official quant thread for cat08

[sidcool007]

Originally Posted by linksuresh

sid, can u explain how would you plot the graph for this expression ?

not sure if i would be able to explain it you
Giving it a try though.




First we plot abs(x+1).at x=-1 , it will be zero & we determine the value by substituting x=-1 which gives 34.
Similarly for other two expressions we get 13 & 11 respectively.

Now to determine when the above eqn gives 20 for x.

The graph increases @ 9x for every 1 increase in x.
so 11 + 9 gives 20 , so one value comes as 5 ( 4+1 )

And 20 will again come b.w x=-1 & x=2.
For every 21 decrease , there's an increase of 3 in x.
so for 14 decrease there will be a 2 in increase in x, so x =1.

I hope i am able to explain it

[Varun Khullar]

Originally Posted by nimisha_2009

9


i'm getting the ans as 5/9+1 whish is not given..



10



its given that iii is correct. how is it correct?

y = log (x+ root(x^2+1))

see nimisha
e^y = x+root (x^2+1)
e^-y = -x+ root (x^2+1)
so three is fine i think

[ganesh99]

Originally Posted by nimisha_2009

9
10



its given that iii is correct. how is it correct?

All the three statements are correct.
log(x+root(x^2+1) = sinh^-1(x) whose graph passes through origin,domain is R and which is a odd function
puys wats ur take on it

[vineet.nitd]

Originally Posted by nimisha_2009

9


i'm getting the ans as 5/9+1 whish is not given..

Nimisha, the vali values of x will be 1 and 5 and hence the sum would be 6. The value that you have got 5/9 comes when you take the domain x<-1 which is not valid.

10



its given that iii is correct. how is it correct?

All the 3 statements are true

F(-x)=log((x^2+1)-x)= log(1/x+(x^2+1))=-log(x+(x^2+1))=-F(x)

[vineet.nitd]

Now solve this DS question:

Find the value of x/y.

Statement 1: X is the smallest even natural number and y is the highest two digit prime number.

Statement 2: 2y=97x

[bishweshwar1234]

Originally Posted by linksuresh

i think the ans is option .. b)3 ?
please confirm....

I think ans is 1. eg : 1 2 4 8 in proportion.

[bishweshwar1234]

Originally Posted by selebratinglife

Subtract the first term from the second and second from third and so on till they all become equal..

In this case 1,0,3,10,21,36,55
Now After the first round we get the series as -1,3,7,11,15,19
After second round we get 4,4,4,4,4..
Since we got this after 2 rounds, its a second degree equation. If after three rounds, its a third degree and so on.
Now consider the equation as ax^2+bx+c..Substitute x=1,2,3 and solve to get a,b and c.

Can you please go few steps further in equating this equation to which numbers when 1,2,3 are substitued with 1,2,3.

[rahulshaitan]

Originally Posted by nimisha_2009

9


i'm getting the ans as 5/9+1 whish is not given..

the answer for this question is 6
the only values for which the expression is satisfied is x=1,5.

[rahulshaitan]

Originally Posted by nimisha_2009

9

10



its given that iii is correct. how is it correct?

for this question f(x)= log[x+sqrt(x^2+1)]
for option 1

x can take any real value as for positive integers it will always hold good and for negative integers also it will hold good as sqrt(x^2+1) > x for all negative integers.

for option 2

for x=1, we get log(1)=0.therefore this option also holds good.

for option 3

now on putting x=-x, we get
f(-x) = log{ (-x) + sqrt[(-x)^2+1]}
or f(-x)= log[ (-x) +sqrt(x^2+1)]

now take (-x)+sqrt(x^2+1)
on rationalizing the numerator we get

(-x)+sqrt(x^2+1)*[x+sqrt(x^2+1)}/[x+sqrt(x^2+1)]

on solving this we get
1/[[x+sqrt(x^2+1)]

now f(-x)= log[ (-x) +sqrt(x^2+1)]

=log{1/[[x+sqrt(x^2+1)] }
=log[x+sqrt(x^2+1)]^-1

= - log[x+sqrt(x^2+1)]

thus all options are correct.
please check the answers again and revert if i m wrong.

regards

[rahulshaitan]

Originally Posted by vineet.nitd

Now solve this DS question:

Find the value of x/y.

Statement 1: X is the smallest even natural number and y is the highest two digit prime number.

Statement 2: 2y=97x

for this both the options are independently sufficient.
please confirm the answer