Q31 of 40 Page 1

Prove that 5 - √3 is irrational, given that √3 is irrational.

OR


An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?


Let’s assume that 5 - √3 is rational.


It can be written in form where a and b are integers and b ≠ 0.




Since a, b and 5 rational, is also rational.


So, √3 is rational. But we know that √3 is irrational.


Thus, our assumption is wrong.


So, 5 - √3 is irrational.


OR


To get the maximum number of columns here, we find HCF.


We can use Euclid’s algorithm to find the HCF.


Here 616 > 32. So we divide greater number with smaller one.


⇒ 616 = 32 × 19 + 8


Now divide 32 by 8, we get quotient 4 and no remainder.


⇒ 32 = 8 × 4 + 0


Thus, our HCF is 8.


So, maximum number of columns in which they can march is 8.


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Prove that

OR


Prove that


32

Prove that the lengths of tangents drawn from an external point to a circle are equal.

 33

Read the following passage and answer the questions that follows:

In a classroom, four students, Sita, Gita, Rita and Anita are sitting at A(3, 4), B(6, 7), C(9, 4), D(6, 1) respectively. Then a new student Anjali joins the class



(i) Teacher tells Anjali to sit in the middle of the four students. Find the coordinates of the position where she can sit.


(ii) Calculate the distance between Sita and Anita.


(iii) Which two students are equidistant from Gita.