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Syllabus

Prove that root 3 + root 5 is irrational

a. To declare completion of German Unification.

b. To restore conservative regime in Europe.

c. To declare war against France.

d. To start the process of Italian unification.

what are co-prime numbers??

prove that root 2+ root 3 is an irrational number

(a) Plebiscite is a direct vote by which only the female members of a region are asked to accept or reject a proposal.

(b) Plebiscite is a direct vote by the female members of a matriarchal system to accept or reject a proposal.

(c) Plebiscite is a direct vote by only a chosen few from the total population of a parti-cular region to accept or reject a proposal.

(d) Plebiscite is a direct vote by which all the citizens of a region are asked to accept or reject a proposal.

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

(a) It was an all British commission

(b) It was formed in Britain

(c) It was set up in response to the nationalist movement

(d) All of the above

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?

(a) strong devotion for one?s own country and its history and culture.

(b) strong devotion for one?s own country without appreciation for other nations.

(c) strong love for one?s own country and hatred for others.

(d) equally strong devotion for all the countries of the world.

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 }The Decimal Expansion of63/72*175 ?

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

(a) German

(b) Swiss

(c) French

(d) American

express 0.3

~~178~~in p/q form, 178 is repeating manner.If b=3 , then any integer can be expressed as a = ?

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

(a) Detention of political prisoners without trial

(b) Forced recruitment in the army

(c) Forced manual labour

(d) Equal pay for equal work

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 ?

Should we find the L.C.M of 8 and 18 and then divide the L.C.M separately by 8 and 18 ?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

a) New symbols

b) New ideas

c) Icons

d) Anti-colonial movement

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

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

i) 16

ii) 34

iii) both 16 or 34

iv) None of these

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.

2, 6, 18, 82, 650

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

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

If HCF(a,8)=4 , LCM(a,8)=24 then find the value of 'a'.

real life examples of hcf and lcm

A. 4^n

B. 2^n

C. 6^n

D. 8^n

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237a) Satyagraha Movement

b) Militant Guerrilla Movement

c) Non-Violent Movement

d) None of the above.

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........

prove that root 2 is irrational

(a) Arrival of the Simon Commission

(b) Working at the firm without payments

(c) Violation of Salt Tax by Gandhi

(d) Fall in demand for agricultural goods

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

a. Victor Emmannual

b. George Meredith

c. Louis XVIII

d. Guizot

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 area of a circular playground is 88704 m sq. find the cost of fencing this ground at the rate of rs 65 per metre...

solve it plzzzz

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

^{ }x^{2}+y^{2}is even but not divisible by 4.prove that if x and y are odd positive integers,the x2 +y2 is even but not divisible by 4.

a) It introduced the Salt Law.

b) It increased taxes on land

c) It gave the British the power to arrest and detain a person without a trial

d) It put a ban on the Congress party.

prove n

^{3}-n is always divisible by 6find the HCF of 180,252 and 324 using euclid division lemma?

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.

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

A,B AND C starts cycling around a circular path in the same direction at same time. Circumference of the path is 360km. If the speed of A is 40m/min, speed of B is 60m/min and that of C is 72m/min and they start from the same point, then after what time interval they will be together at the starting point?

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.

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

(a) The French Revolutionary Code

(b) Napoleonic Code

(c) European Imperial Code

(d) The French Civil Code

how can we prove Euclid's division lemma?

(A) 0 <= M

^{N}<= 2(B) 1 < M

^{N}< 3(C) M

^{N}> B(D) 1 < M

^{N}< 5if 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

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

If "a" is a factor of "b".Then HCF (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?a. 1830

b. 1848

c. 1789

d. 1815

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}a. Rome

b. Prussia

c. Sardinia Piedmont

d. Vienna

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

define non integral number .....with example

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...!!Any one of the number a,(a+2) and (a+4) is a multiple of

^{}explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers ?