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Syllabus

Prove that root 3 + root 5 is irrational

if lmn =1 show that 1/1+l+m-1 +1/1+m+n-1 +1/1+n+1-1 = 1

what are co-prime numbers??

the number 3 power 13 -3 power 10 is divisible by

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

For any positive integer n prove that n

^{3}-n is divisible by 6$\mathit{Q}\mathbf{.}\mathbf{}Howmanyperfectcubesarethereinthesequence{1}^{1},{2}^{2},{3}^{3},{4}^{4},....,{100}^{100}?$

(A) 33 (B) 37

(C) 36 (D) 34

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

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?

_{n}=6n+5, t_{n+1}=?If you are a

Brilliantwhat is the formula fora^{4}+b^{4 }Q. Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some

If n is an even natural number, then the largest number by which n(n + 1)(n + 2) is divisible is

a)24 ; b)6 ; c)12 ; d)9

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

^{3x}- (33)^{3x}can end with either 1 or 2?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)

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

1) The arithmetic mean of 12 observations is 7.5. If the arithmetic mean of 7 of these observations is 6.5, the mean of the remaining observations is.

2) In a continuous frequency distribution, the mean of the data is 25. if each item is increased by 5, then the new median will be.

PLEASE ANSWER THESE QUESTIONS AS SOON AS POSSIBLE. THIS IS VERY URGENT. THANK YOU!!!!

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

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.

I've got this sample paper from somewhere and solved it fully, I am requesting to anyone, if he/she can get me these solutions,

I don't remember from where I'd downloaded it sadly. I'ld be greatful if someone would post the solutions, from google maybe.

SAMPLE PAPER- INTRODUCTION TO TRIGONOMETRYCLASS-X CBSE^{4}θ +cos^{4}θ.3 sinθ – cosθ3 sinθ + cosθ

sin+ sin^{2}20^{0}+ sin^{2}70^{0}^{2}65^{0}+cos65^{0}sin25^{0}cos

^{2}20^{0}+ cos^{2}70^{0 }^{2}A=1, then find the value of sin^{2}A + sin^{4}A.^{0}, find cot5α.^{0}tan2^{0}tan3^{0}…….tan89^{0}.^{0}+ θ) – sec (20^{0}– θ) – tan (50^{0}+ θ) + cot (40^{0}– θ).^{3}B-3cosB.^{2}θ – sin^{2}θ.tanA + tanB1- tanAtanB

^{2}θ + cos^{2}θ = 1.^{2}θ – tan^{2}θ =1.^{2}θ – cot^{2}θ =1.^{2}58^{0}– (2/3)cot58^{0}tan 32^{0}– (5/3)tan13^{0}tan 37^{0}tan 45^{0}tan 53^{0}tan 77^{0}.(2 + 2sinθ) (1 – sinθ)(1 + cosθ) (2 – 2cosθ)

Cos58+^{0}sin22-^{0}cos38^{0}cosec52^{0}Sin32

^{0}cos68^{0}tan18^{0}tan35^{0}tan60^{0}tan72^{0}tan55^{0 }^{2}θ + 2).B + C) = cotA2 2

^{0}<A + B ≤90^{0}; A>B Find A and B.(i) sinA cosC + cosA sinC.

(ii) cosA cosC + sinA sinC.

^{0}.^{2}A(1 + sin A) (1- sinA) =K, Find the value of K.^{2}A – sin^{2}A = sin^{2}A tan^{2}A or not.^{2}θ +cosec^{2}θ = sec^{2}θ cosec^{2}θ.1 + cosθ – sin=cotθ^{2}θsinθ(1 + cosθ)

tanθ+cotθ= 1 + tanθ + cotθ1-cotθ 1-tanθ

sin+ sinA cosA^{3}A +cos^{3}AsinA + cosA

tanθ + cotθ

secθ + tanθ – 1=1+sinθsecθ - tanθ + 1 cosθ

^{2}+ (1 + tanAtanB)^{2}=sec^{2}A sec^{2}B.cosA+sinA= sinA + cosA1-tanA 1-cotA

41. If xcosA – ysinA = a, xsinA+ ycos A = b, prove that x

^{2}+y^{2}=a^{2}+b^{2 }42. S.T Sec

^{2}θ + Cosec^{2}θ can never be less than 2.43. If sin θ = 1/2 , show that 3cos θ - 4cos

^{3}θ = 0.44. If 7sin

^{2}θ + 3cos^{2}θ = 4, show that tan θ = 1/√3.45. If cos θ +sin θ = √2 cos θ, prove that cos θ – sin θ =√2 sin θ.

46. If tanA+sinA=m and tanA-sinA=n, show that m

^{2}-n^{2}= 4.47. If secA= x+, prove that secA+tanA=2x or

48. Solve for θ, if tan5 θ = 1.

49. If 7 cosec θ -3cot θ = 7, prove that 7cot θ - 3cosec θ = 3.

50. If Sec θ +Tan θ =4 find sin θ , cos θ.

write one rational number between root 2 and root 3?

exactly to the right of Ram. Which direction Shyam was facing?

(A) South (B) North

(C) East (D) West

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

define non integral number .....with example

Find the HCF of 81 and 237 and express it as a linear combination of81 and 237show that n

^{2}-1 is divisible by 8 if n is odd positive integerIn 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........

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

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

Please provide me a chart for all the values of sin, cos, tan in terms of pi, pi/2 , pi/4 these types of values.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 12

^{n }cannot end with digit 0 or 5 for any natural number nprove that if x and y are odd positive integers,the x2 +y2 is even but not divisible by 4.

(A) 336 (B) 63

(C) 216 (D) 68

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

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

^{3}-n is always divisible by 6how to write twelve thousand twelve hundred in 5 digits...........???

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

^{59}x (313)^{87}x (438)^{129 }x (399)^{99.}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 of 180,252 and 324 using euclid division lemma?

Find two natural numbers whose difference is 66 & LCMis 360.

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

three tankers contain 187l,231l, and 275l of petrol respectively. using euclids division algorithm find the capcity of the largest containner that can measure the petrol of the three containeers exact number of times

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

show that one and only one out of

n ,n+4,n+8,n+12,n+16is divisible by 5 wherenis any positive integerProve that 5-root 3 is irrational.

^{1/2}- (7+4 root 3)^{-1/2}is equal tofind 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

give mind map on real numbers?

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

Prove that a positive integer n is prime, if no prime p less than or equal to root n divides n.

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

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

3mor3m+1for some integerm?Find the HCFof 65 and 117 and express it in the 65m+117n

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.

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)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...!!if two positive integers p and q can be expressed as p= ab square and q = a cube b ;a , b being prime numbers , then lcm of (p , q ) is

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