## Lakshya Education MCQs

Question: In a seminar, the number of participants for the subjects Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them are for the same subject.
Options:
 A. 7 B. 14 C. 21 D. 28
: C

Number of rooms will be minimum if each room accomodates maximum number of participants.

In each room, the same number of participants are to be seated and all of them must be for the same subject.

Number of participants in each room must be the HCF of 60, 84 and 108.

Prime factorisation of 60, 84 and 108:
60=22×3×5
84=22×3×7
108=22×33

HCF =22×3=12

In each room, 12 participants can be accommodated.

Number of rooms=Total number of participants12
=60+84+10812
=25212
=21

The total number of rooms is 21.

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## More Questions on This Topic :

Question 1. Which of the following is not an irrational number?
1.    5−√3
2.    5+√3
3.    4+√2
4.    5+√9
: D

If p is a prime number, then p is an irrational number.

3 is a prime number.
3 is an irrational number.
53 is an irrational number.

Similarly,5+3 is an irrational number.

2 is a prime number.
2 is an irrational number.
4+2 is an irrational number.

9 is not a prime number.
9=3
5+9=5+3=8 which is a rational number.
5+9 is not anirrational number.
Question 2. HCF of two numbers is __ given that their LCM is 210 and the numbers are 42 and 70.

: Product of two numbers = HCF × LCM

42 × 70 = HCF × 210
HCF = 2940210 = 14
Question 3. Using Euclid's division algorithm, find the HCF of 1650 and 847.
1.    10
2.    11
3.    12
4.    27
: B

Euclid's division algorithm to find HCF of 1650 and 847:
Step 1: 1650 = 847 × 1 + 803
Step 2: 847 = 803 × 1 + 44
Step 3: 803 = 44 × 18 + 11
Step 4: 44 = 11 × 4 + 0 Hence, 11 is the HCF of 1650 and 847.
Question 4. Find the HCF and LCM of 90 and 144 by prime factorisation method.
1.    18 and 720
2.    720 and 18
3.    360 and 180
4.    180 and 720
: A

Prime factorisation of 90 and 144:
90=2×3×3×5
144=2×2×2×2×3×3
HCF=2×32=18
LCM=24×32×5=720
HCF and LCM of 90 and 144 are 18 and 720 respectively.
Question 5. Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a measuring vessel that can be used to exactly measure the petrol from either tankers with no petrol remaining.
1.    200 litres
2.    170 litres
3.    440 litres
4.    360 litres