English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

For some integer m, every even integer is of the form ______.

For some integer q, every odd integer is of the form ______.

n² – 1 is divisible by 8, if n is ______.

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.

Explain why 3 × 5 × 7 + 7 is a composite number.

If two positive integers a and b are written as a = x³ y² and b = xy³; x, y are prime numbers, then HCF (a, b) is ______.

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is ______.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF (a, b) = p^mqⁿ and LCM (a, b) = p^rq^s, then (m + n)(r + s) = ______.

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.

Find the HCF and LCM of 26, 65 and 117, using prime factorisation.

The LCM of smallest 2-digit number and smallest composite number is ______.

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.

Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.