is a factorial.
For ex : Find the remainder when 34! is divided by 71.

Is Wilson's theorem applicable here?If yes,then how?

thanx a ton

two equations are given and said that they have a common root.... what is the condition that needs to be fulfilled for this? do we merely just equate the two equations? reply asap..

What is the remainder when 128^1000 is divided by 153 ?
a) 103
b) 145
c) 118
d) 52

Do show me the approach.

Find the remainder when 50^56^52 is divided by 11.
a) 7
b) 5
c) 9
d) 10

I am concerned with the approach.

How many integer values of x and y satisfy the expression 4x + 3y = 3 where |x| a) 284
b) 285
c) 286
d) None of these.

Approach plz.

@[229334:pk_gt1]

ans is 9.
odd power of 9 and we get unit digit as 9...