Question of solved question

# Question Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

Calculate mode of the following data

Solution:

Explanation:

Mode =50.

A two digit number is 4 times the sum of its digits and twice

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

The number is 36.

Prove that √3 plus √5 is irrational

that √3 + √5  is irrational

Solution:

The angle of elevation of the top of a tower from a point on the ground

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,

The height of the tower :  10 Root 3m

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

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