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Syllabus

Prove that root 3 + root 5 is irrational

If the LCM of 12 and 42 is 10m +4, then the value of m is

what are co-prime numbers??

Find a quadratic polynomial, the sum and product of whose zeroes are 0 and - root2 respectively.

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

If n is any natural number, then which of the following expressions ends in 0?

(3 × 2)

^{n}(4 × 3)

^{n}(2 × 5)

^{n}(6 × 2)

^{n}For any positive integer n prove that n

^{3}-n is divisible by 61) Find the largest number which exactly divides 70, 80, 105 160.

2) Find the largest number which divides 699, 572, and 445 leaving remainders 6, 5 4.

a)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?

LCM of 2

^{3 }* 3^{2 }and 2^{2 }* 3^{3 }is(A) 2

^{3}(B) 3

^{3}(C) 2

^{3}* 3^{3}(D) 2

^{2 }*3^{2}prove that product of 3 consecutive positive integers is always divisible by 6

If b=3 , then any integer can be expressed as a = ?

If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }If m and n are odd positive integer, then m2+n2 is even but, not divisible by

4. JustifyQ. Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some

the HCF and LCM of two numbers are 33 and 264 respectively.when the first number is divided by 2 the quotient is 33.what is the other number?

THE ANSWER GIVEN BY THE EXPERT IS 132,BUT THE ANSWER IN MY GUIDE IS 130.....PLZZZ....WHICH IS THE RIGHT 1...??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.

Let x= 7/22*53 be a rational number. Then x has decimal expansion which terminates:

a) after four places of decimal

b) after three places of decimal

c) after two places of decimal

d) after five places of decimal.

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

3 farmers have 490kg,588kg,and 882kg of wheat respectively.Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags

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 ?

i) -root 0.64

ii) root3+root4) root5 + root 6)

iii)(root3 + 1)^2

iv) root 100

GIVE REASON

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

if p , q are two consecutive natural numbers then HCF(p,q) is: ????

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

two bills of Rs. 6075 and Rs. 8505 respectively are to be paid separately by cheques of same amount. find the largest possible amount of each cheque

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?

Q) (-1)n + (-1)8n = 0 when n is :(a) any positive integer(b) any odd natural number(c) any even natural number(d) any negative integer

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

N is a natural number such that when N

^{3}divided by 9 ,it leaves remainder a.It can be concluded thata)a is a perfect square b) a is a perfect cube c) both of these d ) none of these

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

Find the HCF of 616 and 1300, using Euclid's Division Algorithm.

real life examples of hcf and lcm

What is the L.C.M of x and y if y is a multiple of x?

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237P^N=(A*5)^N FOR P^N TO END WITH 0 A=------------------ FOR NATURAL NO. N

A)ANY NATURAL NUMBER

B)EVEN NUMBER

C)ODD NUMBER

D) NONE

In 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........

If p is a prime number then LCM of p , p2, p3 is :

A ) p

B ) p3

C ) p2

D ) p6

prove that root 2 is irrational

check whether 7n can end with digit 0, for any natural number n

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

There are 3 consecutive traffic lights which turn "green" after every 36, 42 and 72 seconds. They all were at "green" at 9:00 AM. At what time will they all turn "green" simultaneously?Show that square of any positive odd integer is of the form 8m + 1, for some integer m.

show that 12

^{n }cannot end with digit 0 or 5 for any natural number nThe decimal expansion of the rational number

6243/2^{3}x 5^{4 }will terminate afterProve that if x and y are odd positive integers, then

^{ }x^{2}+y^{2}is even but not divisible by 4.Find HCF and LCM of 13 and 17 by Prime factorisation method.

prove that if x and y are odd positive integers,the x2 +y2 is even but not divisible by 4.

the hcf of 45 and 105 is 15 . write their lcm .

prove n

^{3}-n is always divisible by 6Any one of the number a,(a+2) and (a+4) is a multiple of

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

Find the largest positive integer that wil divide 1385, 1457 and 1628 leaving 5,2 and 8 respectively.

1. 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.

why 17+11x13x17x19 is a composite number?explain.

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

Given that H.C.F. ( 1261,1067) = 97, find L.C.M. (1261,1067)

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

show that one and only one out of

n ,n+4,n+8,n+12,n+16is divisible by 5 wherenis any positive integerFind the smallest no. which leaves remainder 8 and 12 when divided by 28 and 32 respectively .

Prove that 5-root 3 is irrational.

2, 6, 18, 82, 650

(1) 2 (2) 18 (3) 82 (4) 650

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

(i) $\mathrm{E}-\mathrm{D}+4=\frac{\mathrm{G}}{4}$.

(ii) The highest number B is a prime number.

(iii) C – G = B – A.

(iv) A is not an even number.

10. Which number is represented by E?

(A) 31 (B) 32 (C) 33 (D) 35

11. Which number is represented by F?

(A) 32 (B) 34 (C) 36 (D) 33

12. Which is the smallest number?

(A) D (B) G (C) A (D) E

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

If m

^{n}= 32, where m and n are positive integers, then the value of n^{m+n}is -----------. Why?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 six digits which on division by 42, 45, 48, 56, and 60 leaves 12 as remainder in each case.

plz answer it fast........

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

Find the HCFof 65 and 117 and express it in the 65m+117n

If two positive integers a and b are written as a xy^{2}and b x^{3}y, where x and y prime numbers. Find LCM (a,b)use euclid's division lemma to show that the square of any positive intiger is either of the form

3mor3m+1for some integerm?if a,b are coprime, then a

^{2}, b^{2 are}(a)coprime (b)not coprime

^{ }(c)odd nos (d)even nosif 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}Q. Mrs. Batra saves Rs. 48,290 every month. How much money will she have after 2 years?

Determine the no. nearest to 110000 but greater than 100000 which is exactly divisible by 8,15 and 21.

A decimal number is of the form 3b.0276, wherebrepresents a digit. The decimal is then written in the form of the simplest fraction. The prime factorisation of the denominator of the fraction is 2

^{2}× 5^{4}× 7^{x}, wherexis a non-negative integer.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 ?