Numbers and Identities

Q1.  If | 2- x/3 | ≤ 1/3
And  | 3- x/y | ≤ 1/6  where x and y are positive real numbers, then which of the following can be the possible values of x^2 / (2x – y) ?
a. √ 3 – 1
b. √2
c. 1/√2
d. √3 /2
e. √(3/2)

Q2. Assume r, s and t be three distinct integers between 0 and 10.
If 1/r + 1/s – 3/t = 2/5r,  then find the number of distinct values of ( r + s – t) ?
a. 1         b. 2         c. 3           d. 4            e. 5

Q3. The largest integer that always divides n5 – 5n3 + 4n for all natural n is
a. 40        b. 60           c. 24           d. 120             e. 48

Q4. If x + y + z = 0, then find the value of  (x2 + xy + y2 )/(y2 + yz + z2) is
a. 1                  b. –1           c. 0              d. 2               e. 3


Q4. If x + y + z = 0, then

Q4. If x + y + z = 0, then find the value of  (x2 + xy + y2 )/(y2 + yz + z2) is
a. 1                  b. –1           c. 0              d. 2               e. 3

Soln.   Take d numerator:
                                   x^2+y^2 + xy
                                   =(x+y)^2 - xy
                                   =z^2 + y^2 + yz[ frm condn xy=-(y^2+z^2), & x+y=-z]

     So,    (x2 + xy + y2 )/(y2 + yz + z2)=1
    
     OPTION (a) is correct.....

Giv ur best to d world.
Nd d best will cm back to u....

Regards,
Dipanjan.....

__________________

n/a

Q3. The largest integer that

Q3. The largest integer that always divides n5 – 5n3 + 4n for all natural n is
a. 40        b. 60           c. 24           d. 120             e. 48

Soln.    Doin factorisation of n5 – 5n3 + 4n = n(n+2)(n-2)(n+1)(n-1)

           To get d largest integer put n=3    
           So dt integer is 3 x 5 x 1 x 4 x 2=120......
 Option (d) is correct....

Giv ur best to d world.
Nd d best will cm back to u......

Regards,
Dipanjan........
 

__________________

n/a

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