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Syllabus

Prove that root 3 + root 5 is irrational

what are co-prime numbers??

prove that root 2+ root 3 is an irrational number

show that one and only one out of n, n+2, n+4 is divisible by 3

For any positive integer n prove that n

^{3}-n is divisible by 6a)Find the H.C.F. of the smallest composite number and the smallest prime number.

b) . If a = 4q + r then what are the conditions for a and q. What are the values that r can take?

prove that product of 3 consecutive positive integers is always divisible by 6

If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }Q. Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some

express 0.3

~~178~~in p/q form, 178 is repeating manner.The HCF of 65 and 117 is expressible in the form 65m-117.Find the value of m. Also find the LCM of 65 and 117 using prime factorisation method.

if alpha beta and gamma are the zeroes of polynomial 6x3+3x2-5x+1 then find the value of alpha raised to -1+beta raised to -1+gamma raised to -1

A circular field has a circumference of 360km. Three cyclist start together and can cycle 48,60 and 72km a day,round the field. When will they meet again ?

find the least number that is divisible by all numbers between 1 and 10(both inclusive)

show that any positive odd integer is of the form 6q+1,6q+3 or 6q+5, where q is some integer. explain the solution

show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8

Find the smallest number which when increased by 17 is exactly divisible by 520 and 468?

1. Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.

2. Find the HCF of 65 and 117 and express it in the form 65m + 117n.

3. If the Hcf of the 210 and 55 is expressible in the form 210 X 5 + 55y, find y.

write one rational number between root 2 and root 3?

show that square of any positive integer cannot be of the form 5q+2 or 5q+3 for any integer q

Find the greatest number of 6 digits exactly divisible by 24, 15 and 36

real life examples of hcf and lcm

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237In a morning walk 3 persons step off together, their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?

Question from R.D. Sharma........

Show that square of any positive odd integer is of the form 8m + 1, for some integer m.

prove that root 2 is irrational

show that there is no positive integer n so that root(n-1)+root(n+1) is rational

show that 12

^{n }cannot end with digit 0 or 5 for any natural number nprove that if x and y are odd positive integers,the x2 +y2 is even but not divisible by 4.

Prove that if x and y are odd positive integers, then

^{ }x^{2}+y^{2}is even but not divisible by 4.prove n

^{3}-n is always divisible by 61. Find the HCF of 81 and 237 and express it as a linear combination of 81 and 237.

Sir i want full explanation to this question and also i want the full reasoning and procedure to solve such kinds of problem to score good marks in mathematics examination.

find the HCF of 180,252 and 324 using euclid division lemma?

on a morning walk 3 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

Evolution of number system: A journey from "counting numbers" to "real numbers" ?

Find the smallest no. which leaves remainder 8 and 12 when divided by 28 and 32 respectively .

show that one and only one out of

n ,n+4,n+8,n+12,n+16is divisible by 5 wherenis any positive integerProve that 5-root 3 is irrational.

find the hcf and lcm of 404 and 96 and verify hcf x lcm = product of two given numbers

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

how can we prove Euclid's division lemma?

if the HCF of 657 and 963 is expressible in the form 657x+963x-15,find x.

write whether 2 root 45 + 3 root 20 divided by 2 root 5 on simplification give a rational or irrational number

Find the greatest number of 5 digits exactly divisible by 12,15,36

use euclid's division lemma to show that the square of any positive intiger is either of the form

3mor3m+1for some integerm?Find the HCFof 65 and 117 and express it in the 65m+117n

if two positive integers a b are written as a = x

^{3 }y^{2}and b = x y^{3 }where x y are prime numbers then the hcf of a b is=(a)xy (b)xy

^{2}(c)x

^{3}y^{3 }(d)x^{2}y^{2}Determine the no. nearest to 110000 but greater than 100000 which is exactly divisible by 8,15 and 21.

Show that one and only one out of n,n+2,n+4 is divisible by 3,where n is any positive integer...???

plzz ans it!!!i really need it...!!explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers ?