JMO - number of ways

If you can travel from Mumbai to Baroda by 6 trains, from Baroda to Jaipur by 4 trains and from Jaipur to Delhi by 3 Trains. Then in how many ways can you travel from Mumbai to Delhi?

numbers

Did you know that for 76 raised to the power of n, where n is an element of Natural numbers, the last 2 digits is always 76!

76¹ = 76

76² = 5776

76³ = 438976

76⁴ = 33362176

76⁵ = 2535525376 

number

Read the pattern:
666 x 666 = 443556
6666 x 6666 = 44435556
66666 x 66666 = 4444355556

numbers

show that the square of any prime number reduced by one is always divisible by 24.

division

A three digit number is entered twice into the calculator. What will be the Remainder when the number in the calculator is divided by 91.

division

If a number is successively divided by 9,11,13 then it leaves a Remainder of 8,9 and 8 respectively.

Find the smallest number that satisfies this condition.

factors

For the number 6¹⁰ x 7¹⁷ x 55²⁷, find

1.       The number of prime factors

2.       The number of all the factors.

tutorials -sum of factors

Sum of Factors

If a number N can be expressed as product of prime factors such that

N = p^a x q^b x r^c...............................

Write the power of each of the prime factors beginning with zero and going to thee highest power of the prime number.

Record the same for each prime number.

An example will help

64= 2⁶

Then the sum of factors (2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶) = 1 + 2 + 4 + 8 + 16 + 32 + 64 =  127

Another Example:

Find the total number of factors of 222.

222 = 2 x 3 x 37

Or, 222 = 2¹ x 3¹ x 37¹

then the sum of factors are (2⁰ + 2¹) (3⁰ + 3¹) (37⁰ + 37¹) = (1+2)(1+3)(1+37) = 3 x 4 x 38 = 456

We will check the answer

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.

Sum of factors = 456

division

When we divide 333435 by 34 the remainder is a and when we divide 333534 by 34 the remainder is b. What is the value of b – a?

tutorial on number of factors

To find the number of factors of a number

If a number N can be expressed as product of prime factors such that

N = p^a x q^b x r^c...............................

Then, the total number of factors including N and 1 is given by

(a + 1)x(b + 1)x(c + 1).................................

Example:

Find the total number of factors of 222.

222 = 2 x 3 x 37

Or, 222 = 2¹ x 3¹ x 37¹

So, the total number of factors = (1+1)x(1+1)x(1+1) = 2x2x2 = 8

We can check the answer as shown below.

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.

Find the total number of factors of 64.

64 = 2⁶

So, the total number of factors = (6+1) = 7

We can check the answer as shown below.

The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

JMO Mock test Paper STD. VI --- Time: 2 hours

JMO Mock test Paper for STD VI ----- Time: 2 hours

JMO division

If 8ⁿ is divided by 6, then for n € N, & n is odd, and for n € N,& n is even what is the Remainder?

JMO

If 23⁵⁶ is divided by 11 what is the Remainder?

Average

There are three numbers, the average of first two numbers is 2 and the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

JMO - DIVISION

Which is the largest number that will perfectly divide 101100–1 
a) 10000
b) 1000
c) 100
d) 100001

JMO - numbers

How many twin prime numbers are there between 1 and 100?
Twin prime numbers are prime numbers which differ from each other by 2.

JMO Division

When a + b is divided by 12, the Remainder is 8. When a - b is divided by 12 the Remainder is 6. If a > b, then find the Remainder when ab is divided by 6?

JMO --- numbers

We have a four-digit number that is a multiple of 9. Of the four digits, three of the consecutive digits are same. How many such numbers are possible?

JMO numbers

Between 1 to 10,000, how many times does the digit 7 appear?

JMO - Division

If S = 123456789101112................9979989991000

What will be the Remainder when S is divided by 9.