Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 2

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$a, b, c, d$ are natural numbers such that $a = b c, b = c d, c = d a$ and $d = a b .$ Then $(a + b) (b + c) (c + d) (d + a)$ is equal to

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Important Questions on Number System

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 3

A three-digit number with digits

A, B, C

in that order is divisible by

9 . A

is an odd digit and

C

is an even digit.

B

and

C

are non zero. The number of such three-digit numbers is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 4

Nine numbers are written in ascending order. The middle number is also the average of the nine numbers. The average of the

5

larger numbers is

68

and the average of the

5

smaller numbers is

44 .

The sum of all the numbers is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 5

If the average of

20

different positive integers is

20

then the greatest possible number among these

20

numbers can be

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 6

If

a, b

are natural numbers such that

a + b = 2008

, then

{(- 1)}^{a} + {(- 1)}^{b}

is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 7

The number

16^{12}

is obtained from the number

8^{4}

by raising the smaller number to the power

n .

Then

n

is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 8

The remainder when the number

(2 \times 3 \times 4 \times 2012 \times 2013 \times 2014 \times 2015) - 2008

is divided by

2015

is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 9

The last digit in the finite decimal representation of the number

{(\frac{1}{5})}^{2004}

is

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 10

A natural number

n

has exactly two divisors and

(n + 1)

has three divisors. The number of divisors of

(n + 2)

is