jnu 2012 doubts

[maahi]

1. if the population of a country increases by 20% in 10 yrs , the annual exponential growth rate of population is
I did : 120=100(1+r)^10. I m getting more than 2% ans says less than 2 %
27. A1 A2 A3   are independent events . d prob. Of event Ai  is Pi , i=1,2,3 . the prob. Of d event union (1 to 3 ) Ai  is ?

33. the names of 7 students when ranked in ascending order of their weights are A,B,C,D,E,F,G. A’s wt is 45 kg and g’s wt is 75 kg .
a>if no pair of students has d same weight ,then d median weight of d grp is ?
b> if 3 students among B,C,D,E,F have d same weight and remaining 2 have different weights , then d median weight of d grp of seven students is ?
c>suppose d name of F is deleted from d list . Then , if d diff. in weights b/w any two consecutively ranked students on d list is a constant positive no. , then d median weight is equal to ??
63) let f be a real valued function defined on the set of all real no. greater than or equal to zero and less than or equal to 1 . suppose f attains a max value in its domain at x* . which of d following must be true ? 1>f’(x*)=0  2>f’’(x*) <0   3> x*=0 or x*=1 or  f’(x*)=0 4> none
Q78 .,79 ,91
93)the function f(x) approaches infinity as x approaches infinity and d limit of d derivative of d function f(x) is 0 as as x approaches infinity. what is d limit of f(x)/x  as x approaches infinity?

[Akshay Jain]

sol 1. annual exponential growth is same as the compound annual growth rate.
solve it by taking an example of simple and compound interest....
if u have principal amt of 100 rs and if you add simple interest of 2% annually upto 10 years then u get total of 120 rs..total interest earned is 20% of principal..
now if u take compound annual interest rate of 2 % on the same principle of 100 rs for ten years then u vil get a value greater then 120..the total interest will be greater than 20 %..
so to earn a total interest of 20 %, the compound annual interest rate shud be less den 2%.
you can apply dis logic to dis question of population growth

[Akshay Jain]

sol 27..all the events are independent so prob of intersection of events is P(A1).P(A2)P(A3).
now prob that all the none of them occurs is (1-P(A1)).(1-P(A2)).(1-P(A3))
prob of union of all events means that atleast 1 of them occurs which is eqaul to 1-P(none of them occurs)
=1-(1-P(A1)).(1-P(A2)).(1-P(A3))

[Sinistral]

1) the way u solved will give the ans < 2%

63) the function can be max either at its boundary or at the point where its first derivative = 0. (as the derivative of the func will not be necessarily 0 at its boundary. we check for maxima or minima at extremum by putting in the values in the func)
      So option (c)

93) use L hospital rule Lim f(x)/x = lim f ' (x)/1 = 0 (in both case as x --> infinity)

[laracroft]

Hey sinistral
I couldn't understand how you figured out the solution to Q. 63??
Can you please explain it in detail ??

[maahi]

thanks sinistral  and jainakshay :-)
i did very silly  mistakes :(

[Sinistral]

as u can see the value of f'(x)is not zero at extremum (ie at x=0,1) yet the value of f(x) is max at x=0. please note that f'(x) = 0 somewhere in b/w 0 and 1 yet it is not the ultimate maxima in the given domain.

[laracroft]

Thanks a lot ! :)

[vandita24x7]

Only one of the following 3 statements regarding the no. of balls in an urn is true:
a)There are atleast 100 balls in the urn
b)There are less than 100 balls in the urn
c)There is at least one ball in the urn

Q. How many balls are there in the urn?
a)1
b)100
c)101
d)0

How to utilize  our think tank in this question?? pls Help!

[Amit Goyal]

Only one of the following 3 statements regarding the no. of balls in an urn is true:
1)There are atleast 100 balls in the urn
2)There are less than 100 balls in the urn
3)There is at least one ball in the urn

Q. How many balls are there in the urn?
a)1
b)100
c)101
d)0

A. One way to do the above problem is do the following:
Given that only one of the three statements is true, you just check each option for how many of the statements are true assuming it to be correct.
If number of balls in urn is 1, then both statements 2) and 3) are correct. Thus option a) 1 is ruled out.
If number of balls in urn is 100, then both statements 1) and 3) are correct. Thus option b) 100 is ruled out.
If number of balls in urn is 101, then both statements 1) and 3) are correct. Thus option b) 101 is ruled out.
If number of balls in urn is 0, then only statement 2) is correct. Thus option d) 0 is the right answer.

[vandita24x7]

Thank u so much sir!
It is so difficult to decide when to go by options and when not to... :(

[Kuldeep]

Heyy... Can you please guide me on the jnu 2012 questions 34-36.... Please...

[maahi]

ABCDEG  6 students  a wt 45 g's 75
diff b.w any 2 cons. pairs is say x
45, 45+x , 45=2x........45=5x

45+5x is wt of G which is given .. 75 equate both get value of x and get all positive values and find d median and then go by d options .

[Kuldeep]

Thaanx maahi gt it....!!!!