Important questions of Maths class 10 chapter 1 Real number

CLASS – X

CHAPTER – 1 REAL NUMBERS

SESSION: 2022-23

OBJECTIVE TYPE QUESTIONS

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 6ⁿ– 5ⁿ always ends with which digits?
How many number of decimal places after which the decimal expansion of the rational number will terminate?
If two positive integers a and b are expressible in the form a = pq² and b = p³q ; p, q being prime numbers then what is L.C. M (a,b) ?
What is the product of H.C.F and L.C.M of the smallest prime number and the smallest composite number?
After how many places will decimal expansion 21/24 terminates?
If the HCF of 85 and 153 is expressible in the form 85n – 153, then find the value of n.
If a and b are prime numbers, then what is their L.C.M?
What is the product of LCM and HCF of 50 and 20?

Important questions of Maths class 10 chapter 1 Real number

SUBJECTIVE TYPE QUESTIONS

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?
Show that any positive integer is of the form 3q or, 3q + 1 or, 3q + 2 foe some integer q.
Show that n² – 1 is divisible by 8, if n is an odd positive integer.
Show that one and only one out of n, n+2 or, n+4 is divisible by 3, where n is any positive integer.
Check whether 4ⁿ 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 √8 is irrational.
Prove that is irrational
The length, breadth and height of a room are 8m 25cm, 6m 75cm, and 4m 50cm. respectively. Determine the longest rod which can measure the three dimensions exactly.
Find the H.C.F and L.C.M of 144, 180 and 192 by prime factorization method.

Important questions of Maths class 10 chapter 1 Real number