## Important Questions for Class 10 Maths Real numbers

__OBJECTIVE TYPE Important Questions for Class 10 Maths Real numbers__

- If the HCF of 210 and 55 is expressible in the form 210 x 5 – 55 y, find y.
- The LCM and HCF of two rational numbers are equal, then the number must be ___
- What is the sum of exponents of prime factors in the prime factorisation of 196?
- What is the product of H.C.F and L.C.M of the smallest prime number and the smallest composite number?
- What is the remainder when the square of any prime number greater than 3 is divided by 6 ?
- If n is any natural number, then 6
^{n}– 5^{n}always ends with which digits? - If two positive integers a and b are expressible in the form a = pq
^{2}and b = p^{3}q; p, q being prime numbers then what is L.C. M (a,b) ? - Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).
- If the HCF of 85 and 153 is expressible in the form 85n â€“ 153, then find the value of n.
- If a and b are prime numbers, then what is their L.C.M?

__SUBJECTIVE TYPE Important Questions for Class 10 Maths Real numbers__

- Explain why 11 X 13 X 15 X 17 + 17 is a composite number?
- If three pieces of planks 63m, 42m and 49 m long have to be divided into planks of same length, then what will be the least possible number of planks?
- Three bells toll at intervals of 9, 12, 15 mins respectively. If they start tolling together, after what time will they next toll together
- Check whether 4
^{n}can end with the digit 0 for any natural number n. - The L.C.M of two numbers is 14 times their H.C.F. The sum of L.C.M and H.C.F is 600. If one number is 280, then find the other number.
- Find HCF of 96 and 404 by prime factorization method. Hence find their L.C.M
- Find the largest positive integer that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
- Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.
- Prove that âˆš8 is irrational.
- Prove that âˆš2 + âˆš5 is irrational.
- Given that âˆš3 is irrational, prove that 5 + 2âˆš3 is irrational.
- Prove that (3+2âˆš5)Â² is irrational.

**Direction for following questions: **A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.

**12. Assertion (A): If HCF (336, 54) = 6, then LCM (336, 54) = 3000.**

**Reason (R): The sum of exponents of prime factors in the prime factorization of 196 is 4**

**13. Assertion (A): HCF of two or more numbers = Product of the smallest power of each common prime factors, involved in the numbers.**

**Reason (R): The HCF of 12, 21 and 15 is 3.**

14. Assertion** (A): 6**^{n}** ends with the digit 0, where n is a natural number.**

**Reason(R): Any number ends with the digit zero, if its prime factors are of the form 2**^{m}** x 5**^{n}** ,where m,n are natural numbers.**

Case Study based question

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.

**1. **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?

**2. **Express 36 as a product of its primes.

3. 7 Ã— 11Ã—13 Ã—15 +15 is a ________number

4. If p and q are positive integers such that p = abÂ² and q= aÂ²b, where a , b are prime numbers, then find the LCM (p, q)

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**

Important Questions for Class 10 Maths Real numbers

Important Questions for Class 10 Maths Real numbers

Important Questions for Class 10 Maths Real numbers

Important Questions for Class 10 Maths Real numbers