Question 5 - Case Based Questions (MCQ) - Chapter 1 Class 10 Real Numbers

Last updated at May 29, 2023 by Teachoo

A sweet seller has 420 Bundi Laddoo and 130 badam barfis. He wants to stack them is such a way that each stack has the same number, and they take up the least area of the tray.

Question 1

The prime factors of 420 are: C
(a) 22 × 32 × 5 × 7 (b) 2 × 3 × 5 × 7

(c) 2 × 3 × 52 × 7 (d) 22 × 3 × 5 × 7

Question 2

Using Euclid’s algorithm, the HCF of 420 and 130 is: C

(a) 10 (b) 30

(c) 20 (d) 15

Question 3

The LCM of 420 and 130 is

(a) 10 (b) 30

(c) 20 (d) 15

Question 4

The sum of exponents of prime factors in the prime factorization of 420 is:

(a) 2 (b) 3

(c) 5 (d) 4

Question 5

The sum of exponents of prime factors in the prime factorization of 130 is:

(a) 1 (b) 3

(c) 2 (d) 4

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Question A sweet seller has 420 Bundi Laddoo and 130 badam barfis. He wants to stack them is such a way that each stack has the same number, and they take up the least area of the tray.
Read carefully the above paragraph and answer the following questions:
Question 1 The prime factors of 420 are: (a) 22 × 32 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 52 × 7 (d) 22 × 3 × 5 × 7
Prime factorisation of 420
420 = 2 × 2 × 3 × 5 × 7
= 22 × 3 × 5 × 7
So, the correct answer is (D)
Question 2 Using Euclid’s algorithm, the HCF of 420 and 130 is: (a) 10 (b) 30 (c) 20 (d) 15
Using Euclid’s Division Algorithm
Since 420 > 130
We divide 420 by 130
Since the remainder is not 0,
We divide 130 by 30
Since the remainder is not 0,
We divide 30 by 10
Since remainder is 0
∴ HCF of 420 & 130 = 10
So, the correct answer is (A)
Question 3 The LCM of 420 and 130 is (a) 4560 (b) 5460 (c) 6540 (d) 5640
We know that
Product of two numbers = HCF × LCM
Putting two numbers as 420, 130 and their HCF as 10
420 × 130 = 10 × LCM
(420 × 130)/10 = LCM
LCM = (420 × 130)/10
LCM = 5460
So, the correct answer is (B)
Question 4 The sum of exponents of prime factors in the prime factorization of 420 is: (a) 2 (b) 3 (c) 5 (d) 4
We know that
420 = 22 × 3 × 5 × 7
Thus,
Sum of exponents = 2 + 1 + 1 + 1 = 5
So, the correct answer is (C)
Question 5 The sum of exponents of prime factors in the prime factorization of 130 is: (a) 1 (b) 3 (c) 2 (d) 4
Prime Factorisation of 130
∴ 130 = 2 × 5 × 13
= 21 × 51 × 131
Thus,
Sum of exponents = 1 + 1 + 1 = 3
So, the correct answer is (B)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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