Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 20

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Earn 100

Find the smallest two-digit number $N$ such that the sum of digits of $10^{N} - N$ is divisible by $170 .$

50% studentsanswered this correctly

Important Questions on Number System

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 21

Let

N = 12345678910111213 \dots \dots 4344

be the

79

digit number obtained that is formed by writing the integers from

1

to

44

in order, one after the other. The remainder when

N

is divided by

45

is

r .

What is

r^{2} ?

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 22

Let

k = 2008^{2} + 2^{2008} .

What is the square of the units digit of

k^{2} + 2^{k} ?

EASY

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 23

Anna randomly picked five integers from the following list

53, 62, 66, 68, 71, 82, 89

and discover that the average value of the five integers she picked is still an integer. If two of the integers she picked were

62

and

89,

find the mean of the remaining three integers.

HARD

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 24

If the remainder when

(1! \times 1) + (2! \times 2) + (3! \times 3) + \dots + (286! \times 286)

is divided by

2^{4} \times 5^{3}

is

r

, then

r - 1900

is

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 25

What is the remainder when

3^{0} + 3^{1} + 3^{2} + \dots + 3^{2009}

is divided by

8 ?

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 26

How many distinct four-digit numbers are divisible by

3

and have

23

as their last two digits?

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.5>Q 27

What is the last two digits of

2015^{2016} - 2017 ?

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.6>Q 1

If

(x - 1) (x + 3) (x - 4) (x - 8) + m

is a perfect square, then

m

is