Solution:

Explanation:

Final Answer:

Mode =50.

 the product of its digits.The number is - - - - - -

Solution:

Explanation:

Let x be the digit in the ones place and y be the digit in the tens place, resulting in the two-digit number = 10 y + x..

Given that the sum of the digits of a two-digit integer equals four,

According to the question

, 

Final Answer:

The number is 36.

that √3 + √5  is irrational

Solution:

which is 30m away from the foot of the tower, is 30^∘. Find the height of the tower.

Solution:

Explanation:

Let us take the height of the tower to be AB

Let C be the point elevation which is 30m away from the foot of the tower

We know that for a given right angled triangle,

Final Answer:

The height of the tower :  10 Root 3m

Solution:

Explanation:

Let us take the three consecutive positive integers as : a,a + 1,a + 2

A number when divided by 3, will have a remainder = 0 or 1 or 2

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 3.

Similarly, we can show that when a number is divisible by 2, we get the remainder as 0 or 1

Clearly, 2m and 2(m+1) both are divisible by 2.

We can clearly see the numbers a,a + 1,a + 2 are always divisible by 2.

We can say that a,a + 1,a + 2 is always divisible by 2 ,3 ,6

Example: 

Let us take: 3,4,5 

3 x 4 x 5 = 60 

We can see that 60 is divisible by 6