## 09 FebThe Colours of Infinity: The Beauty and Power of Fractals

Edited by Nigel Lesmoir-Gordon Springer, 2010, x+207 pp.   In 1980, at the IBM Thomas Watson Research Centre in upstate New York, the mathematician Benoit Mandelbrot was probably the first person to view a geometric picture of an unusual set of pixels on the computer screen and discover...

## 07 FebINMO 2013

The 28th Indian National Mathematical Olympiad (INMO) was held on 3rd February, 2013 across the nation. The questions asked in the exam are provided below. We shall publish solutions to the problems shortly. INMO 2013 [ad#ad-2]...

## 01 Febপেলিনড্ৰম সংখ্যা (Palindrome Number)

যিবোৰ শব্দ, বাক্য বা ছন্দ সচৰাচৰ পঢ়াৰ ধৰণতকৈ বিপৰীত ফালৰ পৰা, অৰ্থাৎ সোঁফালৰ পৰা বাওঁফাললৈ পঢ়িলে একেই হয় সেইবোৰক পেলিনড্ৰম বোলে। যেনে- Refer, level, নৱজীৱন। তথ্য অনুসৰি, মধ্যযুগত ইউৰোপ, আমেৰিকাত পেলিনড্ৰম আৱিস্কাৰ কৰাতো এটি খেলৰ দৰে আছিল আৰু গ্ৰীক, লেটিন আৰু ৰোমান ভাষাত ইয়াৰ চৰ্চা...

## 28 JanFind the Remainder

1) The remainder when $$3^{31}$$ is divided by 5 is A) 2 B) 3 C) 4 D) 1 (Hint: - gcd(3,5)=1 and $$\phi (5)=4,$$ thus $$3^4\equiv 1(mod 5).$$) 2) The reminder when $$5^{99}$$ is divided by 13 is A) 0 B) 8 C) 1 D) 4   3) The reminder when...

## 28 JanNumeral System

1) The symbol $$25_b$$ represents a two-digit number in base b. If the number $$52_b$$ is double the number $$25_b,$$ then b is: [Asked in “FMS”.] A) 7 B) 8 C) 9 D) 11   2) Convert the decimal number 22 to binary number.   3) Convert the decimal number...

## 23 JanH.C.F. and L.C.M.

1) The H.C.F. of $$\frac{9}{4},\frac{3}{20},\frac{9}{10} and \frac{15}{16}$$ is: A) $$\frac{3}{80}$$ B) $$\frac{3}{2}$$ C) $$\frac{1}{40}$$ D) $$\frac{45}{2}$$   2) The L.C.M. of $$\frac{2}{3},\frac{3}{20},\frac{9}{10} and \frac{15}{16}$$ is: A) $$\frac{3}{80}$$ B) $$\frac{3}{2}$$ C) $$\frac{1}{15}$$ D) $$\frac{45}{2}$$   3) The H.C.F. of 1.26, 1.155, 0.21 and 0.315 is: A) 0.05 B) 0.105 C) 1.05 D) 0.03...

## 23 JanProbability

1) $$x_{1}, x_{2}, x_{3},\dots x_{50}$$ are fifty real numbers such that $$x_{r}< x_{r+1}$$ for r = 1, 2, 3...

## 23 Janসাধাৰণ গণিত (১)

প্ৰশ্নসমূহ:- ১) ১.৪২৮৫৭১৪২৮৫৭১৪২৮৫৭১...

## 23 JanCoding and Artificial language (Aptitude test)

1) In a certain code ‘1 7 2 9’ means ‘in a programming language’, ‘7 9 3’ means ‘as a set’ and ‘2 3 4 5 6 7’ means ‘in the set as an element’. What is the code for ‘a’? A) 1 B) 7 C) 9 D) 3   2)...

## 23 JanNumber of Cubes (Aptitude Test)

All the faces of four equal cubes are painted with green color. Then each cube is cut into 64 small equal cubes.   1) How many small cubes will have 4 colored faces and two non-colored faces? A) 32 B) 64 C) 0 D) 12   2) How many small...