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Engineering Entrance Questions: Punch of the Week(06-Feb-10)

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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"?
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Photo 21678 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
Learnhub's Punch
This Week's Punches

Physics

A spherical ball of radius R, is floating in liquid with the half of its volume submerged in liquid. Now the ball is displaced vertically by small distance inside the liquid. Find the frequency of oscillation of ball.

(A) \cfrac{1}{4} \pi [(3g/2R)^{\frac{1}{2}}]

(B) \cfrac{1}{2} \pi [(3g/4R)^{\frac{1}{2}}]

(C) \cfrac{1}{2} \pi [(3g/2R)]

(D) \cfrac{1}{2} \pi [(3g/2R)^{\frac{1}{2}}]

Chemistry

In the process of extraction of gold,
Roasted gold ore + CN^{-} + H_2O \overset{C_2}{\longrightarrow}[X] + OH^-
[x] + Zn \longrightarrow [y] + Au
Identify the complexs [x] and [y]

(A)X = [Au(CN)_2]^-, Y = [Zn(CN)_4]^{2-}

(B)X = [Au(CN)_4]^{3-}, Y = [Zn(CN)_4]^{2-}

(C)X = [Au(CN)_2]^-, Y = [Zn(CN)_6]^{4-}

(D)X = [Au(CN)_4]^-, Y = [Zn(CN)_4]^{2-}

Math

Tangent drawn to ellipse \cfrac{x^2}{27} + y^2 = 1 at (3\sqrt{3} \cos \theta, \sin \theta)(where \theta \in (0, \pi/2)). Then value of \theta such that sum of intercepts on axes made by this tangent is minimum, is

(A) \pi/3
(B) \pi/6

(C) \pi/8

(D) \pi/4

Click here for Previous week's Punch of the Week

Posted on 12-Feb-10

So, folks here are the correct answers D

Physics

Solution:

Restoring force = = \pi R^2 xpg (for small x)
\Rightarrow - m\cfrac{d^2 x}{dt^2} = \pi R^2 xpg
\cfrac{d^2 x}{dt^2} = - \cfrac{3}{2} \cfrac{g}{R} x.
as (\cfrac{4}{3} \cfrac{\pi R^3}{2} pg = mg)
\therefore Motion is SHM
\Rightarrow \omega ^2 = \cfrac{3}{2} \cfrac{g}{R}
\Rightarrow f = \cfrac{1}{2\pi} \sqrt{\cfrac{3g}{2\pi}}



Chemistry
The correct answer is A.

Solution:
2Au + 4 CN^- + H_20 + \cfrac{1}{2} + O_2 \rightarrow2[Au(CN)_2]^- + 2OH^-
2[Au(CN)_2]^- + Zn \rightarrow [zn(CN)_4]^{2-} + 2Au

Math
The correct answer is B.

Solution:

\cfrac{x \cos \theta}{3\sqrt{3}} + y \sin \theta = 1. sum of intercepts 3\sqrt{3} \sec \theta +cosec \operatorname{\theta} = f(\theta) (say)
f'(\theta) = \cfrac{3\sqrt{3} \sin ^3 \theta - \cos^3 \theta}{\sin^2 \cos ^2 \theta} \Rightarrow At \theta = \pi/6 , f(\theta) is minimum.

Click here for Next week's Punch of the Week

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  1. akio saidSun, 07 Feb 2010 15:04:10 -0000 ( Link )

    Answer to the chemistry question is (D).

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  2. angadyuvraj saidWed, 10 Feb 2010 14:45:32 -0000 ( Link )

    Answer to chem question is (A)….confirmed from NCERT

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  3. rahulksinha saidThu, 11 Feb 2010 12:47:56 -0000 ( Link )

    answer to maths question is ©.
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  4. rahulksinha saidThu, 11 Feb 2010 13:47:28 -0000 ( Link )

    answer to physics is D .

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  5. rahulksinha saidThu, 11 Feb 2010 14:01:11 -0000 ( Link )

    answer to chemistry is A.

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  6. varjunnagarjun saidSat, 13 Feb 2010 16:14:37 -0000 ( Link )

    the answer to chemistry is option A
    8KCN + 4Au + 2H2O + O2 —→ 4K[Au(CN)2]

    + 4KOH

    2K[Au(CN)2] + Zn -—→ K2[Zn(CN)4] + 2Au

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