I thought of
providing some stuff for students studying in the range 5

^{th}to 10^{th}standard. This stuff is a combination of two sets. One is Math&Logic based and the other is Knowledge based. This stuff is a mix of some questions that are based on math fundamental concepts and remaining questions that are based on commonsensical and out-of-box thinking. These do not look like standard questions that are given in school-level exams but mostly resemble or can act as base for the math and logic aptitude sort of questions that are asked in various entrance exams. My primary intention is to inculcate in kids an interest and liking on maths. I strongly opine that math solving skills are very much needed to excel in diverse fields of studies ranging from Science, Engineering to Economics, Management studies etc.
To be frank
on my part, I am starting this post with small number of questions at hand but
I will try to enrich this bit bank by updating it from time to time.

__Math and Logic Based Set:__
1. A number when
used in denominator results in an 'undefined' value. What's that number?

2. X is a
number. If you add X to any other number you get the other number. If you
subtract X from any other number, even then you get the other number. What is
the number X?

3. Y is a number.
If you multiply Y with any other number you get the other number. If you divide
any other number with Y, even then you get the other number. What is the number
Y?

4. It's a
geometric figure and there is one point 'X' with in that figure. All points on
that figure are equidistant from X. What is that geometric figure?What is the
point X called?

5. The one and
only number which is even and prime is_____

6. Which of the
English alphabets are symmetric in shape when written in upper case? (If
bisected vertically)

7. Which of the
English alphabets are symmetric in shape when written in upper case? (If
bisected horizontally)

8. How many two
digit numbers having both identical digits are there?

9. Consider a
two digit number such that if you add it's two digits, you should get a sum of
9. How many such two digit numbers are possible?

10. How many
three digit numbers can be formed by using all the digits 0,1,2. Here
repetition of a digit in a number is not
allowed.

11. What are all
the years in twenty first century that use all the four digits 0,1,2,3?

12. What are all
the years in twenty first century that are palindromes?

13. Is 2013 a
prime number?

14. For a right
triangle, if 24 and 25 are two sides then what is the other side?

15. What is the
square of 995?

16. Ram walked 6
m Eastwards and turned 90 degrees to his left and continued to walk for 8m and
stopped there. At what distance and direction is the final point positioned
with respect to the initial point if we join the two points by a straight line?

17. Amar can do a
work in 60 days and Akbar in 90 days. In how many days both of them can jointly
do that work?

18. Anthony
started a journey by car to his home town which is 100 km away. He travels
first 40 km at a speed of 40 kmph, next 40 km at a speed of 80 kmph and the
remaining distance at a speed of 40 kmph. What is the average speed with which
he travelled to reach the destination?

19. Given the
radius of a circle is 5 cm, what is the distance between two points on the
circle which are located exactly opposite to each other?

20. “The radius
of a circular path is 7 m. If I start at a point on the path and travel 88 m
along the path, then I will reach the same point at which I have started”. Is
this statement True/False?

21. The statement
“X/X = 1” does not work when X=____

22. “Square root
of 16 is 4”- is this sentence perfectly correct?

23. “Square of 4
is 16”- is this sentence perfectly correct?

24. If I say “A/B
= C/D”, does it mean A=C and B=D?

25. If I say “A*B
= C*D”, does it mean either A=C or A=D?

26. If X

^{Y}= 0, then X must be___, irrespective of the value of Y.
27. If X

^{Y}= 1, then Y must be___, irrespective of the value of X.

__Knowledge Based Set:__
1. That's an
English word, which is an acronym representing all the four sides. What's it?

2. We all
remember him for his magic square. Who is that great Indian mathematician?

3. The great
Indian lady mathematician famously known for her quick calculations on large
numbers (recently she has passed away)________

4. The great
Indian mathematician who invented Pujyam ('0') is ____

5. “For a right
angle triangle if 'a' is hypotenuse and 'b' and 'c' are sides then, a

^{2}=b^{2}+c^{2}” - whose theorem is this?
6. “Any three
points which are not collinear can form a triangle”. Is this statement
True/False?

7. “For any two
points on a plane, if we join them by a straight line, it gives the shortest
path”. Is this statement True/False?

8. “In a right
angle triangle, hypotenuse is the largest side”. Is this statement True/False?

9. “In a right
angle triangle, length of hypotenuse is the greater than sum of the lengths of
other two sides”. Is this statement True/False?

10. If the length
and breadth of a rectangle are made equal, then it becomes a _____

__Answers (Math & Logic Based Set):__
1. 0

**2.**0

**Clue:**X+0=0+X=X

**3.**1

**Clue:**Y*1=1*Y=Y

4. Circle,
Centre of the circle

5. 2

6. A,H,I,M,O,T,U,V,W,X
(clue: If we bisect each of these letters vertically, the left and right
portions appear as mirror images)

7. D,E,H,I,K,O,X
(clue: If we bisect each of these letters horizontally, the upper and lower
portions appear as mirror images)

8. 9 (they are-
11,22,33,44,55,66,77,88,99)

9. 9 (they are-
18,81,27,72,36,63,45,54,90)

10. 4 (they are-
102,120,201,210)

11. 2013 and 2031

**12.**only one - 2002.

__Notes:__
Palindrome is a word or number with
a unique property that when it is reversed, it yields the same word or number

**Clue:**As it should belong to twenty first century we start with taking 20 as the first two digits. To fulfill the condition of palindrome, the next two digits must be 0 and 2 respectively. Thus 2002 is the only palindrome in the twenty first century. Likewise, 2112 is the only palindrome in the 22

^{nd}century.

**13.**No

**Try to factorize the number. 2013=11*183**

__Notes:__**14.**7

**Let us try to use Pythagoras theorem. First let us find the squares of the given two numbers. 25^2 = 625 and 24^2=576. Then let us check whether sum or difference of these two squares is a perfect square.625+576 = 1201. We are not sure whether this is a perfect square or not. So let us consider difference. 625-576=49=> this is square of 7 and hence 7 is the other side. Here 25, which is biggest of the three sides is called hypotenuse.**

__Notes:__**15.**990025

__short cut:__**:**

__step-1__
consider the part of the number
excepting the unit's digit 5 => 99

__step-2:__
multiply this with it's next number
=> 99*(99+1)=99*100=9900

__step-3:__
append 25 to the right side of 9900
=> we get 990025

16. 10 m NE

17. 36

18. 50 kmph

19. 10 cm

20. True

21. 0

22. No. Square root
of 16 is either +4 or -4

23. Yes

24. No

25. No

26. 0

27. 0

__Answers (Knowledge Based Set):__
1. NEWS –
North,East,West,South

2. Srinivasa
Ramanujam

3. Shakuntala
Devi

4. Aryabhatta

5. Pythagoras'

6. True

7. True

8. True

9. False

10. Square

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