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Two tankers contain \(1305\)liters and \(450\)liters of petrol respectively. Find the maximum capacity of container which can measure the petrol of either tanker in exact number of liters?
The HCF of and is
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HCF is
\(\dfrac{1}{{\sqrt 2 }}\)Is a ______ number?
is an irrational number. An irrational number is a number that can be expressed as the quotient or dfraction of two integers, a numerator p and a nonzero denominator q.
\(\sqrt 2 + \sqrt 5 \)Is ______ number.
is an irrational number.
Euclidโs Division Lemma states that if a and b are any two positive integers then there exists unique whole numbers q and r such that.
Euclidโs division Lemma states that for any two positive integers a and b we can find two numbers q and r such that
Where .
In a school annual day function, a group of students \(550\) need to march behind the band of \(286\) members. The two groups have to march in the same number of columns in which they can march?
HCF of is
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HCF is
Find the largest positive integer that will divide \(1245\) and \(670\) leaving remainder \(13\) and \(10\)respectively?
The HCF of and is
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HCF is
Which of the following is not an irrational number?
Which is not an irrational number?
The LCM of two numbers is 882 and their product is 6174. Find their HCF?
HCF LCM = product of 2 numbers
HCF
HCF
How many prime factors are there in the prime factorization of \(4002075\)?
There are 9 prime factors
Find the smallest number which when increased by \(17\) is exactly divisible by both \(192\) and\( 180\)?
LCM
Smallest number
The product of two irrational number is?
Let us consider
Let as consider
The number \(1.21112111211112\) is a/an?
This number is nonterminating and nonrepeating. Hence it is irrational.
A rational number \(\dfrac{a}{b}\) will have a terminating decimal expansion if b is of the form?
Product of 2 and 5 given 0 at unit place.
If \({n^2} – n\) is _______ for every positive integer n?
If is even for every positive integer n.
Which of the following number form cannot ends with 0 digits?
Cannot ends with 0 digits.
Which is not correct in the following?
The sum of two irrational number is always irrational is incorrect.
\(\sqrt n \) is an irrational number if n is?
is irrational number if n is a prime number.
\({(7 + \sqrt 3 )^2} + {(7 – \sqrt 3 )^2}\) is a/an?
Which one of the following rational numbers have nonterminating decimal representation?
Which one of the following rational numbers has the terminating decimal representation?
In there is a multiple of 25.
\(\dfrac{{2\sqrt 6 }}{{\sqrt 2 + \sqrt 3 + \sqrt 5 }}\) is equal to?
If \(x = 7 + 4\sqrt 3 \)then \(\sqrt x + \dfrac{1}{{\sqrt x }}\) equals?
Find the remainder when \(27 \times 43 \times 46\) is divided by \(10\)?
After multiplication last digit is 6. So when it will get divided by 10 its remainder is 6.
A number in the form \(15q + 7\) can be written as?
The product of three consecutive natural numbers is always divisible by?
Let 3 consecutive natural number is n,n+1,n+2
Product=n(n+1)(n+2)=
Put n=1,p=6
N=2,p=24
N=3,p=60
If 25 is divided by 7 then there exists two other unique non negative integers 1 and r, find the value of q and r?
How many possible values if r are there if \( a = 7q + r \)and 7 is divisor?
If is divisor then number of possible value of r will be โ7โ i.e. 0,1,2,3,4,5,6.
Using division algorithm if q denotes quotient and r denotes remainder then when 432 is divided by 201 the pair (q,r) is?
Comparing equation 1 and 2
Q=2 and r =30
The greatest number of four digits which is divisible by each one of the numbers 12,18,21 and 28 is?
LCM of 12,18,21,28=252
So, 252 will be least dividable by
Maximum four digit number is 9828.
If \({\left( {\sqrt 2 } \right)^x} + {\left( {\sqrt 3 } \right)^x} = {\left( {\sqrt {13} } \right)^{\dfrac{x}{2}}}\)then the number of value of x is?
Here for x=4 above relation will satisfied so x=4.
In p/q form 3.21 can be written as?
Here,
321= number after removing diagonal
32= number without having bar
9= number of โ9โ as digit having
0= number of digits having not
The square of a positive integer canโt be written in the form of?
Square numbers having last digit from 0, 1, 2, 3, 4โฆ.., 9 will not give number having last digit 7.
If x and y are odd positive integers then?
X and y are odd positive integers
So, let x=2N+1
Y=2N+1
How many prime numbers are there between 80 and 100?
83,89,97
If 574 is divided by a positive integer the remainder in one less and the quotient is three less than the divisor, then the divisor is?
Remainder =D1
Quotient=D3
Find the number of divisor of 1080 excluding the divisor which is perfect squares?
Total number is (including divisor)
Actual number of divisor is 321=31
Number of divisor which is not a perfect square =313=28
What is the value of \(6{A^2} + {B^2} + 2AB\) where A and B are the digits of the number 39A80562B which is multiple of 72?
39A80562B will be divisible by 72,79 I.e.
let
For divisible by 8
Last digit should be 2,4,6,8 or 0
S0, 33+A+B=9K
If b is 0 then A is 3
B is 2 then A is 1
B is 4, A is 8
Find the number of integral solution for x and y if 3x+4y=17 and x>0,y>0
Let x is 1 then y is
X is 2 then y is
X is 3 then y is
X is 4 then y is
X is 5 then y is
Only x is 3 and y is 2 can be taken so, number of integral solution is 1.
If \(\dfrac{{ – 1}}{2} \le x \le \dfrac{1}{3}\& \dfrac{{ – 1}}{3} \le y \le \dfrac{1}{2}\)then what will be the smallest value of \({x^2} – {y^3}\)?
For minimum of , y should be maximum that is y is
And x should be minimum i.e., x is 0
Then
A number when divided by 1207 gives a remainder 88. What remainder should be obtained by dividing the same number by 17.
N = 1207K+88