Burnet institute Interview Questions, Process, and Tips

(x**2 – 6* x + 5) = (x-1)*(x-5)
(x**2 + 2 * x + 1) = (x + 1) * (x+1) = (x+1)**2
For what x is (x-1)*(x-5)/( (x+1)**2) a minimum?
One way to answer this question is by using calculus.
Take the derivative, and set to zero.
Since this is a fraction of polynomials, and a fraction is
zero only if it’s numerator is zero, we need calculate only
the numerator of the derivative and set it to zero.
The numerator of the
Derivative of (x-1)*(x-5)/( (x+1)**2) is
( (x-1) + (x-5) ) ( x+1)**2 – (x-1)(x-5)( 2 (x+1) )
= (2 x – 6) (x+1)**2 – (2) (x-1)(x-5) (x+1)
= 0
Divide through by 2 (x+1)
(x-3)(x+1) – (x-1)(x-5) = 0
(x**2 – 2 x – 3 ) – (x**2 – 6 x + 5) = 0
x**2 – x**2 – 2 x + 6 x – 3 – 5 = 0
4 x – 8 = 0
x = 2
Plugging in x = 2 into the original
(x**2-6*x+5)/(x**2+2*x+1)
gives us (2**2 – 6 * 2 + 5)/(2**2 + 2*2 + 1)
= (4 – 12 + 5) / (4 + 4 + 1) = -3/9 = -1/3
Least value is -1/3

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I need a answers from hakuna matata questions

(x-2)^3==x^3-6x^2+12x-8
(x-2)^3==(2^(2/3)+2^(1/3))^3
therefore,by solving
Ans: x^3-6x^2+x== -8-5*2^(2/3)-5*2^(1/3)

xy+2y-x=6
xy+2y-x-2=6-2
y(x+2)-1(x+2)=4
(y-1)(x+2)=4
so c is 4

I would design a voice integrated clock that reads out the time aloud whenever people ask for time

B. 32%

( a ) 10 metres

25

Let the age of the man be x
Then age of his son becomes (x−24)

2 years later from now,

Age of man will be = x+2
and age of his son will be =(x−24+2)=x−22

According to question,

2(x−22)=x+2

i.e., 2x−44=x+2

i.e., x=46

Therefore ,
Present age of man=46 years
And present age of his son =46−24=22 years

Sachin is 14 years old whereas Rahu is 18 years old.

21

Relative velocity of trains = 49kmph -25 kmph = 24kmph
=6.67m/s
Time taken to cross the first train = 10 sec
Length of the second train = Relative Velocity * Time taken
to cross the first Train = 6.67 *10 = 66.7 metres