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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.
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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.

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6 Comments

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

    Answer to the chemistry question is (D).

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

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

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

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

    answer to physics is D .

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  5. rahulksinha said – Thu, 11 Feb 2010 14:01:11 -0000 ( Link )

    answer to chemistry is A.

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  6. varjunnagarjun said – Sat, 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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