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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 n3-n is divisible by 6
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?
If you are a Brilliant what is the formula for a4+b4
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 0.3178 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
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 TRIGONOMETRY
3 sinθ + cosθ
cos2200 + cos2700
(1 + cosθ) (2 – 2cosθ)
Cos580 + sin220 - cos380 cosec520
Sin320 cos680 tan180 tan350 tan600 tan720 tan550
(i) sinA cosC + cosA sinC.
(ii) cosA cosC + sinA sinC.
sinθ(1 + cosθ)
sinA + cosA
tanθ + cotθ
secθ - tanθ + 1 cosθ
41. If xcosA – ysinA = a, xsinA+ ycos A = b, prove that x2+y2=a2+b2
42. S.T Sec2 θ + Cosec2 θ can never be less than 2.
43. If sin θ = 1/2 , show that 3cos θ - 4cos3 θ = 0.
44. If 7sin2 θ + 3cos2 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 m2-n2 = 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?
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 of 81 and 237
show that n2-1 is divisible by 8 if n is odd positive integer
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........
N is a natural number such that when N3 divided by 9 ,it leaves remainder a.It can be concluded that
a)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.
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 12n cannot end with digit 0 or 5 for any natural number n
prove that if x and y are odd positive integers,the x2 +y2 is even but not divisible by 4.
Prove that if x and y are odd positive integers, then x2+y2 is even but not divisible by 4.
prove n3-n is always divisible by 6
how 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
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+16 is divisible by 5 where n is any positive integer
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
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 3m or 3m+1 for some integer m?
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=
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...!!
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 ?
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