IPM / MTSE / IMO test paper for STD IX

IPM / MTSE / IMO test paper for STD IX ( Answers are provided)

IPM / MTSE / MAT STD VI Test Paper

IPM / MTSE / MAT STD VI Test Paper

puzzle

Your mother stays in Pune. You want to pay  a visit on her birthday, and give her a gift of 2 cakes.
On the way to Pune, you will run into 7 check post for collecting toll. You can pay them in kind. In such a case they will demand 1/2 of all your cakes as the price of entry. As a goodwill gesture they return back 1 cake to you.
How many cakes do you need to carry to be able to give 2 cakes to your mom.

fun with numbers

Remembering Ramanujam

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111

fun with numbers

Remembering Ramanujam

more with numbers

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

fun with numbers

Remembering Ramanujam

more on interesting numbers

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321

numbers

Remembering Ramanujam
Fun with numbers --- note the symmetry
1 x 9 + 2 = 11
12 x 9 + 3 = 121
123 x 9 + 3 = 12321
1234 x 9 + 4 = 1234321
12345 x 9 + 5 = 123454321
123456 x 9 + 6 = 12345654321
1234567 x 9 + 7 = 1234567654321
12345678 x 9 + 8 = 123456787654321
123456789 x 9 + 9 = 12345678987654321

numbers

10th was the BD of Ramanujam

to remember him here is some interesting symmetry in numbers

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321 

15 questions for IPM and MTSE -- STD VIII

15 questions for IPM and MTSE -- STD VIII

numbers

The number 142857 has the remarkable property that multiplying it by 1, 2, 3, 4, 5, and 6 cyclically permutes the digits.

142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142

can you think of any other number?

divisibility

 Let x and y be integers. Prove that (2x + 3y) is divisible by 17 if (9x + 5y) is divisible by 17.

puzzle

Puzzle:
Here is a list showing the month and the number for each month...
January                     7110
February                     826
March                       5313
April                           541
May                          3513
June                          4610
July                           4710
August                        681
Decipher the logic and find the number for September?

indices

If p =100.48, q =100.70 and pz = q2, then the value of z is:

number series

Solve this logical number series puzzle by replace question mark with the correct number
9090 = 4
1234 = 0
6055 = 2
9081 = 4
8888 = ?

number puzzle

solve the following:

if
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
then find the value of 7+2+5 =

magic square

Find a 4 x 4 magic square who's sum of sides and diagonals is 60

HCF and LCM,

Delegates from 5 different schools are coming to Srimati sulochanadevi singhania school. The number of delegates from Kendriya vidyalaya is 42, 60 from Poddars', 210 from Hiranandani, 90 from Jamnalal and 84 from Lodha. They are being put up at Satkar Residency Hotel. What is the minimum number of rooms that would be required to accommodate so that each room has the same number of occupants and occupants are all from the same school?

distance and speed

If we exclude stoppages, then the speed of a bus is 45 km/h and if we include stoppages, it is 36 km/h. For how much time does the bus stop per hour?

Magic squares

solve the magic square

hint: treat all the 4 x 4 boxes as separate magic square, and follow the rule for even order magic square to fill it up

magic square

complete the magic square

 

HCF and LCM

A number p is such that:
p = 5k1 + 4,
p = 6k1 + 5,
p = 7k1 + 6,
p = 8k1 + 7,
p = 9k1 + 8,

Find the smallest number that satisfy this condition

HCF and LCM

The product of 2 numbers and its HCF is 1080. How many such pair of numbers are possible which satisfy the above condition?

Brihan Mumbai Ganit Adhyapak Mandal Maths practice paper

STD IV question paper for IPM, MTSE

STD IV question paper for IPM, MTSE

JMO PRACTICE PAPER STD VI

JMO PRACTICE PAPER STD VI

JMO PRACTICE PAPER STD VI

JMO PRACTICE PAPER STD VI

JMO STD VI

JMO (VI Std) Practice Paper

divisibility

divisibility test

Show that 1000....................001  (containing 200 zeroes) is divisible by 1001.

Geometry STD V

counting

JMO - application of addition, subtraction and multiplication

Your are given that 12345 x 33 = 407385
Use this information, and the concept of addition, subtraction, multiplication and division to arrive at the multiplication of 12345 x 336567.
You cannot  multiply directly.

factors

How many factors of 7¹⁴ x 8⁷ x 10⁵ are a multiple of 160?

factors

How many factors are there for the number 264?

factors

How many even factors are there for the number 6¹² x 7¹⁴ x 8⁷ x 10⁵

inequality, JMO

How many positive integer values can x take that satisfy the inequality 
(x - 8) (x - 10) (x - 12).......(x - 50) < 0

factors and number

If the sum of the factors of a number is 124. What is the number?

JMO, numbers

HCF and LCM

Three numbers are in the ratio of 3:6:9 and their LCM is 2700. What is the HCF?

even number as difference of 2 squares

Express 124 as difference of 2 squares.

mixtures

Nanu bought two varieties of rice, costing 50 Rs/kg and 60 Rs/kg each, and mixed them in some ratio. Then he sold the mixture at 70 Rs/kg, making a profit of 20 percent. What was the ratio of the mixture?

ratio and proportion

The ratio of marks obtained by Nanu and Bhanu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted. 

ratio and proportion

Two alloys A and B are composed of two basic elements p and q. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?

ratio and proportion, ipm, mtse

A house has dogs, cats and parrot in the ratio of 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7 then what is the minimum of pets in the house possible?

Information

If any of you need the answer fill up sheet to simulate actual exam you may email me. I will send you the sheet so that you can take a printout.

IMO Test paper STD VIII

IMO Test paper STD VIII

IMO test paper for STD VII

IMO test paper for STD VII

STD VI IMO Test Paper

STD. VI IMO Test Paper

Arithmetic progression

In a Society, the houses are arranged in one line numbering 1 to 49. What is that value of 'x' for which the sum of the numbers of the houses preceding the house number 'x' is equal to the sum of the numbers of the houses following it.

Arithmetic Progression

 The sequence  p₁, p₂ ... and q₁, q₂ … are in arithmetic progressions such that p₁ + q₁ = 50 and p₁₁ − p₁₀ = q₉₉ − q₁₀₀. Find the sum of the first 100 terms of the progression, 

( p₁ + q₁),( p₂ + q₂) …

average

There are 10 numbers, u₁, u₂, u₃........u₁₀, having a mean/ average of u_m. If the absolute value of the difference of the number and the mean are 5, 3, 10, 15, 12, 8, 6, 9, 2 and 4 respectively then which of the numbers lie on one side of the mean.

divisibility, numbers

Let n be the total number of different 5 digit numbers that are divisible by 4. The digits comprise of 1, 2, 3, 4, 5 and 6. No digit is repeated in a number. What is the value of n?

divisibility

If n is a positive integer and (n + 1)(n + 3) is odd, then show that (n + 2)(n + 4) must be a multiple of 8.

LCM and HCF

Three numbers are in the ratio of 3:4:5 and there LCM is 2400. What is the HCF?

Number Puzzle

If A³ = _ _ _ _ 76, where A is an element of Natural number. Find A and all the missing numbers.

Algebra

Express 35 as a difference of 2 squares

simple equations

A and B start at noon from two towns 60 km apart, A's rate of walking is twice that of B's. If they walk 5 hours before they meet, find their rate of walking.


answer:
A = 8 km/hr, B = 4 km/hr

simple equation

If P and Q represent two towns 48 kms apart, and if A is walking from P to Q at 7 km/hr while B walks from Q to P at 5 km/hr, both starting at 9:00 am, at what time will they be 12 km apart?

Simple Equation

Of the two boys one was taller than the other by 15 cm; the shorter boy has grown by 9 cm and the taller boy has grown by 5 cm, and at present the difference of their heights is 1/15 the of the height of the taller boy. What were their former heights?

alphamatics, JMO

alphamatics, JMO

alphamatics, JMO

Division, STD XI

Find the Remainder when 2¹⁶⁴ is divided by 7.

indeterminate equation, JMO

Find all the possible combinations in which  1000 can be 

divided into two parts so that one may be a multiple of 13 and

the other a multiple of 49. 

indeterminate equation

The librarian observes that one of the first 9 pages and one other page of two digit is missing from a book. The sum of all the pages in the book now is 260. What are the possible combinations of missing pages?

JMO - miscellaneous examples

1.    Nanu was asked to divide a number by 6 and then add 12 to the quotient. She, however added 12 to the number first and then divided it by 6, getting an answer of 112. What was the correct answer?

2.    If Nanu travels at 40 km/hr speed, she reaches school from home at 9:30 am. If she travels at 50 km/hr speed, she reaches at 9:00 am. What is the distance from home to her school?

3.    Solve the alpha-numbers, given that each alphabet represents a unique digit.

                    S   E   N  D

 +    M  O   R  E

-----------------------------------------

            M   O   N  E  Y

Alphamatics, JMO

The alphabets given below represent a unique number between 0 to 9.
find the alphabets

                    E   I   N
                    E   I   N
                    E   I   N
     +             E   I   N
------------------------
               V  I    E   R

Alphamatics, JMO

Each of the alphabets represent a unique number between 0 to 9.
find them

Z E R O E S
  + O N E S
-----------
B I N A R Y

indeterminate equation, JMO

Can integral multiples of 13 and 68 add up to 2000. if so how many such possibilities are there.

alphamatics, JMO

If 9 x HATBOX = 4 x BOXHAT
where every Alphabet is unique and has a value of 0 to 9.
Find each of the digits represented by the alphabet.

alphamatics

A B C D E F
x                6
---------------
D E F A B C

All alphabets represent a unique digit between 1 to 9.

Find the values of the alphabets A,B,C, D, E, F

series, JMO

The following number is formed by a special pattern and is the only 
one of its kind: 8549176320. 

What is the pattern?

Look and say sequence

The series given below is called the "look - and - say" sequence.

 

1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... 

To generate a member of the sequence from the previous member, one must read  the digits of the previous member, thus:

• 1 is to be  read as "one 1" or 11.
• 11 is to be  read as "two 1s" or 21.
• 21 is to be  read as "one 2, then one 1" or 1211.
• 1211 is to be  read as "one 1, then one 2, then two 1s" or 111221.
• 111221 is to be  read as "three 1s, then two 2s, then one 1" or 312211

indeterminate equation, JMO

Divide 112 into two parts one of which when divided by 3 leaves remainder 2 and the other divided by 8 leaves a remainder 7.

indeterminate equation, JMO

Find the fractions, having 7 and 11 for their denominators, such that their sum is 1(34/77)

indeterminate equation, JMO

Divide 152 into two parts so that one may be a multiple of 7 and the other a multiple of 12.

Alphamatics

 For questions on letter numbers (alpha-matics)
http://mathforum.org/library/drmath/sets/select/dm_letter_number.html

reference site for puzzles

For puzzles in Alphametics, you may visit the given website:

http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/

indeterminate equation, JMO

Is it possible to have the sum of multiples of 29 and 48 to be equal to 500.
i.e 48m + 29n = 500, where m and n are natural numbers.

indeterminate equation, JMO

Is it possible to have the sum of multiples of 44 and 18 to be equal to 1000.
i.e 44m + 18n = 1000, where m and n are natural numbers.

Indeterminate equation, JMO

Is it possible to have the sum of multiples of 47 and 19 to be equal to 1000.
i.e 47m + 19n = 1000, where m and n are natural numbers.

JMO STD VI

MTSE STD VIII practice paper

15 questions for MTSE STD VIII

indeterminate equations, JMO

The total age of some 7 years old children and some 5 years old children is 60 years. If a team is to be selected from these children such that their total age is 48 years, then in how many ways can it be done?

indeterminate equation, JMO

Students of a class are made to stand in rows. If 4 students are extra in each 

row, there would be 2 less rows. If 4 students are less in each row, there would 

be 4 more rows. Find the total number of students which satisfies this condition 

if the number of students is less than 100.

continued fraction

 

continued fraction

                                                                                                                                           



   

number, division --- JMO

 

numbers / Division - JMO

JMO questions STD V / STD VI

1.       You are given that 47658 x 39876 = 1900410408. Without directly multiplying, use the given information to solve the following question:

52.342 x 0.60124

2.       Find the value of 19999 x 299999 using the information 19999 = 20000 – 1 and 299999 = 300000 – 1.

3.       Consider the number 12345.....11121314........566. Find the 500^th digit.

                                                                                                                                  

Find 4 fractions which lie between 2/3 and 3/4  such that they divide the fractions in 5 equal parts.                           

information

https://sites.google.com/site/tripuramathematicalsociety/olympiad

This site carries a lot of information on reference books for Olympiad.

IMO test papers for STD V

IMO test papers for STD V

IMO test papers for STD IV

IMO test papers for STD IV

IMO test paper --- STD III

IMO test paper --- STD III

STD II IMO test paper

STD II --- IMO test paper

series

fill in the next numbers:
2, 7, 10, 22, 18, 37, 26,........

pipes and cistern

A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. How many liters does the cistern hold?

pipes and cisterns

Three pipes A, B and C can fill a tank in 6 hours. All the three pipes are kept open for 2 hours, C is then closed and A and B fills the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is ................

pipes and cisterns

A tank is filled in 10 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

pipes and cisterns

Three pipes A, B and C can fill up a tank from empty to full in 10 minutes, 20 minutes, and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution P in the liquid in the tank after 6 minutes?

numbers, JMO

If x ε N in f(x) = 6x + 1 and g(x) = 6x – 1. Then the Venn diagram representation for f(x), g(x) and prime numbers P is given by: