Q27 of 40 Page 1

Given that √5 is irrational, prove that (2√5−3) is an irrational number.

OR


If HCF of 144 and 180 is expressed in the form 13m-16. Find the value of m.


Proof :


Given - √5 is irrational


To prove - (2√5−3) is an irrational number


Property - Rational number is one which can be represented in the form p/q, where q is not equal to 0.


Answer –


As given √5 is irrational.


Now, let us assume that (2√5−3) is a rational number.


We know that rational numbers can be represented in the form of p/q where p & q are integers and q is not equal to 0.





In above equation p, q, 3, 2 are integers, hence must be rational.


But √5 is irrational number.


Therefore, above equation is contradiction.


Hence, our assumption is false.


Therefore, (2√5−3) is an irrational number.


OR


m = 4


Given – HCF of 144 and 180 is 13m – 16


To find – value of m


Property –


HCF of two integers m & n is


HCF = m mod n , where m>n


(m mod n = remainder after dividing m by n)


Answer –


HCF of 144 and 180 is


180 mod 144 = 36


(we get 36 as a remainder after dividing 180 by 144)


But as given HCF of 144 and 180 is 13m – 16


∴ 13m - 16 = 36


∴ 13m = 52


∴ m = 4


Hence, the value of m is 4.


More from this chapter

All 40 →
25

Jayanti throws a pair of dice and records the product of the numbers appearing on the dice. Pihu throws 1 dice and records the squares the number that appears on it. Who has the better chance of getting the number 36? Justify?

OR


An integer is chosen between 70 and 100, Find the probability that it is


(a) a prime number (b) divisible by 7


 26

Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy as she got first position in the class. While coming back to their home, Isha asked for a treat from her father as a reward for her success. They went to a juice shop and asked for two glasses of juice.

Aisha , a juice seller, was serving juice to her customers in two types of glasses. Both the glasses had inner radius 3cm. The height of both the glasses was 10cm.



First type: A Glass with hemispherical raised bottom.



Second type: A glass with conical raised bottom of height 1.5 cm.


Isha insisted to have the juice in first type of glass and her father decided to have the juice in second type of glass. Out of the two, Isha or her father Suresh, who got more quantity of juice to drink and by how much?


 28

If the sum of first m terms of an AP is the same as the sum of its first n terms, show that the sum of its first (m+n) terms is zero.

 29

In the figure, ABCDE is a pentagon with BE||CD and BC||DE. BC is perpendicular to CD. AB= 5cm, AE=5cm, BE= 7cm, BC= x-y and CD= x+y. If the perimeter of ABCDE is 27cm. find the value of x and y, given x, y ≠0.


OR


Solve the following system of equations: