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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.

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...

Apr 15

• 28 Likes
• 150634 Views

Apr 15

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 =...

Jan 18

• 12 Likes
• 123458 Views

Jan 18

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

...

Apr 20

• 7 Likes
• 92600 Views

Apr 20

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

...

May 22

• 6 Likes
• 79470 Views

May 22

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...

Apr 27

• 6 Likes
• 75886 Views

Apr 27

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...

Sep 9

• 1 Like
• 55094 Views

Sep 9

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
...

Jul 16

• 8 Likes
• 54852 Views

Jul 16

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.
...

Aug 16

• 3 Likes
• 54650 Views

Aug 16

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

Prove that root 5 is irrational.

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

...

Sep 7

• 3 Likes
• 50627 Views

Sep 7

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

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

Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1
Hence x2 + y2 = (2k + 1)2 + (2p + 1)2
= 4k2</

...

Aug 26

• 3 Likes
• 44134 Views

Aug 26

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

• 6 Likes
• 41457 Views

Asked by Mr davinder pal

Jun 12

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

Product of two consecutive positive integers is divisible by 2

Let the two consecutive positive integers be  and
Product of two consecutive positive integers

Case (i):  is even number
Let

...

Jul 18

• 5 Likes
• 37672 Views

Jul 18

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

...

May 21

• 5 Likes
• 37463 Views

May 21

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

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

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....

Apr 2

• 1 Like
• 37356 Views

Apr 2

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

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

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)...

Sep 16

• 1 Like
• 36249 Views

Sep 16

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...

Jul 12

• 3 Likes
• 34820 Views

Jul 12

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

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

...

Jul 6

• 3 Likes
• 33902 Views

Jul 6

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...

May 21

• 3 Likes
• 32303 Views

May 21

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.

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...

Jun 17

• 3 Likes
• 31233 Views

Jun 17

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...

Apr 27

• 1 Like
• 30203 Views

Apr 27

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