Question of Exercise 2 (Subjective)

# Question The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices.

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