For an integer n , let S n = n + 1 , n + 2 , … . , n + 18 . Which of the following is true for all n ≥ 10 ?

S n has at least four multiples of 5

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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

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Important Questions on Fundamentals of Mathematics

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

A number

M

is divisible by

25

. If

(M + 5) (M + 1)

is divided by

25

, then what will be the remainder?

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

For an integer

n

, let

S_{n} = \{n + 1, n + 2, \dots ., n + 18\}

. Which of the following is true for all

n \geq 10

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Which of the following numbers is divisible by

9

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

The HCF of

\frac{2}{3}, \frac{8}{9}, \frac{10}{27}, \frac{32}{81}

is.

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

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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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Which among the following is not an irrational number?

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Which of the following numbers is perfectly divisible by 4?

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

How many numbers are there between

330

and

450

which are divisible by both

7

and

9

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Let

n > 1

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

3

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

The number of digits in the decimal expansion of

16^{5} 5^{16}

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Which of the given value is exactly divisible by

30

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Let

S

be the set of all point

(\frac{a}{b}, \frac{c}{d})

on the circle with radius

1

centred at

(0, 0)

where

a

and

b

are relatively prime integers,

c

and

d

are relatively prime integers (that is

H C F (a, b) = H C F (c, d) = 1

), and the integers

b

and

d

are even. Then the set

S

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

A number when divided by

72

leaves remainder

10

. What will be the remainder when the same number is divided by

9

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

What is the HCF of

\frac{15}{24}, \frac{12}{39} a n d \frac{40}{49}

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

Which smallest number must be added to

300

. So that the resulting number is completely divisible by

13

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

A two-digit number

\bar{a b}

is called almost prime if one obtains a two-digit prime number by changing at most one of its digits

a & b

. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

How many numbers are there from $14$ to $159$ which are divisible by both $2$ and $8$ ?

HARD

Mathematics>Algebra>Fundamentals of Mathematics>Number System

Suppose

a, b, c

are positive integers such that

2^{a} + 4^{b} + 8^{c} = 328 .

Then

\frac{a + 2 b + 3 c}{a b c}

is equal to-

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Mathematics>Algebra>Fundamentals of Mathematics>Number System

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

HARD

Mathematics>Algebra>Fundamentals of Mathematics>Number System

The number of

6

-digit numbers of the form

a b a b a b

(in base

10

) each of which is a product of exactly

6

distinct primes is

Consider the following statements: For any integer n, I.. n2+3 is never divisible by 17 . II.. n2+4 is never divisible by 17. Then

Important Questions on Fundamentals of Mathematics

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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