** **__CPS RAMANUJAM CLUB__

__CPS RAMANUJAM CLUB__## PREVIOUS QUESTIONS: 105

- q)Find smallest natural number which consists of only 5's and 0's and divisible by 7.
- Q) Find the smallest number to have 120 factors(clue: answer is 5-digit number)
- q)Find the smallest square greater than 1 in the fibonacci series (0,1,1,2,3,5,8,...)
- Stress buster : count number of dogs in chennai (The answer should not have any comma and it should be rounded off to nearest thousands)
- q) 4__5__6__7 = 33 Fill the blanks with (+,-,x,/) Type answer as only operators (i.e., +++ or -++ or like that)
- What is special in this sentence :How i wish i could calculate pi (answer is only a decimal number)
- Tricky question : Imagine that you are standing in a 3x3 grid in bottom left corner box . You have to go to top right corner box .You can only move either top or right in one step. how many ways you can reach the destination(top right box)
- q) Find the number less than 100 to have most number of factors.
- Q)Unscramble the following : HABTAAYAR
- q)What is the probability that the fan will fall off from the ceiling ? (answer in decimal form)
- What is the sum of the digits of the smallest positive integer which is divisible by 99 and has all of its digits equal to 2
- Imagine a circle is inside a bigger quadrant circle (1/4 of bigger circle) .The smaller circle is touching bigger quadrant at 3 points. What is the ratio of areas of smaller circle and bigger quadrant circle.
- Find smallest possible 2 distinct natural numbers such that their sum is a square and their difference is a cube.
- what is smallest palindrome prime > 100 ?
- q) 12 square is 144 . if you reverse 144 , it is 441 which is 21 square(21 is reverse of 12) Similarly 13 square is 169 , 961 is 31 square . This property holds true only for some numbers .Find the number of numbers that satisfy the condition and are >100 and <200
- Fill the missing ? :

- In how many ways can you arrange 10 identical balls into 3 boxes such that no box is empty ?

- A 3digit number is the sum of factorials individual digits (IE, abc= a! +b! +c!) Find the number:

- Find the smallest 3 digit number N , so that whatever digit d is attached to right of N , is divisible by d .

- q) In how many ways can you choose 60 squares in 11x11 chessboard(121 squares) such that no square have a side in common.

- q) In a 6x6 chess board , how many ways you can color the 36 squares with red or blue such that each row and column has exactly 3 red and 3 blue squares.

- Solve equation a
^{2}+ b^{2}<= 4a+6b-13 , find a+b ?

- In triangle ABC , AB=7 , AC=7, BC=2 .Point D lies in extended line of BC such that AD = 8 , Find BD .

- Find the smallest number when divided by 11,7,13 gives remainder 3,5,2 respectively

- A five digit number 2A9B1 is a perfect square . There is another 3 digit number CBA such that its square also ends with CBA . There is also another 4 digit number 9DEC whose square also ends with 9DEC . A,B,C,D,E are digits. Let 2F = A+C+E . Find the name of famous mathematician who was born in this date : 0E-0B-18FF (dd-mm-yyyy)

- How do you make number 1000 from only one 8. Answer is a 6 letter word

- Solve and find the values of x:

(x^{2}-3x+2)^{x4-7x2+12}=1

- What is the smallest number which can be expressed as sum of 2 primes in 2 ways.

- Find a
^{2}+b^{2}+c^{2}-ab -bc -ac where a= 9999 b = 9998 c=9997 ?

- Find Radius of red circle

- Find the lowest value of N such that the probability of finding a prime number less than N is exactly 20%.

- Let a number be N and the sum of digits of N be s. Find the smallest number N which satisfies the condition : N = 2s
^{2}

- What is the minimum value of : 7a
^{2}+14a+2b^{2}+4b+32

- Complete the series 15, 21, 39, 77, 143,?

- a
^{b}= b^{a}, c^{2}= 2a+b-1.Find c where a,b, and c are distinct natural numbers.

- Is it possible to form a word with first , fifth and sixth letter of the word EDUCATION .If no words are possible , Type "NO" .If only one word is possible , type that word . If many words are possible , Your answer should be the last in alphabetical order among the possible words.

- q) Imagine that in your city , 1 person is infected with corona virus in first day. Each infected person spreads the virus to 1 another person in next day. If a person is infected with the virus , he/she will die in next 5 days . Find the number of persons in your city who are alive but infected on end of 10th day.

- Imagine a square on a circle such that 2 adjacent vertices of the square are on the circle and the other opposite side of square is touching the circle (tangential). If the ratio of length of square and radius of circle be x. Find 5x.

- Find the smallest number that can be written as the sum of 3 squares in 4 ways.

- What is the smallest prime number leaving remainder 3 when divided by 100 and leaving remainder 35 when divided by 39.

- q) Let the function S(n) means the sum of digits of n. For example S(102)=1+0+2=3, S(999)=9+9+9 = 27, S(S(99)) =S(9+9)=S(18)=1+8=9.
Find the smallest number N such that S(S(S(N)))=3.

- Let ABCD be a quadrilateral inscribed in a circle . If AB = 10 , BC=11, CD = 12 , AD = 13 , Find the product of diagonals : (AC x BD) ?

- How can u make number 24 with 4 zeroes .

- q) Find the sum of first five numbers which have exactly 8 factors including 1 and itself.

- q) What is the smallest 6 digit number which is a square and cube

- q) What is the smallest odd number which is a square , cube and also to power 4.

- Q) In a triangle ABC, D is a point on BC such that AD is the internal bisector of ∠A. Suppose ∠B = 2∠C and CD = AB. Find ∠A in degrees

- q) What is the smallest number which has 13 factors and also its digit sum is 20.

- q) How many words can you form from the word "wheat" ?

- q) There are 2 cycle rides who ride in a circular track . One rides at 17kmph and other rides at 23kmph in same direction . If both start from a same point , how many distinct places on the track do they meet (including the starting point) Given Radius of circle is 100m .

- Q) Imagine there are 2 chords perpendicular to circle and one chord is divided by other chord as 2 , 6 . The length of other chord is divided as 3 and x . If Radius is R , find 2R
^{2}

- q) Lets consider a series L = {list of all fibonacci numbers} , consider another series M = {List of units digit of all fibonacci numbers }. After how many elements , does the series M get repeated.
(Hint : L ={0,1,1,2,3,5,8,13,21,33,..} M = {0,1,1,2,3,5,8,3,1,3,...} )

- Is 1100 AD , a leap year ? (True or False..) and also explain the reason...

- How do you get number 100 , using 4 sevens and 1 one . (7,7,7,7,1) You can use any kind of operation but use only these numbers .

- How many numbers are between 100 and 200 which are multiple of 43

- Is 27000001 a prime number (True or False)

- What is smallest prime even number ?

- What is the smallest fibonacci number which is a sum of 2 primes?

- q)Find the smallest number to have 100 factors

- q) If a number has exactly 11 factors , is it a perfect square ? (True/False)

- If 3 cats can catch 3 bunnies in 3 minutes, how long will it take 100 cats to catch 100 bunnies?

- What is last digit of 36 to power 36 :

- Why 'x' and 'y' letters are most commonly used alphabets in mathematics ?

- 1 , 1 , 2 , 5 , 14 , 42 , ____. Find the next number

- How was the equal to ' = ' sign invented ?

- A person was 7 years old before 10 years .Before 10 years His father was 5 times his age .How old is his father now ?

- Can you find 4 points on a roughly drawn loop such that when they are joined , they form a square.

- 6 = 4 , 4 = 5 , 5 = 5 , 10 = 4 , 0 = 5 , 1 = ?

- q) Lets assume you are playing a game with the computer . The game is to find the missing number . You have to Guess a number , the computer would reply whether the missing number is lesser or greater or equal to ...
- But one condition , the computer can lie !
- But computer cannot lie two times in a row !
- If the number is equal , the computer has to say equal to (no other go) .
- Only for < or > it can lie !.

Given that the missing number is from 1 to 1000000000. Find the minimum number of moves(or replies) you can make to guess the number . (You should make your moves very optimal! )

see this example ,lets say the computer thinks number 5 .

- You : 2 computer : Lesser
- You : 4 computer : Greater
- You : 4 computer : Greater
- You : 5 computer : Equal

In this case , computer to lie in the first question, so it has to tell the truth in the second question. In the third question, computer decides to tell the truth, and in the final question, computer answers 'Equal', since You asked about the correct value.

- Q)Let N be the smallest number to have 13 factors , find log2(N)

- Which number is cube of itself ? If many numbers are there , type them seperated by a comma in ascending order

- In how many ways can you arrange 8 queens in chessboard of 64 squares such that no queen attacks any other queen.

- q) Let you read a book with 20 pages . On each day you read some set of pages which are coprime to each other . For example On day 1 , you read page 1,2,3,5,11,13,17,19 . On day 2 you read 4,9,16 , this goes on . In how many days will you finish the book. Also try to crack the logic for what page numbers do you read on each day.

- Type Answer in number

- q) Find the number of ways you can arrange 3 pairs of shoes in any order such that the left shoe comes first and right shoe comes next . (Eg LRLRLR ,LLLRRR , LLRRLR are valid arrangements whereas RLRLRL,RRRLLL are not)

- q) Find question mark

- In how many ways can you reach a 4x4 grid from top left corner to bottom right corner . You should only go right or bottom.

- Write the operations alone involved , eg : +-+/

- What does this expression evaluate ?(accurate to 3 decimal places)

- What is 23 + 12 ?

- What is 120 + 80 ?

- What is the smallest number which has exactly 12 factors , but also have only 1 prime factor ?