Q25 of 40 Page 1

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


Pihu has a better chance of getting number 36


Let, S be the event that contains all possibilities/ combinations occur when Jayanti throws a pair of dice.


There will be total 6 × 6 = 36 outcomes.


∴ n(S) = 36


Let, A be the event such that Jayanti will get the product of the numbers appearing on the dices as 36.


As there is only one possibility (6, 6) for getting product 36.


∴ n(A) = 1


Therefore, the probability of getting product of the numbers appearing on the dice as 36 is



Now, let, S’ be the event that contains all possibilities that Pihu gets after throwing 1 dice.


∴ n(S’) = 6


Let, B be the event such that Pihu will get square of the number appearing on the dice as 36.


As there is only one possibility 6 of which square is 36.


∴ n(B) = 1


Therefore, the probability of getting square of the number appearing on the dice as 36 is



As is greater than , hence, Pihu has a better chance of getting number 36.


OR


(a) (b)


Let, S be the sample space that contains numbers between 70 and 100.


S = {70, 71, 72, 73, …….., 99}


∴ n(S) = 100 – 70 = 30


Now, let A be the set which contains prime numbers between 70 and 100.


∴ A = {71, 73, 79, 83, 89, 97}


∴ n(A) = 6


Therefore, the probability that an integer chosen between 70 and 100 is a prime number is



Now, let B be the set which contains numbers between 70 and 100 which are divisible by 7.


∴ B = {70, 77, 84, 91, 98}


∴ n(B) = 5


Therefore, the probability that an integer chosen between 70 and 100 is divisible by 7 is



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23

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OR


In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.


 24

‘Skysails’ is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towing kite to gain a height of anything between 100 metres – 300 metres. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a ‘telescopic mast’ that enables the kite to be raised properly and effectively.

Based on the following figure related to sky sailing, answer the questions:



(i) In the given figure, if sin Ө = cos (3Ө − 30⁰), where Ө and 3Ө − 30⁰ are acute angles, then find the value of Ө.


(ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle Ө (calculated above) and be at a vertical height of 200 m?


 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?


 27

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.