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The product of two irrational numbers is

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Important Questions on Number Systems

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Numerical and Mental Ability>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:

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The largest non-negative integer

k

such that

24^{k}

divides

13!

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Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The number of digits in the decimal expansion of

16^{5} 5^{16}

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Numerical and Mental Ability>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. $19$

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Numerical and Mental Ability>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

HARD

Numerical and Mental Ability>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?

HARD

Numerical and Mental Ability>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

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Numerical and Mental Ability>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. $44$

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Numerical and Mental Ability>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

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Numerical and Mental Ability>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

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Numerical and Mental Ability>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 ?

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Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

A thrice of the square of a natural number decreased by

4

times the number is equal to

50

more than the number. Find the number.

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Numerical and Mental Ability>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. $20$

HARD

Numerical and Mental Ability>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?

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Numerical and Mental Ability>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 ?

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Numerical and Mental Ability>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

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Numerical and Mental Ability>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. $9$

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Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The number of distinct primes dividing