Engineering Entrance Questions:Punch of the Week(23-Mar-10)

by Deepa Mittal

What is "Punch Of The Week"?

Every week Learnhub's team will post one question each on Physics, Chemistry and Mathematics of the IIT-JEE, AIEEE and BITSAT Test Preparation
Members can post their answers along with explanations for the next one week.
After one week, Learnhub's team will post the official answer along with the explanation.Besides answering the previous week's questions, Learnhub's Team will come up with the next set of questions for that week as well.

What are the rules of "Punch Of The Week"?

Every user must refrain from posting sarcastic comments on the answers posted by others.

Once the Learnhub's team posts the official answer along with the explanation, no comments must be made regarding those questions. In case of further clarification please send a personal message to the respective team member

If you think that there is something wrong with the explanation of the Learnhub's Team, which seldom happens, please send a personal message to the respective team member informing him/her the same. Posting the same here will not be considered and will be deleted

Please bear in mind that only Learnhub's Team members have the privilege of posting questions here. Questions posted by other members will not be entertained and hence will be deleted immediately.

"Punch Of The Week" Team Members

This Week's Punches

Physics

Two particles of mass m each are tied at the ends of the light of length 2a. The whole system is kept on the frictionless horizontal surface with strings held tight to tight so that each mass is at the distance 'a' from the center p (as shown figure). Now the mid point of the same strings is pulled vertically upwords with a small but constant force F. As a result, the particles moves towards each other on the surface. the magnitude of accelerations, when the seprations between them becomes 2x is.

(A) $\cfrac{F}{2m} \cfrac{a}{\sqrt{a^2 - x^2}}$

(B) $\cfrac{F}{2m} \cfrac{x}{\sqrt{a^2 - x^2}}$

('c) $\cfrac{F}{2m} \cfrac{x}{a}$

(D) $\cfrac{F}{2m}\cfrac{\sqrt{a^2 - x^2}}{x}$

Chemistry

When ammonia is added to the solutions, $p^{H}$ is raised to 11. Which half cell reactions is affected by $p^{H}$ and by how much?

(A) $E_{oxd}$ will increase by the factor of 0.65 from $E_{0xd} ^{0}$

(B) $E_{oxd}$ will decrease by the factor of 0.65 from $E_{0xd} ^{0}$

© $E_{red}$ will increase by the factor of 0.65 from $E_{red} ^{0}$

(D) $E_{red}$ will decrease by the factor of 0.65 from $E_{red} ^{0}$

Math

Let $g(x) = \cfrac{(x-1)^n}{\log \cos^m (x-1)}$ ; 0 < x < 2< , m and n integers, $m \not = 0$ , n >2 and p left hand derivative of |x - 1| at x =
1. If $\underset{x\rightarrow 1}{lim}g(x) = p$ , then