Real numbers NCERT CHAPTER 1 previous question paper class 10 MATHEMATICS

Q 1. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively

Q2. Express 98 as a product of its primes?

Q3.If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.

Q4. Find HCF and LCM of 13 and 17 by prime factorisation method. (2013)

Q5.  HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number. (2012)

Q6.  Find the LCM of 96 and 360 by using fundamental theorem of arithmetic. (2012)

Q7. Find the HCF (865, 255) using Euclid’s division lemma. (2013)

Q8. Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively. (2015)

Q9. Prove that 2 + 3√5 is an irrational number. (2014)

Q10. Show that 3√7 is an irrational number. (2016)

Q11.  Explain why (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number? (2015)

Q12.  Check whether 4n can end with the digit 0 for any natural number n. (2015)

Q13.   Can two numbers have 15 as their HCF and 175 as their LCM? Give reasons. (2017 OD)

Q14. Prove that √5 is irrational and hence show that 3 + √5 is also irrational. (2012) 3 marks

Q16.  Prove that 3 + 2√3 is an irrational number. (2014)

Q15. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together? (2013)

Q17. Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times. (2012)

Q18.   The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly. (2015)

Q19. Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together? (2015)

Q20.  By using Euclid’s algorithm, find the largest number which divides 650 and 1170.