This blog makes available plenty of questions for practice, for the Mathematics competitive exams. We also try to bring to students interesting ways of approaching the questions. If you need any assistance in questions from IPM, MTSE, SCHOLARSHIP, OLYMPIAD, CBSE , ICSE or Board test papers, you may write to us.
Monday, October 6, 2014
Sunday, October 5, 2014
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?
Saturday, October 4, 2014
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 Friday, October 3, 2014
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.
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
Another Example:
If a number N can be expressed as product of prime factors such that
N = pa x qb x rc...............................
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 = pa x qb x rc...............................
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.
Tuesday, September 30, 2014
Monday, September 29, 2014
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?
Saturday, September 27, 2014
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 101 100 – 1
a) 10000
b) 1000
c) 100
d) 100001
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.
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 - Division
If S = 123456789101112................9979989991000
What will be the Remainder when S is divided by 9.
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.
find the Remainder when the first 1000 digits are divided by 16.
Friday, September 26, 2014
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 6 x + 1 or 6 x − 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
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
With the 5 digits 3,4,5,6 and 7, how many possible numbers can be formed which is divisible by 11.
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?
Thursday, September 25, 2014
JMO
Suppose n is an integer such that the sum of digits on n is 2, and
|
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)?
Wednesday, September 24, 2014
Tuesday, September 23, 2014
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?
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?
Monday, September 22, 2014
Sunday, September 21, 2014
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?
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.
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?
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
5 - 4 = 23
8 - 1 = 63
6 - 16 = 32
9 - 9 = 78
3 - 9 = 6
then find the value of 3 - 81
Thursday, September 18, 2014
Sunday, September 14, 2014
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?
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?
Wednesday, September 3, 2014
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.
if at 10 meters, the intensity is 100 lux, what is the intensity of the light at 15 meter distance.
Monday, September 1, 2014
Sunday, August 31, 2014
Saturday, August 30, 2014
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?
Friday, August 29, 2014
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:
I was toying with the idea of handpicking video tutorials that qualify under the following heading:
- content
- clarity of concept
- presentation
- throw and accent of the speaker
- the pace at which the subject unfolds
- 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.
Answer: Rs 20.
remainder theorem
Without actually dividing prove that x4
+ 2x3 – 2x2 + 2x – 3 is exactly divisible by x2
+ 2x – 3
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.
Thursday, August 28, 2014
Wednesday, August 27, 2014
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
Monday, August 25, 2014
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 1/3rd 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?
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