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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

from the Rashtrapati Bhawan along the Rajpath in New Delhi. Several regiments of the army,

navy, and air force, along with their bands, march to India Gate. The parade is presided over by the

President of India, who is the Commander-in-Chief of the Indian Armed Forces. As he unfurls the

tricolour, the national anthem is played. The regiments of the Armed Forces then start their march

past. Prestigious awards like Kirti Chakra, Ashok Chakra, Paramvir Chakra and Vir Chakra are

given out by the President. Nine to twelve different regiments of the Indian Army, in addition to the

Navy and Air Force march toward India Gate along with their bands. Contingents of paramilitary

forces and other civil forces also participate in the parade.

On 71th republic day parade, captain RS Meel is planing for parade of following two group:

(a) First group of Army troops of 624 members behind an army band of 32 members.

(b) Second group of CRPF troops with 468 soldiers behind the 228 members of bikers.

These two groups are to march in the same number of columns. This sequence of soldiers is

followed by different states Jhanki which are showing the culture of the respective states.

(i) What is the maximum number of columns in which the army troop can march?

(a) 8 (b) 16

(c) 4 (d) 32

(ii) What is the maximum number of columns in which the CRPF troop can march?

(a) 4 (b) 8

(c) 12 (d) 16

(iii) What is the maximum number of columns in which total army troop and CRPF troop together

can march past?

(a) 2 (b) 4

(c) 6 (d) 8

(iv) What should be subtracted with the numbers of CRPF soldiers and the number of bikers so

that their maximum number of column is equal to the maximum number of column of army

troop?

(a) 4 Soldiers and 4 Bikers (b) 4 Soldiers and 2 Bikers

(c) 2 Soldiers and 4 Bikers (d) 2 Soldiers and 2 Bikers

(v) What should be added with the numbers of CRPF soldiers and the number of bikers so that

their maximum number of column is equal to the maximum number of column of army

troop?

(a) 4 Soldiers and 4 Bikers (b) 12 Soldiers and 12 Bikers

(c) 6 Soldiers and 6 Bikers (d) 12 Soldiers and 6 Bikers

For any positive integer n prove that n

^{3}-n is divisible by 6books 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?

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

If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }(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.

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

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.

express 0.3

~~178~~in p/q form, 178 is repeating manner.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)

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.

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

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)

(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 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) German

(b) Swiss

(c) French

(d) American

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

a. Victor Emmannual

b. George Meredith

c. Louis XVIII

d. Guizot

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 237Check whether (39)

^{n }is divisible by 3 for any n which is a natural number (N).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........

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...??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. Rome

b. Prussia

c. Sardinia Piedmont

d. Vienna

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, then

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

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

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" ?

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 .

what is the HCF of two consecutive integers X and X+1 is?

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

how can we prove Euclid's division lemma?

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

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

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

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

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

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

3mor3m+1for some integerm?m and n are two integers such that m=n2-n.show that m2-2m is divisible by 24?

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...!!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?

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

A number N when divided by 14 gives the remainder 5.Find the remainder when the same number is divided by 7