ISI 2013 ME - I Answer Key

[Sinistral]

i think this ques was solved in this forum a few weeks back:

take f(x)=exp(x+2)
note that it satisfies all the 3 given conditions.
integrate to get option c

[ArpitGLBTK]

For Ques 25, u need to find that f(x0 which satisfies all the three conditions:
1. f''(x)/f'(x)=1
2. f(0) =e^2
3. f(1) = e^3

U can derive the function f(x) from these.

(1) implies that f(x) might be such a function whose first order and second order derviative are same making its division equal to one. In Differentiation, e^x is such a function whose both order derivatives are the same.
If we put f(x) = e^(x+2)
it satisfies (2) => f(0) = e^(0+2) = e^2
               (3) => f(1) = e^(1+2) = e^3
and its satisfies (1) also... f'(x) = e^(x+2)
                                    f''(x) = e^(x+2)
Finally u get your f(x) = e^(x+2)
Integrating it => {e^(x+2)} from -2 to 2
=> e^(2+2)  -  e^(-2+2)
=> e^4  -  e^0
(we know e^0 = 1)
Ans. (c) e^4 - 1

[dasyam]

can anybody please explain how to solve Q.26 the objective function problem

[Ridhika]

How many maths questions does one need to look at getting right to crack the exam? About 23 right?

[Dheeraj]

Q.26 is a simple Linear programming Problem..what you need to do is just plot the constraints on the X-Y plane s.t. x, y >= 0. Now shade the region that satisfy all of the constraints and find the corner points of that region. In this case these corner points turn out to be (0,2), (0,4), (3,0), (5,0), (1,5) and (6,3).

   Now we put these points in Z= 5x + 7y

and it turns out to be that for (0,2), Z is minimum and is equal to 14, which is the answer.

[neha 1]

pls explain ques 28 and 18

[manisha]

can someone please explain Q-3,4 and 18

[munjal7]

Hi,
In ques no 9
lets say |x|=z
then z^3+az^2+bz+c=0
minimum real root=1 of the above equation as complex root always appear in conjugate.
i.e. Z=alpha(lets say) be the real root then x=+ alpha and x= - alpha
2 real roots minimum
Can you please tell what's wrong in this approach?

Thanks

[riyaf]

can someone explain ques no 2 please ? I am still doubtful about the exact procedure to be used.

[sam92]

In q15 I have tried to integrate first w.r.t.to y.and then X but I am not getting a constant but a fn of X. Can someone tell me where I am gng wrong?

[bhavya jain]

why will the answer to 4th question be b) 1/n+1. It shud be c) n/n+1. Solving both p(x=0)&p(x=1), we'll get c only. Someone plz check. Amir sir plz check..

[duck]

Hi Bhavya.. :)

you'll get the following equation:
1-p-np=0
after solving this.. p = 1/n+1
So, option(b)

[Ridhika]

@ Sam - I am having the same issue.. :(

@ Manisha

q3--> a1.a2..an=1 so all ai = 1
so the function is 2^n

q4) nC0 (1-p)^n = nC1 . p. (1-p)^(n-1)
=> 1-p = np(1-p)

solve this and u get ans (b)

Can somebody please please explain how to go about 24, 16, 28 and 9 ( I do not understand the explanation given in the post previously for 28 and 9 .. what is the logic for solving?)

[Ridhika]

@ Sinistral.. in your explanation for 2..

n(n+1)(2n+1)       1.2 +2.3 +3.4 + ... n(n+1)        (n+1)(n+2)(2n+3) -6 
-------------  <  -------------------------   <   ---------------------
      6n^3                      n^3                                     6n^3      


ratio of coefficients of highest order of n in the numerator and denominator gives the limit of the fraction as n tends to infinity.
which is nothing but 2/6 = 1/3 for both the LHS & RHS terms.
hence option c

What is the condition for using this rule (the part I have italicized?) Do we have to always express as an inequality on both sides to use this?

[Ridhika]

Also where did the -6 (in bold) appear from?

[Tanushree]

Can some one help me with detailed answers for

Q1. 10 outcomes of a random variable were recorded. The sample mean is 0 and sample variance is 4. It is discovered that two outcomes were recorded incorrectly: one outcome was -5 instead of -6 and another was 11 instead of 12. What is correct variance?

a) 4            b) 3.6              c) 7.4                 d) 5.2

Q2. Amit has a box with 6 red and 3 green balls. Amita has a box with 4 red and 5 green balls. Amit randomly draw a ball and put it into Amita's box and Amita too randomly pics up a ball from her box. What 's the probability that the ball drawn by the two were of diff colors.

a) 1/3         b) 2/15       c) 4/15          d) 7/15

Q3. A traffic light on the way to the University is red 40% of the time. What's the probability of getting red  light (i) two days in a row, (ii) two out if three days.
 
a) 0.16 & 0.20     b) 0.16 & 0.29     c) 0.24 & 0.29      d) none of the above

Which book should I go for cost functions, production function and market sums?

Please help me.

Guys how to solve ques 7 of this paper. Please help

[dhruv]

@mittar.chardikala

Take (x + 1/x) = t. After squaring it and proper substitution you will get,

2t^2 - 3t - 5 = 0

after solving,

t = 2.5, -1

since min(x + 1/x) = 2, t = -1 not possible

therefore, x = 2 or 1/2,

hence, their product = 1

[Jim_Moriarity]

Economics 6 & 7.
PLease have a look.


My answer in 6 Employment decreases , Output same for both.

For 7 I FEEL its true. But how?

Please let me know.

[onionknight]

7.) Investment goods are supplied from imports which means savings are 0. Therefore marginal propensity to consume is >=1 otherwise some amount will be saved and invested. Therefore, multiplier will be non positive.

Could you please explain how you did the 6th question?