Here we are with the **Important 4 markers Class 10th**. We have listed here the most important questions from chapter **Real Numbers**. in this article, we have listed some **Important 4 markers questions for Class 10th** and we are a few steps away from launching our next series with important 1 marker, 2 marker, and 3 marker questions.

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(NOTE: Symbol ^ has been used to show the square of a number. Herex^2means x is to the power 2)

**Questions:**

*1. If the HCF of 657 and 963 is expressible in the form of 657 p + 963 (-15), find p. (CBSE 2010)*

*2. Prove that 3+2√5 is irrational. (CBSE 2012, 2017)*.

*3. There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class. (CBSE 2013)*

*Find the maximum number of parallel rows of each class for the seating arrangement.**Also, find the number of students of class IX and Class X in a row.**Tell what is the objective of the school administration behind such an arrangement?*

*4. Ramu has two vessels containing 720 ml and 405 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of gasses that can be filed. (CBSE 2014)*

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*5. Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16, and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together? (CBSE 2013)*

*6. Find the HCF of numbers 134791, 6391, and 6339 by Euclid’s division algorithm. (CBSE 2015)*

*7. If two positive integers x and y are expressible in the form of primes as x=p^2 q^3 and y= p^3 q, what can you say about their HCF and LCM? Is the LCM a multiple of HCF? Explain. (CBSE 2014)*

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*8. Show that one and only one of n, (n+1) and (n+2) is divisible by 3, where n is any positive integer. (CBSE 2015)*

*9. Find the HCF and LCM of 306 and 657 and verify that LCM x HCF = Product of two numbers.*

*10. Show that any positive odd integer is of form 4q+1 or 4q+3 where q is a positive integer.*

*11. Find the HCF of 110, 420. Express it in the form of 420 = 420p+110q for some values of p and q.*

*12. For any positive integer n, prove that n^3-n is divisible by 6. (NCERT Exemplar)*

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