Number System Questions

Find the value of $\sqrt{2p^2+4}$ such that a 6-digit number $52p304$ is divisible by 11.

Find the greatest 5-digit number divisible by 12.

How many numbers less than 1,000 are multiples of both 7 and 11?

Which of the following numbers is divisible by 4.
(i) 67920598
(ii) 618703592
(iii) 618703594
(iv) 67920590

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 13. What is the value of the divisor?

If 5
55
is divided by 4, then the remainder is:

Ram gives a six-digit number 468312 to Shyam to check the divisibility. Shyam tells Ram that the number is divisible by 57. Shyam asks Ram, "If we rearrange the digits of this number in descending order, then by which number will it be always divisible?"

The five-digit number 725yz is divisible by 15. What is the maximum possible value of the product of y and z?

The number 1254216 is divisible by which of the following numbers?

Which of the following numbers is divisible by 36 ?

Find the nearest integer to 5347 which is exactly divisible by 137.

The natural number nearest to 3070 which is completely divisible by 17 is:

If $1433\times 1423\times 1425$ is divided by $12$, then what will be the remainder?

If the $6$ -digit number $479xyz$ is exactly divisible by $7,11$ and $13$, then the product of the digits $x,y$ and $z$ will be:

The sum of the first 24 natural numbers is:

Complete the series: $28,126,344,1332,\dots$

A number when divided by 49 leaves a remainder 9. If the same number is divided by 7, then the remainder will be:

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all 200 questions and scored 500 marks. What is the number of questions he answered correctly?

Find the least value of K for which 7864K3 is divisible by 7.

Find the remainder when 11
7
+9 is divided by 10.

The product of L.C.M. and H.C.F. of two numbers is 336 and their difference is 10. Then the numbers are?

If the sum of the numbers $5x9$, $327$ and $2y8$ is $1114$, then the largest value $y$ can take is:

The least positive digit $x$, so that the number $324x342$ is divisible by 11 is:

In a classroom, the number of boys is three times the number of girls. Which of the following totals cannot represent the number of children in the class?

Which of the following is not true?

If $13^{50}$ is divided by $14$, the remainder is

Which of the following statements is true ?

The largest number of four digits that is divisible by 12, 15 and 18 is ________.

Which of the following is a pair of coprime numbers?

Find the LCM of $32$ and $640$.

If a nine-digit number 385x3678y is divisible by 72, then the value of (y−x) is:

Find the sum of the greatest 4-digit number divisible by 6 and the smallest 4-digit number divisible by 3.

If a nine-digit number 785x3678y is divisible by 72, then the value of (7x−5y) is:

If the seven-digit number 5x634y2 is divisible by 88 such that x

=y, then what is the value of (2y−3x)?

If the sum of two numbers is 126 and their HCF and LCM are 7 and 180, respectively, then the sum of the reciprocals of the two numbers is:

Which of the fractions given below is not equal to $\frac{13}{19}$?

Find the greatest number of four digits which is divisible by 14, 30 and 42.

A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?

What is the sum of the digits of the least number which when divided by 12, 16 and 20 leaves the same remainder 6 in each case and it is divisible by 9?

Which of the following numbers is not a perfect square?

Arrange the following real numbers in ascending order:
$$\frac{2}{\sqrt{2}},1.41,1.4142,1.414$$

If the 7-digit number x468y05 is divisible by 11, then the maximum value of (x + y) is :

If the 7-digit number 2y6810x is divisible by 88, then what is the value of the product of x and y?

On dividing $4999$ by $7$, what will the remainder be?

In a division problem, the divisor is $12$ times the quotient and $9timestheremainder.Iftheremainderis$ 96$, find the dividend.

The Highest Common Factor of three consecutive even numbers is:

Evaluate the expressions: $5^0,0!,1^5,(-1{)}^{2n}$ (where $n$ is an integer). Then list their numerical values in increasing order. If a value appears more than once, include it as many times as it occurs.

A number is selected at random from $100$ to $199$. What is the probability that the number is divisible by $2$ and has exactly two even digits?

$\frac{840}{x}$ and $\frac{960}{x}$ are both positive integers, and so is $x$. What is the largest possible value of $x$?

The LCM of $47$, $141$ and $188$ is:

Which of the numbers given below is exactly divisible by 12?

Mohan divides 18935 by a certain number. If the quotient and the remainder he gets are 102 and 65, respectively, then the divisor is:

Which of the following is NOT divisible by 4?

Find the dissimilar number from the following:
$1331,2197,4913,5832,6859$

If the 10-digit number 96530y15x8 is divisible by 72, then what is the value of (3x−7y) for the maximum value of x?

If the seven-digit number 49x29y6 is divisible by 72, then what will be the value of (x+2y) for the largest value of x and y?

A number is chosen at random from $1$ to $200$. What is the probability that it is a perfect square or a multiple of $6$?

What is the unit digit in the expansion of $(478749{)}^{(1\times 5\times 2\times 4)}$?

Two numbers are in the ratio $3:4$. The product of their HCF and LCM is $2028$. The sum of the numbers will be

A non-terminating but recurring decimal is

The smallest number, which multiplies to $33275$ to get a perfect cube, is

Find the biggest 4-digit number which is a perfect square.

If a, a + 2, a + 4 are prime numbers, then the number of values of a is

The HCF and LCM of two numbers are $13$ and $1989$ respectively. If one of the numbers is $117$, then the other number is

Find the largest 4-digit number which is a perfect square.

If a,a+2,a+4 are all prime numbers, then the number of possible values of a is

The HCF and LCM of two numbers are 13 and 1989 respectively. If one of the numbers is 117, then the other number is