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Syllabus

Prove that root 3 + root 5 is irrational

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

what are co-prime numbers??

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........

prove that root 2+ root 3 is an irrational number

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.

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

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

For any positive integer n prove that n

^{3}-n is divisible by 6Ram 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)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

The length, width,and height of a room are 6m 30cm,5m 85cm, 3m 60cm resp. what will the greatest lenght of tape which can measure the dimensions of the rooms in exact number of times?

If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }Three runeers running around a circular track,can complete one revo;ution in 2,3 and 4 hours respectively..They will meet again atthe starting point after how many hours???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.b = 8 root 6 + 8 root 5

c = 6 root 6 + 6 root 5

d = 4 root 6 + 4 root 5

e = root 6 + root 5

Then which of the following is a rational number

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 ?

a. 3/4

b. 4/5

c. 1/2

d. 1/4

Solution for this question...

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

Find the largest number which devides 378 and 510 leaving remainder 6 in each case.

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

can 2 numbers have 16 as their hcf and 320 as their lcm ?show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8

prime factorisation.method.

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.

(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.

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 of 12 and 40=40 x 1 + 4 x x

then find the value of x.

real life examples of hcf and lcm

two equilateral triangles have the sides of length 34 and 85 respectively.what is the length of tape that can measure the sides of both of them..?

rnplzzzzz answrr fastt...:O

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237two 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

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.

express 0.69 as a rational number in P/Q form?

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

^{3/16}so that the product becomes 3^{5/4}?prove n

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

fill in the blanks with justification

Q.1 a number divided by 17 leaves remainder 7. the least positive number to be subtracted from this number to make it divisible by 17 is ----------------

Q.2a number divide by 15 leaves remainder 6 the least positive number to be added to this number to make it divisible by 15 is ----

Q.3cube of any positive is of the form 9m, 9m+1 or 9m+8 for some integer m. this means that if the cube of a positive integer is divided by 9 the remainder will be -------------,------------- or -------------

Q.4in most of the questions containing the words largest ,greatest, highest, tallest maximum ,most etc. we determine --------------------

true or false with justifcation

.Q.1 the product of thee consecutive positive integers is divisible by 6

Q.2 the square of any positive integer can be of the form 3m+2 where m is a natural number

Q.3 if a positive integer is of the form 3q+1, q being a natural number ,its square can be in any form other 3m+1 for some integer m

Q.4 every positive integer can be written in the form 4q+2 where q is an integer.

Q5 the product of two consecutive positive integers is divisible by 2

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.

Find the HCF and LCM of a

^{2}b^{3}c^{9}and b^{2}c^{5}e^{3}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) None (B) One (C) Two (D) More than three

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 integerQ.2. Three consecutive positive integers are raised respectively to the first, second, and third powers, the resulting integers are then added together. This sum is a perfect square whose principal square root is the sum of the original three consecutive integers. Find the largest of the three integers.

(A) 6

(B) 4

(C) 7

(D) 5

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

(a) German

(b) Swiss

(c) French

(d) American

Prove that 5-root 3 is irrational.

a. 1830

b. 1848

c. 1789

d. 1815

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

? , 17, 33, 51, 75

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

^{n}(where n is a natural number )so that it ends with the digit 0??write whether 2 root 45 + 3 root 20 divided by 2 root 5 on simplification give a rational or irrational number

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.

The Sum of Two Numbers is 1660 and The HCF is 20. Find The Two Number Number.

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

(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

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 ?