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1. (d)
2. (d)
3. (b)
4. (d)
5. (c)
6. (c)
7. (d)
8. (a)
9. (c)
10. (b)
11. (d)
12. (c)
13. (a)
14. (d)
15. (c)
16. (a)
17. (d)
18. (b)
19. (d)
20. (b)
21. (c)
22. (c)
23. (a)
24. (a)
25. (b)
26. (a)
27. (b)
28. (c)
29. (c)
30. (b)


Hi. Can you please help me with Q.7. I take log and then try to equate using Lopital's rule? What am I doing wrong? Maybe I cannot apply the rule when f(x) is not equal to 0, while g(x) = 0. However, I get stuck after that. A little help please?
Can you also discuss Q.19. What two functions do you subtract? Is it {p,r} and {r,P}? Thank you in advance.


For Q7, you can take an example and do it. For eg, f(x)=3x^3 satisfies the given conditions and once you apply ln, you get 0/0 form and applying Lhospital's will be very simple now.


can u pls xplain why the answer of the question no 25 is 65?? it should be 55 i think


hey can u post 2011 isi sample paper here?? or any link to it ?


can some one plz explain questions 7,11, 17 and 18.


q7  take f(x) = 3x^3 (or any function that satisfies the equation) and solve
q11. because the terms are in AP x2 = x1 +d ; x3= x1 + 2d and so on till xn = x1 +(n1)d; No subsitute this ino the equation and solve.. the answer comes different from the 3 equations that are witten.. so ans is (d)
q18) It is clear by looking that the equation will be satisfied at (0,1). So we know x+y will be 1 at least. So we can eleminate options a and c immediately.
Now if we can show x+y = 2 (d) is our answer else (b) must be answer.
if x+y = 2; then to satisfy the eq of the circle, we need x^2 + (2x)^2 = 1 => we find this has no real solution. So (b) must be the answer.
Hope this helps.
Somebody, please help with questions 16 and 17? and 21, 24 and 25
In q1 I get 6^1/2 .. which means option b.. how is it d?


Someone pls help me with quest 17
MA Economics
DSE
201416


Hi Sonia, As f(x)= px + qx^2, thus f(y)= py + qy^2. Replace it in integral. Hope it will work fine!
Regards, Aditya
"Woh mara papad wale ko!"


Radhika,
25. log x*x1+log x*x2+ log x/x1+log x/x2
Now we rearrange terms as log x*x1+log x/x1+log x*x2+log x/x2
Let we focus on first two terms log x*x1+log x/x1
log x*x1+log x/x1=log x+ log x1+log x log x1=log x1+ log x+log x1 log x, because of absolute value.
Now,
log x1+ log x+log x1 log x>=log x1+ log x+log x1 log x=log x1+ log x1=2 log x1=2log x1
Similarly,
log x*x2+log x/x2>=2log x2
So, log x*x1+log x/x1+log x*x2+log x/x2>=2log x1+2log x2>=2log x1+log x2
So, log x*x1+log x*x2+ log x/x1+log x/x2=log x1+log x2 only in case when each term is zero. But, that can happen only when (x,x1,x2)=(1,1,1)
Will you please help me with 22 ?


Hi Neha 1,
Idea is to use det(A^n) = (det(A))^n. If there's any doubt please let me know.
Aditya
"Woh mara papad wale ko!"


Pls help me with quest 19..


Hi Ron,
For an onto function, every element in b in B must have an element a in A such that f(a)=b. condition (i) thus total # of functions possible= 2^4=16. this includes those functions as well where one or more elements from set B are excluded
say for all a in A, f(a)=p or f(a)=r, thus violating condition (i) for onto fn.
thus we need to take of these 2 cases. thus total # of onto fns = 162=14.
"Woh mara papad wale ko!"


can someone please explain Q3 and Q6


Thanks a lot Singham.
For 22, I solved by elimination of options:
a) if 2A is an ineger => A is an integer . If A+B is an integer and we know A is an integer, then B must also be an ineger. In this case for f(x) to be an integer, C must be an integer. However that is not true.
b) Now if C is an integer we need x(Ax + B) [let this funtion be g] to be an integer as well. x is an integer. so for g to be an integer, Ax +B must be an integer. we know 2A is not an integer, therefore A is not an integer. if A+B is an integer, it is not necessary for Ax+B to be an integer. Therfeore this is not sufficient.
c) If 2A is an integer => A is an integer. if A is an integer and A=B in an integer, B must also be an integer. And finally C must be an integer. And if A , B , C are all integers, f(x) must be an integer. Therefore this condition is sufficient.
There may be a more amthematical way of approaching this, but Im not sure how.. this seems to make sense though and it was quick.. ;)


Aditya I dont follow what u mean by this? please help!
Someone please help with 16, 20 and 25 !?! Please please!!


For 20th, the coefficient of rth term in expansion of (1+x)^n is given by nC(r1)......now substitute the values.... Plz help me wid the concept used in solving q24

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