The Top Unsolved Questions in Mathematics Remain Mostly Mysterious

  Credit:  Getty Images Twenty-one years ago this week, mathematicians released a list of the top seven unsolved problems in the field. Answ...

A Random Walk through the English Language

  Andrei Andreyevich Markov , the atheist ( left ) and  Pavel Alekseevich Nekrasov , the believer ( right ). Credit: Alamy Here’s a game  Cl...

A Modest Proposal: Let’s Change Earth’s Orbit

  Credit:  Getty Images During a congressional hearing last week, Republican Representative Louie Gohmert of Texas asked a U.S. Forest Servi...

A rectangular fish tank is 80 cm long, 50cm wide and 35cm high. If it is 3/4 full of water, calculate the volume of water in litres [1000cm^3 = 1 litre] and the depth of the water in the tank.

safety regulations say that there should be at least 12m^3 for each person in a room where people sleep. a room is 12m long, 15m wide and 5m high. what is the maximum number of people who can sleep in it safely?

Find the square of 132 and 528

Show that 3650 is not a perfect square

  Not a perfect square

State whether the following statements are true or false

a)  The square of an odd number is always odd True b) The square of an even number may be odd False c) The square of a negative number may b...

Insert two rational numbers between each of the √5 and √11 ,√26 and √34 , √2 and √8

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Insert three rational numbers between each of the following

  a)  5 and 6.5 Find the mean of two numbers b) 4.5 and 7.25    Find the mean two numbers c) 10.4 and 13.6

Insert a rational number between each of the following and then arrange in ascending order

Group the following numbers as rational or irrational.

Find x if (x,3) = (2,3)

 Find x if (x,3) = (2,3) Solution :     (x,3) = (2,3)     x = 2 and 3 = 3     x = 2 Ans

Is (3,5) equal to (5,3) ?

 Is (3,5) equal to (5,3) ? Solution :          Since 3  ≠ 5 and 5 ≠ 3     Also (  x, y )  ≠ (y,x) There (3,5) is not equal to (5,3)

Which of the following sets are null sets? (i) A = {x/x^2 = 16 and 2x =4} (ii) B = {x/x + 6 =6}

  Which of the following sets are null sets?   (i)  A = {x/x 2  = 16 and 2x =4}       (ii)  B = {x/x + 6 =6} Solution : A = {x/x 2  = 16 and...

Let S = {1,2,10,20} and T = {a,b,c,d}. Then show that S ~ T but S ≠ T.

 Let S = {1,2,10,20} and T = {a,b,c,d}.      Then show that S ~ T but S ≠ T. Solution :     S = {1,2,10,20} and T = {a,b,c,d} The number of ...

Show that N = {1,2,3,...}, E = {2,4,6,...} and Q = {1,3,5,...} are equivalent sets.

 Show that N = {1,2,3,...}, E = {2,4,6,...} and Q = {1,3,5,...} are equivalent sets. Solution :  The equivalent sets having the same number ...

Write down all the subsets of { x,y,zt} and find the power set of S = {4,8,12}.

 Write down all the subsets of { x,y,zt} and find the power set of S = {4,8,12}. Solution : The possible subsets of {x,y,z,t} are { },{x},{y...

Decide which sets are proper subset of other.

 Decide which sets are proper subset of other. (i) T = {t/t is a rectangle} (ii) P = {p/p is a parallelogram} (iii) S = {s/s is a square} (i...

Q.1: Distinguish between the sets Φ , {0} and {Φ}.

  Q.1: Distinguish between the sets Φ , {0} and {Φ}. Solution:      Φ is the Null set or empty set having no element.     {0} Exactly one el...