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
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........
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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
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