JMO / MTSE / IPM Practice paper

JMO

How to construct a 3 x 3 or 5 x 5 or 7 x 7 magic square

Magic square

This is a nice video on Magic square. Do not forget to click on the link that appears at the end of the video. That tells you how to construct a magic square 

Magic square

This is a nice tutorial on Magic Square

http://mathforum.org/alejandre/magic.square/adler/adler4.html

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.

JMO - division

If P =1234567891011.............9989991000

find the Remainder when the first 1000 digits are divided by 16.

JMO - number

If P =1234567891011.............9989991000

Find the 1000th digit from the left

Tutorial

Two prime numbers A,B (A<B) are called twin primes if they differ by 2.

Also, any prime number greater than 3 will be in the form of 6x+1 or 6x−1.

Eg. of twin prime

5,7

11,13

17,19

29,31

eg. of prime numbers with 6x + 1

7,13, 19, 31, 37, 43, 61.......

eg. of prime numbers with 6x - 1

5, 11, 17, 23, 29, 41.......

JMO - division

What is the Remainder when 231 is divided by 5?

JMO - division

When a certain number is divided by 222, it leaves a remainder of 35, another number when divided by 407 leaves a remainder 47. What is the remainder when the sum of these two numbers is divided by 37?

JMO --- numbers

Find the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?

JMO - division

Find the remainder when 7187 is divided by 800.

JMO

What is the Remainder in  7⁵ ÷ 6

JMO

What is the difference between the units place in (461⁴⁶¹ - 456⁴⁵⁶) ?

JMO

With the 5 digits 3,4,5,6 and 7, how many possible numbers can be formed which is divisible by 11.

JMO, numbers

In the number 259260261262263....490491492. How many 8's are there?

numbers, JMO

Nanu wrote all the numbers from 200 to 300. Then she started counting the number of two's that has been used while writing all these numbers. What is the number that she will get?

JMO, numbers

How many keystrokes are needed to type numbers from 1 to 2000 on a standard keyboard?

JMO

For what value of 'n' will the remainder of 351n and 352n be the same when divided by 7?

JMO

Suppose n is an integer such that the sum of digits on n is 2, and 1010<n<1011. The number of different values of n is:

JMO

The least common multiple of two natural numbers a and b, is 399. What is the minimum possible sum of the digits of the number a(given a > b)?

JMO

What is the unit's digit of the number 6256–4256

JMO

What is the remainder when 91+92+93+....+98 is divided by 6?

JMO

Find the remainder when 3164 is divided by 162

JMO

How many natural numbers below 860 are divisible by 5 and 11 but not by 3

logarithm

division

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

numbers

show that the product of four consecutive even number is always divisible by 384

geometry

A circle of unit radius, houses a square of maximum size inside it. What is the ratio of area of square to area of circle?

15 questions for MTSE/ MAT/ IPM STD VIII

answers available under respective topics

clock puzzle

At how many minutes past 8 O' clock does the minute arm and the hour arm coincide between 8 O' clock and 9 O' clock?

clock puzzle

In an accident the minute arm and the second arm of the wrist watch is lost. The watch now has only the hour arm in the correct position.
What is the minimum time that can be measured accurately?

number puzzle

Number Puzzle

 

number puzzle

Number Puzzle

 

Puzzle

A, B and D are good in Hockey and Volleyball. C and A are good in Hockey and Baseball. D and B are good at Cricket and Volleyball. C, D and E are good at Football and Baseball.

Find out, who of the following is good in all the games.

Puzzle

Out of 5 friends A is shorter than B but taller than E. C is tallest and D is little shorter than A. Which one is the shortest?

Puzzle

Nanu and Bhanu are charged for overspeeding on the  Express Highway. Nanu was charged with exceeding the speed limit by 10 km/hr, whereas Bhanu was charged with exceeding the same limit by thrice as much. If Bhanu was driving at 100 km/hr, at what speed was Nanu driving her vehicle?

puzzle

if 6 girls A, B, C, D, E and F have 10 marbles each. A and B take 4 marbles each from D and E respectively. C gives 3 marbles to F who in turn gives 2 marbles to D and 4 marbles to E. E takes back the marbles she had given to B and gives these to C.

Who has got 1 more marble than E?
How many marbles has D less than B?

number puzzle

If 
5 - 4 = 23
8 - 1 = 63
6 - 16 = 32
9 - 9 = 78
3 - 9 = 6
then find the value of 3 - 81 

Puzzle

JMO problems on Direction

JMO Std VI mock test paper

JMO mock test paper for STD. VI

factorization

If, 2x⁴ + x³ – 11x² + x + 2 = 0, then find the value of (x + 1/x)

factorization

Factorize: y² – 4 – x² + 4x

factorization

Factorize:
9x2+24x
+34+24x-1+9x−2

Puzzles

Puzzle --- JMO

An unfortunate mouse has entered the trash compactor whose walls are 15 meters apart. The walls of the compactor begin to close in on the mouse at a speed of 0.2 meter per hour. The mouse panics and starts to runs from one of  walls' that is closing in, to the opposite wall in order to escape, over and over  until the compactor walls meet each other . The mouse runs at a speed of 10 meters per hour. How much distance does the mouse run before it dies?

ICSE mock test paper

ICSE mock test paper for STD X

ICSE mock test paper

ICSE mock test paper STD X

JMO - numbers

If you have an operator (!) such that:

1! = 1

2! = 2 x 1

3! = 3 x 2 x 1

And it is also given that 0! = 1

You are given 4 zeros. Can you get a value of 24. You can use the operator as many times as you want.

variation

The intensity of light is measured in Lux. It is found that the intensity of light varies as the inverse square of the distance between light source and point of measurement.
if at 10 meters, the intensity is 100 lux, what is the intensity of the light at 15 meter distance.

percentage

Refer to the path followed by the ball in the diagram below. every time the ball hits the ground it looses 20% of its energy. what is the energy left in the ball just after it hits the ground for the third time.

mensuration

Ladoos of radius 5 cm rest are stacked in the fashion shown above for the Ganesh Chaturthi. what is the area of the shaded region.

circle

 wooden cubes of unit cross section (1 cm x 1 cm) are used to keep the pipe in place as shown above. What is the horizontal distance between the two cubes.

circle

find the coordinates of point of contact between the bigger and the smaller circle.

circle

The 2 circles of radius "r" are resting on a horizontal plan. A smaller circle is housed in the gap of the two bigger circles as shown. What is the radius of the smaller circle?

ICSE mock test paper

ICSE mock test paper

time and work

two pipes running together can fill up a cistern in 40/13 mins. If one pipe takes 3 mins more than the other to fill the cistern, find the time in which each time would fill the cistern?

distance and speed

Two trains leave the railway station at the same time. One train is travelling due north and the other due east. The first train is 5 km/hr faster than the second train. If after 2 hours, the trains are 50 km apart, what is the speed of each train?

circle

The sum of the areas of two circles is 116π cm2 (refer diagram below). the centre of the circles is 6 cm apart. find the radius of the circles.

food for thought

hello everyone, if you are from India then I wish you happy Ganesh Chaturthi.

I was toying with the idea of handpicking video tutorials that qualify under the following heading:

1. content 
2. clarity of concept
3. presentation
4. throw and accent of the speaker
5. the pace at which the subject unfolds
6. examples to elucidate the point.

Although it might sound very innocuous, but it turns out to be very time taking given the vast mine of data available on the internet.

I feel it will help the parents by fulfilling manifold purposes, namely;

• know that the content is reliable
• children don't have to mine through the youtube endlessly, so that would save a lot of time.
• it will increase the effectiveness of learning and at the same time reduce the load (because most videos are for 7 to 10 mins duration)

kindly share your thought in this matter.

happy reading

shubhro

profit and loss

A shopkeeper buys an article at a rebate of 20% on the printed price. He spends Rs 100 on the transportation of the article. After charging a sales tax of 6% on the printed price, he sells the article at Rs 1060. Find the profit percentage.

quadratic equation

in a positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by 1/14. Find the fraction.

time and work

Pipe A can fill a tank in 3 hours less than pipe B. they together can fill the tank in 6 hours and 40 mins. find the time each tank will take to fill the tank.

distance and speed

The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hours and 45 mins. Find the speed of the stream.

profit and loss

By selling an article for Rs 24 the profit percentage made is equal to the cost price of the article. Find the cost price of the article.

Answer: Rs 20.

remainder theorem

Without actually dividing prove that x⁴ + 2x³ – 2x² + 2x – 3 is exactly divisible by x² + 2x – 3 

ratio and proportion

ratio and proportion

coordinate geometry

Show that the lines x = 0 and y = 0 trisect the line segment formed by joining the points (-10, -4) and (5,8). Find the point of trisection.

trigonometry

If A, B and C are interior angles of a triangle ABC, show Tan (A + B – C)/2  = cot C

circle

In the diagram given below, if AD = DC and AB = AC, then show that AP = 1/4 AB

 

trigonometry

circle

Find angle X.

circle

questions on rationalization

15 Practice Questions for STD IX for IPM /IMO / MTSE with answers

15 Practice Questions for STD IX for IPM /IMO / MTSE  with answers

15 Practice Questions for STD VIII for IPM /IMO / MTSE with answers

15 Practice Questions for STD VIII for IPM /IMO / MTSE  with answers

geometry

ABCD is a square. With centre B and C and radius equal to the side of the square, circles are drawn to cut one another at E inside the square. What is the measure of angle BDE?

geometry

ABCD is a square. P is a point in the square such that triangle ABP is equilateral. What is the measure of angle PCB

trigonometry

Circle

A circle with radius 2 cm is placed against a right angle. Another small circle is placed in the gap between the circle and the right angle. What is the radius of the smaller circle?

simple equations

Three friends returning from a movie, stopped to eat at a restaurant. After the dinner, they paid their bill and noticed a bowl of mints at the front counter. Shikha took 1/3^rd of the mints, but returned four because she had a momentary pang of guilt. Farah then took ¼ of what was remaining but returned three for similar reasons. Aditi then took half of the remaining but threw back two into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?