Maths Quiz

ST.XAVIER’S COLLEGE(AUTONOMOUS),KOLKATADEPARTMENT OF MATHEMATICSPi-Let’s be more irrational presentsANALYTICA 2011 -If you can’t see, Imagine!!!MATHS QUIZ its all in the mind….. : ST.XAVIER’S COLLEGE(AUTONOMOUS),KOLKATADEPARTMENT OF MATHEMATICSPi-Let’s be more irrational presentsANALYTICA 2011 -If you can’t see, Imagine!!!MATHS QUIZ its all in the mind…..

ROUND I : ROUND I Choose Correctly

RULES : RULES For a CORRECT ANSWER ,each team/group will be awarded 10 marks. There is NO BONUS MARKS for this part. NO NEGATIVE MARKING. NO JUSTIFICATION NEEDED. TIME: 30 SECONDS for each team.

What is the number of real roots of 5x4-4x+1=0 in [0,1]? : What is the number of real roots of 5x4-4x+1=0 in [0,1]? (a)0 (b)1 (c)2 (d)5

Answer: : Answer: (c)2

log27 is - : log27 is - (a)A positive integer (b)A rational number (c)An irrational number (d)In the form 1/n where nєZ+

Answer: : Answer: (c)An irrational number

If A is a skew symmetric matrix of order n and X is a nx1 column matrix, then XTAX is a - : If A is a skew symmetric matrix of order n and X is a nx1 column matrix, then XTAX is a - (a)Orthogonal Matrix (b)Unit Matrix (c)Null Matrix (d)None Of These

Answer: : Answer: (c)Null Matrix

If A={1,2,3,…,m} and B={1,2,3,…,n} where m,n є z+ m≤n then the number of functions that can be defined from A to B is? : If A={1,2,3,…,m} and B={1,2,3,…,n} where m,n є z+ m≤n then the number of functions that can be defined from A to B is? (a) mn (b) nm (c)nPm (d)m!

Answer: : Answer: (b) nm

The position vector of two given points A and B are 4i-3j-k and 5i-5j+k respectively. If α is the angle between AB vector and Z axis, then cos α=? : The position vector of two given points A and B are 4i-3j-k and 5i-5j+k respectively. If α is the angle between AB vector and Z axis, then cos α=? (a)1/3 (b)2/3 (c)-2/3 (d)0

Answer: : Answer: (b)2/3

If zєC,the minimum value of |z|+|z-1| is attained at- : If zєC,the minimum value of |z|+|z-1| is attained at- (a)Exactly one point (b)Exactly two points (c)Infinite number of points (d)None of these

Answer: : Answer: (c)Infinite number of points

END OF ROUND I : END OF ROUND I

Round II : Round II Hurry up

RULES : RULES Marking for a correct answer: 1) 10 marks if it was a direct question to a group. 2) 5 marks – bonus No Negative marking. Answer without PROPER LOGIC will be treated as a wrong answer. TIME :- 1 MINUTE for DIRECT QUESTION 5 SECONDS for BONUS QUESTION.

If a+b+c=3 and a>0,b>0,c>0, find the greatest value of a2b3c2. : If a+b+c=3 and a>0,b>0,c>0, find the greatest value of a2b3c2.

Answer: : Answer: (310. 24)/77

Let z1,z2,z3 be three complex numbers and a,b,c be real numbers not all zero such that a+b+c=0 and az1+bz2+cz3=0.Can z1,z2,z3 be co-linear? : Let z1,z2,z3 be three complex numbers and a,b,c be real numbers not all zero such that a+b+c=0 and az1+bz2+cz3=0.Can z1,z2,z3 be co-linear?

Answer: : Answer: Yes

If |z|=2,then what is the locus of the points representing the complex numbers -1+5z? : If |z|=2,then what is the locus of the points representing the complex numbers -1+5z?

Answer: : Answer: Circle, with radius 10 and centered at (-1,0)

Can there be an A.P. whose terms are distinct prime numbers? : Can there be an A.P. whose terms are distinct prime numbers?

Answer: : Answer: No

The interior angles of a polygon are in A.P. The smallest angle is 120˚ and common difference 5˚. What is the number of sides of the polygon? : The interior angles of a polygon are in A.P. The smallest angle is 120˚ and common difference 5˚. What is the number of sides of the polygon?

Answer: : Answer: 9

What is the the number of functions h:Z+R+ satisfying the formulah(1)=3h(i)=h[h(i-1)-1]1/2 ? : What is the the number of functions h:Z+R+ satisfying the formulah(1)=3h(i)=h[h(i-1)-1]1/2 ?

Answer: : Answer: 0

END OF ROUND II : END OF ROUND II

Round III : Round III Tricks

RULES : RULES Marking for a correct answer: 1) 10 marks if it was a direct question to a group. 2) 5 marks – bonus No Negative marking. Answer without PROPER LOGIC will be treated as a wrong answer. TIME :- 1 MINUTE for DIRECT QUESTION 5 SECONDS for BONUS QUESTION.

A flag is to be designed with 6 vertical stripes using some or all of the colors yellow,red,violet & black. In how many ways can this be done so that no two adjacent stripes have the same color? : A flag is to be designed with 6 vertical stripes using some or all of the colors yellow,red,violet & black. In how many ways can this be done so that no two adjacent stripes have the same color?

Answer:- : Answer:- 4 x 35

Twenty one persons have first names Ram, Rajiv, Anwesha, Priya & last names Chowdhury, Kapoor, Sarkar, Agarwal, Mitra. Then at least how many persons must have the same first & last names? : Twenty one persons have first names Ram, Rajiv, Anwesha, Priya & last names Chowdhury, Kapoor, Sarkar, Agarwal, Mitra. Then at least how many persons must have the same first & last names?

Answer : : Answer : Two ( 2 )

Given a group of n women & their husbands, how many people must be chosen from this group of 2n people to guarantee that the set contains a married couple? : Given a group of n women & their husbands, how many people must be chosen from this group of 2n people to guarantee that the set contains a married couple?

Answer : : Answer : (n+1)

For n≥4 , can 1!+2!+3!+……+n! be the square of a positive integer? : For n≥4 , can 1!+2!+3!+……+n! be the square of a positive integer?

Answer : : Answer : No

A person when asked about his age, told “ the day before yesterday I was 15 & I will be 18 the next year!” Is it possible that he is telling the truth? : A person when asked about his age, told “ the day before yesterday I was 15 & I will be 18 the next year!” Is it possible that he is telling the truth?

Answer : : Answer : Yes He is telling on 1st January & his birthday is on 31st December

A determinant of the second order is made with the elements 0 & 1. what is the probability that the determinant made is non-negative? : A determinant of the second order is made with the elements 0 & 1. what is the probability that the determinant made is non-negative?

Answer : : Answer : 13/16

END OF ROUND III : END OF ROUND III

ROUND IV : ROUND IV Let’s Play With Numbers

RULES : RULES Marking for a correct answer: 1) 10 marks if it is a direct question to a group. 2) 5 marks : bonus No Negative marking. Answer without PROPER LOGIC will be treated as a wrong answer. TIME :- 1 MINUTE for DIRECT QUESTION 5 SECONDS for BONUS QUESTION.

Find the number of positive integers which divides 10999 but not 10998. : Find the number of positive integers which divides 10999 but not 10998.

Answer : : Answer : 1999

Find the remainder when 12+22+112+222+1112+2222+…..+1111111112 +2222222222 is divided by 8. : Find the remainder when 12+22+112+222+1112+2222+…..+1111111112 +2222222222 is divided by 8.

Answer: : Answer: 7

Find all the positive numbers which can be expressed as the sum of three distinct composite numbers. : Find all the positive numbers which can be expressed as the sum of three distinct composite numbers.

Answer: : Answer: All n≥18

Show that 11997+21997+…+19961997 is divisible by 1997. : Show that 11997+21997+…+19961997 is divisible by 1997.

Answer: : Answer: Being explained on-stage…

Find whether 4545+5454 is prime or composite. : Find whether 4545+5454 is prime or composite.

Answer: : Answer: Composite

With how many consecutive zeros does a=(2000! – 1900! + 1800! – 1700! ….. + 200! – 100!) end up? : With how many consecutive zeros does a=(2000! – 1900! + 1800! – 1700! ….. + 200! – 100!) end up?

Answer: : Answer: 24

END OF ROUND IV : END OF ROUND IV

ROUND V : ROUND V Buzzer Round

RULES : RULES Questions will be open to all to the participants. Only the team which will hit the buzzer first will be allowed to answer. For a correct answer:- 20 marks For a wrong answer:- -10 marks Justification is needed for any answer( excluding question 6 ) Time: 1 minute for each question. for question 6 :- Four hints ( each of 15 seconds )

There are n chocolates in a box. If 2 babies want to share it,1 remains extra.3 babies want to share it,2 remains extra.4 babies want to share it,3 remains extra.5 babies want to share it,4 remains extra.6 babies want to share it,5 remains extra.7 babies want to share it,6 remains extra.Which is the smallest possible number of chocolate? : There are n chocolates in a box. If 2 babies want to share it,1 remains extra.3 babies want to share it,2 remains extra.4 babies want to share it,3 remains extra.5 babies want to share it,4 remains extra.6 babies want to share it,5 remains extra.7 babies want to share it,6 remains extra.Which is the smallest possible number of chocolate?

Answer: : Answer: lcm(2,3,4,5,6,7)-1

A and B alternately draw diagonals of a regular 2012 gon. A started drawing. Then B can draw any diagonal which does not cut the diagonal A had drawn. A again repeats the same process. In brief, the rule is, one can connect two vertices if that diagonal does not intersect any previous one. The loser is the one who can’t draw. Can you make a strategy such that A always win? A- B- : A and B alternately draw diagonals of a regular 2012 gon. A started drawing. Then B can draw any diagonal which does not cut the diagonal A had drawn. A again repeats the same process. In brief, the rule is, one can connect two vertices if that diagonal does not intersect any previous one. The loser is the one who can’t draw. Can you make a strategy such that A always win? A- B-

Answer: : Answer: Strategy: A has to draw a diagonal which will divide the whole polygon into two equal halves.

In how many ways can 2 small squares be selected from a chessboard(8x8) such that selected squares are connected at only one corner? OR : In how many ways can 2 small squares be selected from a chessboard(8x8) such that selected squares are connected at only one corner? OR

Answer: : Answer: 98

Prove that “an 8x8 chessboard cannot be covered by 15 T-tetraminoes and 1 square tetramino.” T-tetramino 1 square tetramino : Prove that “an 8x8 chessboard cannot be covered by 15 T-tetraminoes and 1 square tetramino.” T-tetramino 1 square tetramino

Answer: : Answer: Being explained on-stage…

Among 0 to 100, if you choose any 52 positive numbers , then prove that you can always manage to take 2 of those such that their sum is divisible by 100. : Among 0 to 100, if you choose any 52 positive numbers , then prove that you can always manage to take 2 of those such that their sum is divisible by 100.

Answer: : Answer: Being explained on-stage…

Who Am I…??? : Who Am I…???

HINT 1:I am a mathematician, born in Paris in 1789 and my family was forced to flee during the reign of terror(French Revolution). : HINT 1:I am a mathematician, born in Paris in 1789 and my family was forced to flee during the reign of terror(French Revolution).

HINT 2: I had contributed to many areas of mathematics incl. real and complex analysis, number theory, differential eqn., mathematical physics and probability. : HINT 2: I had contributed to many areas of mathematics incl. real and complex analysis, number theory, differential eqn., mathematical physics and probability.

HINT 3: I entered the Ecole Polytechnique in 1805. : HINT 3: I entered the Ecole Polytechnique in 1805.

Slide 78 :

Answer: : Answer: Augustine-Louis Cauchy

End of Maths Quiz… Thank You…  : End of Maths Quiz… Thank You… 