All Courses
Get the App Signup / Login
Sign in Open App
Class 10 Exam  >  Class 10 Tests  >  Extra Documents, Videos & Tests for Class 10  >  Test: Real Numbers (Hard) - Class 10 MCQ

Test: Real Numbers (Hard) - Class 10 MCQ


Test Description

20 Questions MCQ Test Extra Documents, Videos & Tests for Class 10 - Test: Real Numbers (Hard)

Test: Real Numbers (Hard) for Class 10 2024 is part of Extra Documents, Videos & Tests for Class 10 preparation. The Test: Real Numbers (Hard) questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Real Numbers (Hard) MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Real Numbers (Hard) below.
Solutions of Test: Real Numbers (Hard) questions in English are available as part of our Extra Documents, Videos & Tests for Class 10 for Class 10 & Test: Real Numbers (Hard) solutions in Hindi for Extra Documents, Videos & Tests for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt Test: Real Numbers (Hard) | 20 questions in 20 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study Extra Documents, Videos & Tests for Class 10 for Class 10 Exam | Download free PDF with solutions
Test: Real Numbers (Hard) - Question 1
Save

Show that x is rational if: x2 = 0.0004

Detailed Solution for Test: Real Numbers (Hard) - Question 1
x2 = 0.0004

= 2 / 100 = 0.02, which is rational

Test: Real Numbers (Hard) - Question 2
Save

Without doing any actual division, find which of the following rational numbers have terminating decimal representation:

(i) 7 / 16

(ii) 23 / 125

(iii) 9 / 14

(iv) 32 / 45

(v) 43 / 50

(vi) 17 / 40

(vii) 61 / 75

(viii) 123 / 250

Detailed Solution for Test: Real Numbers (Hard) - Question 2
The rational not having denominator as multiple of 2m x 5n will be non terminating.

(i) 7 / 16 = 7 / 2 x 2 x 2 x 2 denominator multiple of 2m x 5n hence terminating.

(ii) 23 / 125 = 23 / 5 x 5 x 5 denominator multiple of 2m x 5n hence terminating.

(iii) 9 / 14 = 9 / 7 x 2 denominator is not multiple of 2m x 5n hence non-terminating.

(iv) 32 / 45 = 32 / 3 x 3 x 5 denominator is not multiple of 2m x 5n hence non-terminating.

(v) 43 / 50 = 43 / 5 x 5 x 2 denominator multiple of 2m x 5n hence terminating.

(vi) 17 / 40 = 17 / 2 x 2 x 2 x 5 denominator multiple of 2m x 5n hence terminating.

(vii) 61 / 75 = denominator is not multiple of 2m x 5n hence non-terminating.

(viii) 123 / 250 = 123 / 5 x 5 x 5 x 2 denominator multiple of 2m x 5n hence terminating.

(i), (ii), (v), (vi) and (viii) will have terminating decimal.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Real Numbers (Hard) - Question 3
Save

Prove that 3 + √5 is an irrational number.

Detailed Solution for Test: Real Numbers (Hard) - Question 3
Let us assume that √5 is a rational number which can be expressed in the form of p / q, where p and q are integers, q ≠ 0 and p and q are co prime that is HCF (p, q) = 1.
Test: Real Numbers (Hard) - Question 4
Save

Find the greatest number that will divide 93, 111 and 129, leaving remainder 3 in each case.
Detailed Solution for Test: Real Numbers (Hard) - Question 4
Since Remainder is 3 in each case numbers are

93 - 3 = 90

111 - 3 = 108

129 - 3 = 126

Required number will be H.C.F of 90,108 and 126

H.C.F of 90 and 108

∴ The greatest number is 18.

Test: Real Numbers (Hard) - Question 5
Save

If the product of two numbers is 540 and their HCF is 30, find their LCM.
Detailed Solution for Test: Real Numbers (Hard) - Question 5
The product of two numbers = 540

HCF x LCM = 540

30 x LCM = 540

LCM = 540 / 30 = 18

Test: Real Numbers (Hard) - Question 6
Save

π is an irrational number.
Detailed Solution for Test: Real Numbers (Hard) - Question 6
π is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That's because pi is what mathematicians call an "infinite decimal" — after the decimal point, the digits go on forever and ever. ... (These rational expressions are only accurate to a couple of decimal places.)
Test: Real Numbers (Hard) - Question 7
Save

The sum of two irrational numbers is an irrational number.
Detailed Solution for Test: Real Numbers (Hard) - Question 7
An irrational number is a number that cannot be expressed as a fraction for any integers and. Irrational numbers have decimal expansions that neither terminate nor become periodic.
Test: Real Numbers (Hard) - Question 8
Save

If the product of two co-primes is 553, then their LCM = _____
Detailed Solution for Test: Real Numbers (Hard) - Question 8
The HCF of co-prime no.s is 1

∴ Product of the two numbers = HCF × LCM

Thus LCM = 553

Test: Real Numbers (Hard) - Question 9
Save

The value of x in following factor tree is ____
Detailed Solution for Test: Real Numbers (Hard) - Question 9
1 × 42 = 42

2 × 21 = 42

3 × 14 = 42

6 × 7 = 42

Therefore, the factors of 42 in pairs are (1, 42), (2, 21), (3, 14) and (6, 7).

Test: Real Numbers (Hard) - Question 10
Save

Product of any irrational number with a rational number 'x' is always rational. Then, x is ____.
Detailed Solution for Test: Real Numbers (Hard) - Question 10
Product of any rational no. with irrational is always irrational only when irrational no. is not a perfect square and is not having 0 , 1 as roots.
Test: Real Numbers (Hard) - Question 11
Save

The prime factorisation of 320 is____.
Detailed Solution for Test: Real Numbers (Hard) - Question 11
320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

320 = 26 x 51

Test: Real Numbers (Hard) - Question 12
Save

Any number ending with '0' must have ___ and ___ as its prime factors.
Detailed Solution for Test: Real Numbers (Hard) - Question 12
For example: 10, 20, 30, .....

The factors of 10 = 1, 2, 5 and

The prime factors of 10 = 2 and 5

The factors of 20 = 1, 2, 4, 5, 10 and 20

The prime factors of 20 = 2 and 5

∴ Any number ending with '0' must have '2' and '5' as its prime factors.

Test: Real Numbers (Hard) - Question 13
Save

HCF of two numbers is always a factor of their LCM.
Detailed Solution for Test: Real Numbers (Hard) - Question 13
This statement HCF of two numbers is always a factor of their LCM is TRUE.

Because HCF is a factor of both the numbers which are factors of their LCM.

Hence, HCF of two numbers is always a factor of their LCM.

Test: Real Numbers (Hard) - Question 14
Save

Every even integer is of the form 2m, where m is an integer.
Detailed Solution for Test: Real Numbers (Hard) - Question 14
This statement every even integer is of the form 2m, where m is an integer is TRUE.

For Example : Let the value of m be -2, 4 & 0

Then the values for 2m = 2 × -2 , 2 × 4 & 2 × 0

= - 4 , 8 & 0

Test: Real Numbers (Hard) - Question 15
Save

If p and q are relatively prime numbers, what is their LCM?
Detailed Solution for Test: Real Numbers (Hard) - Question 15
If p and q are prime numbers, they do not have any common factor.

p = 1 × p

q = 1 × q

HCF of a and b = 1.

Their LCM = 1 × p × q

LCM of p and q = pq

Test: Real Numbers (Hard) - Question 16
Save

For what value of n, 2n x 5n ends in 5.
Detailed Solution for Test: Real Numbers (Hard) - Question 16
2m × 5n can also be written as

2n × 5n = (2 × 5)n = (10)n

which always ends in zero, as 102 = 100, 103 = 1000,.....

Thus, there is no value of n for which (2n × 5n ) ends in 5.

Test: Real Numbers (Hard) - Question 17
Save

LCM of two prime numbers is 1.
Detailed Solution for Test: Real Numbers (Hard) - Question 17
A prime number is a natural number greater than 1 which has no divisor other than 1 and itself. The least common multiple (LCM) of two numbers is the smallest non zero number which is a multiple of both numbers. considering the L.C.M of two primes : 2 and 3 , here the L.C.M = 2 × 3 = 6.
Test: Real Numbers (Hard) - Question 18
Save

LCM of two or more ____ is equal to their product.
Detailed Solution for Test: Real Numbers (Hard) - Question 18
Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are called composite numbers.
Test: Real Numbers (Hard) - Question 19
Save

If a and b are two odd prime numbers, then a2 - b2 is ____(prime/composite/neither prime nor composite).
Detailed Solution for Test: Real Numbers (Hard) - Question 19
Composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers, because they are divisible by more than two numbers.
Test: Real Numbers (Hard) - Question 20
Save

HCF of 870 and 225 is:
Detailed Solution for Test: Real Numbers (Hard) - Question 20
Factors of 870 = 5 × 2 × 3 × 29

Factors of 225 = 5 × 5 × 3 × 3

Common factors = 5 × 3 = 15

H.C.F = 15

5 videos|292 docs|59 tests
Join Course
Information about Test: Real Numbers (Hard) Page
In this test you can find the Exam questions for Test: Real Numbers (Hard) solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Real Numbers (Hard), EduRev gives you an ample number of Online tests for practice

Top Courses for Class 10

Download as PDF

Top Courses for Class 10

Important Questions for Real Numbers (Hard)

Find all the important questions for Real Numbers (Hard) at EduRev.Get fully prepared for Real Numbers (Hard) with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Real Numbers (Hard) syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Real Numbers (Hard) resources.

Real Numbers (Hard) MCQs with Answers

Prepare for the Real Numbers (Hard) within the Class 10 exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Real Numbers (Hard) Extra Documents, Videos & Tests for Class 10

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Real Numbers (Hard) with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup