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Syllabus

Prove that root 3 + root 5 is irrational

what are co-prime numbers??

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.

prove that root 2+ root 3 is an irrational number

(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.

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 6(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.

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?

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

a. Victor Emmannual

b. George Meredith

c. Louis XVIII

d. Guizot

If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }(a) German

(b) Swiss

(c) French

(d) American

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

Ram and Shyam go for morning walk daily. They run in a circular track in the park and take 180 seconds and 150 seconds respectively to complete one round. They start together at 6 am from the same point and in the same direction.

(i) How long would it take for them to meet again for the next time?

(ii) At what time willl they meet first time after they start?

(iii) Which concept has been used here?

(iv) Which values of Ram and Shyam have been depicted in this activity?

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 ?

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

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

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.

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

a. Rome

b. Prussia

c. Sardinia Piedmont

d. Vienna

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

sump will be modelled by V(x) = x3 + x2 ? 4x ? 4 .

(i) He planned in such a way that its base dimensions are (x + 1) and (x + 2) . How much

he has to dig ?

(a) (x + 1) (b) (x - 2) (c) (x - 3) (d) (x + 2)

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?

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

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

find HCF and LCM of 306 and 54 verify that HCFxLCM= Product of the two numbers

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

(a) British ruled India because the latter was militarily weak

(b) British ruled India because Indians cooperated with them

(c) British ruled India because they got international support

(d) None of these

real life examples of hcf and lcm

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237(a) Detention of political prisoners without trial

(b) Forced recruitment in the army

(c) Forced manual labour

(d) Equal pay for equal work

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

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

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

A forester wants to plant 66 apple trees 88 banana trees and 110 mango trees in equal row also he wants to make distinct rows of trees i.e only one type of tree in one row .the number of minimum rows requiredare:-

(A)2

(B)3

(C)10

(D)12

show that 12

^{n }cannot end with digit 0 or 5 for any natural number nthe hcf of 45 and 105 is 15 . write their lcm .

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.

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

A ) p

B ) p3

C ) p2

D ) p6

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.

The Decimal Expansion of63/72*175 ?

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

(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

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

a) Satyagraha Movement

b) Militant Guerrilla Movement

c) Non-Violent Movement

d) None of the above.

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 .

Find the smallest positive rational number by which 1/7 should be multiplied so that its decimal expansion terminates after 2 places of decimal.

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

0.57 can b written as p/q, q is not equal to 0 as:

a) 26/45 b) 13/27 c)13/29 d) 57/99

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

books dealing with cleanliness,in english,hindi and sociology,have to be stacked in such a way that all books are stored topicwise and height of each stack is the same.the number of english books is 240,number of hindi books is 96 and the number of sociology books is 336. assuming that the books are of same thickness,find the number of stacks of each books? which mathematical concept is used in this problem? which good habit is discussed in this problem?

how can we prove Euclid's division lemma?

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

(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

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

a) Leave their village

b) Settle in the city

c) Leave their plantation without permission

d) Allow the women to leave farmlands without permission

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

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

3mor3m+1for some integerm?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 ?

if a,b,c,d are in continued proportion prove that:

(b-c)

^{2}(c-a)^{2}+(d-b)^{2}= (a-d)^{2}