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Case Based Questions Test: Real Numbers - 1 - Bank Exams MCQ


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10 Questions MCQ Test NCERT Mathematics for Competitive Exams - Case Based Questions Test: Real Numbers - 1

Case Based Questions Test: Real Numbers - 1 for Bank Exams 2024 is part of NCERT Mathematics for Competitive Exams preparation. The Case Based Questions Test: Real Numbers - 1 questions and answers have been prepared according to the Bank Exams exam syllabus.The Case Based Questions Test: Real Numbers - 1 MCQs are made for Bank Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions Test: Real Numbers - 1 below.
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Case Based Questions Test: Real Numbers - 1 - Question 1

Direction: Read the following text and answer the following questions on the basis of the same:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

If p and q are positive integers such that p = ab2 and q = a2b, where a, b are prime numbers, then the LCM (p, q) is

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 1

Given, p = ab2 = a × b × b

q = a2b = a × a × b

LCM of (p, q) = a2b2

Case Based Questions Test: Real Numbers - 1 - Question 2

Direction: Read the following text and answer the following questions on the basis of the same:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 2

Prime factor 32 is 2 x 2 x 2 x 2 x 2

Prime factor 36 is 2 x 2 x 3 x 3

HCF is 2 x 2 i.e 4

HCF of 32 and 36 is 4.

Case Based Questions Test: Real Numbers - 1 - Question 3

Direction: Read the following text and answer the following questions on the basis of the same:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

7 × 11 × 13 × 15 + 15 is a

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 3
7 × 11 × 13 × 15 + 15 is composite number.

Take 15 common

15 ( 7 × 11 × 13 + 1)

So, given number has factor other than 1 and itself so it is a composite number.

Case Based Questions Test: Real Numbers - 1 - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 4
We have to find the LCM of 32 and 36.

LCM(32, 36) = 25 × 9 = 288

Hence, the minimum number of books required to distribute equally among students of section A and section B are 288.

Case Based Questions Test: Real Numbers - 1 - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

36 can be expressed as a product of its primes as

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 5
The product of its prime factors are:-

36 = 2 × 2 × 3 × 3

= 22 × 33

Case Based Questions Test: Real Numbers - 1 - Question 6

Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

Find the sum of exponents of the prime factors of total number of plants.

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 6
Total number of plants = 135 + 225 = 360

The prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5

= 23 × 32 × 51

∴ Sum of exponents = 3 + 2 + 1 = 6.

Case Based Questions Test: Real Numbers - 1 - Question 7

Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

Find the total number of plants

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 7
Total number of plants 135 + 225 = 360 plants
Case Based Questions Test: Real Numbers - 1 - Question 8

Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

What is total numbers of row in which they can be planted

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 8
Number of rows of Rose plants = 135/45 = 3

Number of rows of marigold plants = 225/45 = 5

Total number of rows = 3 + 5 = 8

Case Based Questions Test: Real Numbers - 1 - Question 9

Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

What is the maximum number of columns in which they can be planted ?

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 9
No. of rose plants = 135

No. of marigold plants = 225

The maximum number of columns in which they can be planted

= HCF of 135 and 225

∴ Prime factors of 135 = 3 × 3 × 3 × 5

and 225 = 3 × 3 × 5 × 5

∴ Prime factors of 135 = 3 × 3 × 5 = 45.

Case Based Questions Test: Real Numbers - 1 - Question 10

Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.

Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.

Detailed Solution for Case Based Questions Test: Real Numbers - 1 - Question 10
We have proved that the maximum number of columns = 45

So, prime factors of 45

= 3 × 3 × 5 = 32 × 51

∴ Sum of exponents = 2 + 1 = 3.

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