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Syeda
answered
1 year(s)
, 10 month(s) ago

Show that one and only one out of n,n+2,n+4 is divisible by 3, where n is any positive integer.

Answer.

We applied Euclid Division algorithm on n and 3.

a = bq +r on putting a = n and b = 3

n = 3q +r , 0 i.e n = 3q -------- (1),n = 3q +1 --------- (2), n = 3...

- 2 Answers
- 28 Likes
- 150634 Views

Priyanshu
answered
1 year(s)
, 5 month(s) ago

What are the values of log from 1 to 10?

log 1 = 0

log 2 = 0.3010

log 3 = 0.4771

log 4 = 0.6020

log 5 = 0.6989

log 6 = 0.7781

log 7 = 0.8450

log 8 = 0.9030

log 9 = 0.9542

log 10 =...

- 3 Answers
- 12 Likes
- 123458 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Find the greatest 6 digits number exactly divisible by 24, 15,and 36.

We will find out the LCM of 24,15 and 36 is 360.

Now, greatest 6-digit number is 999999.

Now, We will divide this number by LCM of 24,15 and 36, we will get,

999999/360 will get remai

...- 2 Answers
- 7 Likes
- 92600 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Find the largest number which divide 615 and 963 leaving remainder 6 in each case.

To find the largest number which divides 615 and 963 leaving remainder 6 in each case i.e. HCF.

Consider HCF be x.

In order to make 615 and 963 completely divisible by x, we need to deduct th

...- 2 Answers
- 6 Likes
- 79470 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Prove that the product of three consecutive positive integer is divisible by 6.

Sol;

Let us three consecutive integers be, n, n + 1 and n + 2.

Whenever a number is divided by 3 the remainder obtained is either 0 or 1 or 2.

let n = 3p or 3p + 1 or 3p + 2, where p is so...

- 2 Answers
- 6 Likes
- 75886 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

1] what is the smallest no. that when divided by 35,56,91 leaves a remainder 7 in each case?

Sol:

The smallest number which when divided by 35, 56 and 91 = LCM of 35, 56 and 91

35 = 5 x 7

56 = 2 x 2 x 2 x 7

91 = 7 x 13

LCM = 7 x 5 x 2 x 2 x 2 x 13...

- 2 Answers
- 1 Like
- 55094 Views

Priyanshu
answered
1 year(s)
, 7 month(s) ago

A rectangular courtyard is 18m 72cm long and 13m 20cm broad

Given length of rectangular courtyard = 18 m 72 cm

= 1872 cm

Width of rectangular courtyard = 13 m 20 cm

...

- 9 Answers
- 8 Likes
- 54852 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

show that (n2-1) Is divisible by 8??

Sol:

If 'n' is an odd positive integer, show that (n
^{2}-1) Is divisible by 8??

Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.

...

- 2 Answers
- 3 Likes
- 54650 Views

Chandan
answered
1 year(s)
, 8 month(s) ago

Prove that root 5 is irrational.

Answer.

let root 5 be rational

then it must in the form of p/q [q is not equal to 0][p and q are co-prime]

root 5=p/q

=> root 5 * q = p

squaring on both sides

=> 5*q*q

- 4 Answers
- 3 Likes
- 50627 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Prove that if x and y are odd positive integers, then x2 + y2 is even

Answer.

Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1

Hence x^{2 }+ y^{2} = (2k + 1)^{2} + (2p + 1)^{2}

= 4k^{2</}

- 2 Answers
- 3 Likes
- 44134 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Any positive odd integer is of the form 4q+1 or 4q+3

Use Euclid's division lema to show that square of any positive integer is either of the form 3m or3m+1integer m

Asked by Mr davinder pal

Jun 12

- 3 Answers
- 6 Likes
- 41457 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

Product of two consecutive positive integers is divisible by 2

Answer.

Let the two consecutive positive integers be and

Product of two consecutive positive integers

Case (i): is even number

Let

...

- 2 Answers
- 5 Likes
- 37672 Views

Pragasam
commented
3 year(s)
, 10 month(s) ago

If the HCF of 210 and 55 is expressible in the form 210 x 5 - 55y, find y.

Let us first find the HCF of 210 and 55.

Applying Euclid division lemna on 210 and 55, we get

210 = 55 × 3 + 45

55 = 45 × 1 + 10

45 = 4 × 10 + 5

10 = 5 × 2 + 0

...- 1 Answer
- 5 Likes
- 37463 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

for any positive integer n,prove that n3-n is divisible by 6

Answer.

By the mathematical induction we have to prove this.

⇒ Given that S(n) = n
^{3}-n divisible by 6.

Let n =1 then we get '0'

which is divisible by 6....

Asked by Chandanagouda

Apr 2

- 2 Answers
- 1 Like
- 37356 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

After how many places of decimals, decimal expansion will terminate?

Answer.

147/120

= (3 x 49) / (2 x 2 x 2 x 3 x 5)

= (49) / (2 x 2 x 2 x 5)

= ( 49 x 5 x 5) / (2 x 2 x 2 x 5 x 5 x 5)

= (1225) / (2
^{3} x 5
^{3})...

- 2 Answers
- 1 Like
- 36249 Views

Agam
answered
1 year(s)
, 9 month(s) ago

prove squre root 2 is irrational

Sol:

Given √2 is irrational number.

Let √2 = a / b wher a,b are integers b ≠ 0

we also suppose that a / b is written in the simplest form

Now √2 = a / b ⇒ 2 = a
^{2} / b...

Asked by Rambabuandey

Jul 12

- 3 Answers
- 3 Likes
- 34820 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

One of the two numbers a+b/2 and a-b/2 is odd and the other is even

Answer.

Let a and b are any two odd positive integers.

Hence and where m and n are whole numbers.

Consider

Therefore is a positive integer.

Now,

But give

...- 2 Answers
- 3 Likes
- 33902 Views

Raghunath
answered
3 year(s)
, 10 month(s) ago

prove that n 2 - n is divisible by 2 for every integer n ?

Casei: Let n be an even positive integer.

When n = 2q

In this case , we have

n
^{2} - n = (2q)
^{2 }- 2q = 4q
^{2} - 2q = 2q (2q - 1 )

n
^{2} - n...

- 2 Answers
- 3 Likes
- 32303 Views

Syeda
answered
1 year(s)
, 10 month(s) ago

prove that the square of any positive integer is of the form 5q or 5q+1 or 5q+4, for some integer q.

Answer.

Let x be any positive integer

Then x = 5q or x = 5q+1 or x = 5q+4 for integer x.

If x = 5q, x
^{2 }= (5q)
^{2} = 25q
^{2} = 5(5q
^{2}...

- 2 Answers
- 3 Likes
- 31233 Views

Ramesh
answered
3 year(s)
, 11 month(s) ago

Determine the longest rod which can measure the three dimensions of the room exactly.

Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm, respectively.

Length = 825 cm

Breadth = 675 cm

Height = 450 cm

HCF of 825, 675, 450...

- 1 Answer
- 1 Like
- 30203 Views

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