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WHICH IS THE BEST AMONG THESE???

Correspondence Course :

* BRILLIANT TUTORIALS

* NARAYANA

*FIIT JEE

*RESONANCE

*ANY OTHER





WHICH IS THE BEST AMONG THESE???

Correspondence Course :

* BRILLIANT TUTORIALS

* NARAYANA

*FIIT JEE

*RESONANCE

*ANY OTHER



WHICH IS THE BEST AMONG THESE???

Let 'F' be the first term of the A.P. and 'L' be the last term of the A.P.

Given:

a  =  ( p / 2 )( F + L )

b  =  ( q / 2 )( F + L )

c  =  ( r / 2 )( F + L ) 

Therefore:

( a / p )( q - r )  +  ( b / q )( r - p )  +  ( c / r )( p - q )   =   ( 1 / 2 )( F + L )  [  {q - r} + {r - p} + {p - q}  ]

                                                                                       =   0 

Question 2

If we consider the +ive x - axis, +ive y - axis and +ive z - axis, then  X  X  Y =  Z ie, X  X  Y is along +ive z - axis

Now consider the vector A pointing vertically upwards( along +ive x - axis ) and B pointing north ( along +ive y - axis ), then A X B is along the +ive z - axis, that is, along the west.  

Question 1

Dimensionless quantities may have units. For example : Angle is a dimensionless quantity, but one of its unit is "radian".

Let the G.P. be :       a , ar , ar² , ar³ , ............ ar^{2n - 1}       where 'r' is the common ratio

Given :   S1  =  a + ar² + ar⁴ + ........... + ar^{2n - 2}   =  a( (r² )ⁿ  -  1 ) / r² - 1

               S2  =  ar + ar³ + ar⁵ + ............. + ar^{2n - 1}   =  ar ( (r²)ⁿ  -  1 ) / r² - 1

Therefore : S2 / S1  =  r

Please get me some ebooks including

I.E.Irodov's....

Fundamentals of Physics( HALLIDAY, RESNICK, WALKER )

Organic Chemistry ( Morrison & Boyd )

Other good books

log 2 , log (2^x - 1) , log (2^x + 3) are in A.P.

So:   2log (2^x - 1)  =  log 2 + log (2^x + 3)

          log (2^x - 1)²  =  log 2.(2^x + 3)

          (2^x - 1)²  =  2.(2^x + 3)

          (2^x)²  -  2.2^x  + 1   =   2.2^x  +  6

           (2^x)²  -  4.2^x  -  5   =   0

This is a quadratic equation in 2^x. Solving we get, 2^x  =  5    OR   2^x  =  -1.

If 2^x  =  -1, then log( 2^x - 1) will become log ( -2 ) which is not possible. So, 2^x  =  5. Therefore, x  =  log 5 / log 2  =  log ₂ 5

Date : 12 - 5 - 2008

Day : Monday

QUESTION OF THE DAY

Let  f : N * N N  be a function such that 

• f ( 1 , 1 )   =   2
  
  


• f ( m + 1 , n )   =   f ( m , n )  +  m
  
  


• f ( m , n + 1 )   =   f ( m , n )  -  n
  
  

for all m, n    N. If  f ( p , q )  =  2001, then which of the following is(are) true?

( A )  ( p , q )  =  ( 2000 , 1999 )

( B )  ( p , q )  =  ( 1001 , 999 )

( C )  ( p , q )  =  ( 1001 , 1999 )

( D )  ( p , q )  =  ( 2000 , 999 )

I KNOW THE ANSWER. I AM JUST TRYING TO PUT DOWN A MAXIMUM NUMBER OF GOOD QUESTIONS TO HELP YOU ALL TO SHARPEN YOUR BRAIN.



NOW TRY TO GET THE CORRECT ANSWER TO THIS QUESTION.

THE  QUESTION  HAS  BEEN  ANSWERED  WITHOUT  USING  ANY  SPECIAL  METHODS.  I  JUST  CIRCULATED  THROUGH  THE  COMMON  TYPE  OF  FUNCTIONS:

1.  POLYNOMIAL

2.  TRIGONOMETRIC

3.  LOGARITHMIC

4.  EXPONENTIAL        etc.......  SO THAT THE GIVEN CONDITIONS ARE SATISFIED............

THEREFORE

f (x)   =   - [ log ( x - a + 1 ) ] ^{2n + m}   +   b       where 'm' is any even natural number.

f (x)   =   - ( x - a )^{2n + m}   +  b      where 'm' is any even natural number.