dse 2009

[Abhirupa Debroy]

1. Integrate e^(-x^2) [e to the power -x square by 2] from 1.96 to infinity.

2. Suppose P(x) and Q(x) are polynomials of degree m and k, respectively, where both m and k are less than or equal to the positive integer n. Suppose the equation P(x)=Q(x) has at least (n+1) distinct solutions. Which of the following choices best describe what this situation implies?
 a. m=k=n
 b. m=k<n
 c. P(x) and Q(x) are identical
 d. P(x) and Q(x) are linear

please explain me as to how to proceed in such kinds of questions..

[Shruti]

Hey! were u able to do Q no. 42? If possible explain ...

[Amit Goyal]

For problem 1, use the normal density and you will get the required result. For problem 2, P(x)=Q(x) has at most max{m,k} solutions if the polynomials are distinct. Since max{m,k}<n+1. n+1 distinct solutions to the polynomials implies that the polynomials are same.

[Khagesh]

umm i didnt get d explanation for q1, plz elborate sir

[ritu]

dse 2007
smbdy pls tell hw to di question 37 nd 38 of dse 2007 ...
khagesh for 1st question ...use the fact that pdf of std normsl curve is 1/root2 pi.e^-x^2/2
pls reply...

[ritu]

under a standard normal curve area btwn 1.96 nd infinity is 0.025...
nw use the above equatn....

[Khagesh]

isnt it supposed to be normal integration ??? O.o

[ritu]

actually this doesnt require integration..its just abt substituting values...just think abt it...

[Ayushya Kaul]

Sir, could you show the calculation for your solution of the first problem?