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Shyam factorised a number as $ 2\times 2\times 3$. The smallest factor of the number is

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Important Questions on Number Systems

HARD

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

For a real number

r

let

[r]

denote the largest integer less than or equal to

r .

Let

a > 1

a real number which is not an integer and

k

be the smallest positive integer such that

[a^{k}] > {[a]}^{k}

Then which of the following statement is always true?

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The number of digits in the decimal expansion of

16^{5} 5^{16}

HARD

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

For a real number

r

we denote by

[r]

the largest integer less than or equal to

r

. If

x, y

are real numbers with

x, y \geq 1

then which of the following statements is always true?

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

A number of two digits is equal to '

k

' times to the sum of these digits. If the places of these digits are mutually exchanged. the newly formed number is equal to the sum of these digits multiplied by which one of the following options ?

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The number of positive integers

n

in the set

\{2, 3, \dots . ., 200\}

such that

\frac{1}{n}

has a terminating decimal expansion is

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The sum of three consecutive numbers is $126$ . Find the highest number-

1. $41$
2. $42$
3. $43$
4. $44$

HARD

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The function

f : N \to I

defined by

f (x) = x - 5 [\frac{x}{5}]

, where

N

is the set of natural numbers and

[x]

denotes the greatest integer less than or equal to

x

, is:

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

1 USD = Rs. 67.89. A money changer adds a margin of Rs. 1.11. What will be the cost of 150 USD ?

1. Rs. 10,183
2. Rs. 10,350
3. Rs. 10,330
4. Rs. 10,450

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The number of distinct primes dividing

12! + 13! + 14!

HARD

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

Let

n > 1

be an integer. Which of the following sets of numbers necessarily contains a multiple of

3

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

Twice the difference between two numbers is equal to their sum. If one number is $15$ , Find the other number.

1. $15$
2. $10$
3. $5$
4. $20$

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

Consider the following statements: For any integer $n,$

I.. $n^{2} + 3$ is never divisible by $17$ .

II.. $n^{2} + 4$ is never divisible by $17$ . Then

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

P and Q are two examination halls. If

10

examinees are sent from P into Q, the number of examinees becomes equal in both the halls. If

20

examinees are transferred from Q into P, the number of examinees becomes double in P in comparison with Q. What is the number of examinees in each P and Q separately ?

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

How many times does the number $3$ occur in unit's place for numbers ranging from $1$ to $100$ ?

1. $20$
2. $11$
3. $10$
4. $19$

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

B has $32$ pens, $24$ pencils and $16$ erasers. How many sets of these three items can B make without any left over?

1. $6$
2. $7$
3. $8$
4. $9$

EASY

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The difference of the cubes of two consecutive numbers is

127

. What are the numbers?

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

59

is added to a square of a number, the result is

900

. What is the number?

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

The largest non-negative integer

k

such that

24^{k}

divides

13!

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

There are exactly twelve Sundays in the period from January

1

to March

31

in a certain year. Then, the day corresponding to February

15

in that year is

MEDIUM

Mathematics>Arithmetic>Number Systems>Basics of Number Systems

How many natural numbers

n

are there such that

n! + 10

is a perfect square ?

Shyam factorised a number as $ 2\times 2\times 3$. The smallest factor of the number is

Important Questions on Number Systems

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