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question_answer1) The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept inside the container is 1: 4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
2: 5
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B)
1 : 4
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C)
1 : 64
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D)
1 : 8
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question_answer2) Correct set up to verify Ohm?s law is :
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
done
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B)
done
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C)
done
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D)
done
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question_answer3) Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angel of contact \[\theta \]and the height h up to which water rises change. These changes are:
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[\theta \]increases and h also increases
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B)
\[\theta \]decreases and h also decreases
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C)
\[\theta \]increases and h decreases
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D)
\[\theta \]decreases and h increases
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question_answer4) A particle of mass 2 kg is moving such hat at time t, its position, in meter, is given by \[\overset{\to }{\mathop{\operatorname{r}}}\,(\operatorname{t})=5\hat{i}-2{{\operatorname{t}}^{2}}\hat{j}.\]The angular momentum of the particle at \[\operatorname{t}=2s\] about the origin in kg \[{{\operatorname{m}}^{-2}}\]\[{{\operatorname{s}}^{-2}}\] is :
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[-80\hat{k}\]
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B)
\[\left( 10\hat{i}-16\hat{j} \right)\]
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C)
\[-40\hat{k}\]
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D)
\[40\hat{k}\]
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question_answer5) Which of the following statement is Not correct?
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
Ground wave signals are more stable than the sky wave signals.
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B)
The critical frequency of an ionospheric layer is the highest frequency that will be reflected back by the layer when it is vertically incident.
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C)
Electromagnetic waves of frequencies higher than about 30 MHz cannot penetrate the ionosphere.
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D)
Sky wave signals in the broadcast frequency range are stronger at night than in the day time.
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question_answer6) Electrons are accelerated through a potentialdifference V and protons are acceleratedthrough a potential difference 4 V. The de-Broglie wavelengths are \[{{\lambda }_{e}}\] and \[{{\lambda }_{\operatorname{p}}}\] for electrons and protons respectively. The ratio of \[\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}\] is given by: (given\[{{\operatorname{m}}_{e}}\]is mass of electron and\[{{\operatorname{m}}_{\operatorname{p}}}\]is mass of proton)
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{\operatorname{p}}}}{{{\operatorname{m}}_{\operatorname{e}}}}}\]
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B)
\[\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}\]
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C)
\[\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=\frac{1}{2}\sqrt{\frac{{{\operatorname{m}}_{e}}}{{{\operatorname{m}}_{\operatorname{P}}}}}\]
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D)
\[\frac{{{\lambda }_{e}}}{{{\lambda }_{\operatorname{P}}}}=2\sqrt{\frac{{{\operatorname{m}}_{\operatorname{P}}}}{{{\operatorname{m}}_{e}}}}\]
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question_answer7)
A thin tube sealed at both is 100 cm long. Itlies horizontally, the middle 20 cm contacting mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? 
(Given: cross section of the tube can be assumed to be uniform)
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
2.95 cm
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B)
5.18 cm
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C)
8.65 cm
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D)
0.0 cm
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question_answer8)
Which of the four resistances P, Q, R and S generate the greatest amount of heat when a current flows from A to B? 
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
Q
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B)
S
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C)
P
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D)
R
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question_answer9) Bob of a simple pendulum of length \[l\]is mode of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then:
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[T=2\pi \sqrt{\frac{l}{g}}\]and damping is smaller than in air alone.
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B)
\[T=2\pi \sqrt{\frac{l}{g}}\]and damping is larger than in air alone.
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C)
\[T>2\pi \sqrt{\frac{l}{g}}\]and damping is smaller than in air alone.
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D)
\[T<2\pi \sqrt{\frac{l}{g}}\]and damping is larger than in air alone.
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question_answer10)
The plot given below is the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is: 
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
5.0
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B)
2.0
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C)
2.5
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D)
0.4
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question_answer11)
A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic filed\[\overset{\to }{\mathop{\operatorname{B}}}\,\]pointing out of the plane of the paper. A clockwise current is set up such that i> mg/Ba, where a is the width of the loop. Then: 
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
The weight rises due to a vertical force caused by the magnetic field and work is done on the system.
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B)
The weight do not rise due to vertical for caused by the magnetic field and work is done on the system.
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C)
The weight rises due to a vertical force caused by the magnetic field but no work is done on the system.
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D)
The weight rises due to a vertical force caused by the magnetic field and work is extracted from the magnetic field.
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question_answer12) A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. if the young?s modulii of copper and steel are respectively \[1.0\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}\]and\[2.0\times {{10}^{11}}\,N{{m}^{-2}}\], the total extension of the composite wire is:
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
1.75 mm
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B)
2.0 mm
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C)
1.50mm
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D)
1.25 mm
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question_answer13) 500 g of water and 100 g of ice at \[{{0}^{0}}\operatorname{C}\]are in a calorimeter whose water equivalent is \[40g.\]\[10\,g\]of steam at \[{{100}^{0}}C\] is added to it Then water in the calorimeter is : (Latent heat of ice =80 cal/g, Latent heat of stem = 540 cal/g)
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
580g
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B)
590gs
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C)
600g
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D)
610g
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question_answer14) A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart toward the wall, then the final distance of the boy from the wall will be:
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
15 m
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B)
12.5 m
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C)
15.5 m
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D)
17 m
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question_answer15) Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
less than the charged conductor more than at infinity
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B)
more than the charged conductor and less than at infinity.
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C)
more than the charged conductor and more than at infinity.
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D)
less than the charged conductor and less than at infinity
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question_answer16) This question has Statement-1 and Statement -2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Very large size telescopes are reflecting telescopes instead of refracting telescopes. Statement 2: It is easier to provide mechanical support to large size mirrors than large size lenses.
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
Statement1 is true and Statement 2 is false.
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B)
Statement1 is false and Statement2 is true.
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C)
Statement1 and Statement 2 are true and Statement 2 is correct explanation for Statement 1.
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D)
Statement 1 and Statement 2 are true and Statement 2 is not the correct explanation for Statement 1.
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question_answer17) A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1:3:4?
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
At 36 cm and 84 cm from one end
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B)
At 24 cm and 72 cm from one end
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C)
At 48cm and 96 cm form one end
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D)
At 72 cm and 96 cm from one end
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question_answer18) A particle of charge \[16\times {{10}^{-16}}\] C moving with velocity \[10{{\operatorname{ms}}^{-1}}\] along \[x-\] axis enters enters a region where magnetic field of induction \[\overset{\to }{\mathop{\operatorname{B}}}\,\] is along the \[y\]-axis and an electric field of magnitude \[{{10}^{4}}{{\operatorname{V}}^{-1}}\] is along the negative z-axis. If the charged particle continues moving along \[x-axis\], the magnitude of magnitude of \[\overset{\to }{\mathop{\operatorname{B}}}\,\]is :
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[16\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}\]
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B)
\[2\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}\]
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C)
\[1\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}\]
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D)
\[4\times {{10}^{3}}\operatorname{Wb}{{\operatorname{m}}^{-2}}\]
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question_answer19)
A light ray falls on square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to: 
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[\left( \sqrt{2}+1 \right)/2\]
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B)
\[\sqrt{\frac{5}{2}}\]
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C)
\[\frac{3}{2}\]
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D)
\[\sqrt{\frac{3}{2}}\]
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question_answer20) In the Bohr?s model of hydrogen- like atom the force between the nucleus and the electron is modified as \[\operatorname{F}=\frac{{{e}^{2}}}{4\pi {{\in }_{0}}}\left( \frac{1}{{{\operatorname{r}}^{2}}}+\frac{\beta }{{{\operatorname{r}}^{3}}} \right),\] Where \[\beta \]is a constant. For this atom, the radius of the \[{{\operatorname{n}}^{\operatorname{th}}}\] orbit in terms of the Bohr radius \[\left( {{a}_{0}}\frac{{{\in }_{0}}{{\operatorname{h}}^{2}}}{\operatorname{m}\pi {{e}^{2}}} \right)\] is
[JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[{{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}\operatorname{n}-\beta \]
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B)
\[{{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}{{\operatorname{n}}^{2}}+\beta \]
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C)
\[{{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}{{\operatorname{n}}^{2}}-\beta \]
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D)
\[{{\operatorname{r}}_{\operatorname{n}}}={{\operatorname{a}}_{0}}\operatorname{n}+\beta \]
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question_answer21) A projectile of mass M is fired so that the horizontal range is 4 km At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part states falling down vertically with zero initial speed. The horizontal range (distance from point of firing of the lighter part is):
JEE Main Online Paper ( Held On 23 April 2013 )
A)
16 km
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B)
1 km
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C)
10 km
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D)
2 km
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question_answer22) If the time period \[t\] of the oscillation of a drop of liquid of density \[d\]radius \[r,\]vibrating under surface tension s is given by the formula \[t=\sqrt{{{r}^{2b}}{{s}^{c}}{{d}^{a/2}}.}\]It is observe that the time period is directly proportional to \[\sqrt{\frac{d}{s}.}\] The value of \[b\] should therefore be:
JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[\frac{3}{4}\]
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B)
\[\sqrt{3}\]
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C)
\[\frac{3}{2}\]
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D)
\[\frac{2}{3}\]
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question_answer23) A parallel plate capacitor of area 60 \[{{\operatorname{cm}}^{2}}\] and separation 3 mm is charged initially to \[90\mu \operatorname{C}.\] If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of \[2.5\times {{10}^{-8}}\operatorname{C}/s,\] then what is the magnetic field between the plates?
JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[2.5\times {{10}^{-8}}\operatorname{T}\]
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B)
\[2.0\times {{10}^{-7}}\operatorname{T}\]
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C)
\[1.63\times {{10}^{-11}}\operatorname{T}\]
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D)
Zero
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question_answer24) This question has statement -1 and statement -2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement-1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume. Statement 1: A perfect gas is heated keeping pressure constant pressure is lower than that at constant volume.
JEE Main Online Paper ( Held On 23 April 2013 )
A)
Statement-1 is true, Statement-2 is true, and Statement 2 is the count explanation of Statement 1.
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B)
Statement -1 is true, Statement-2 is false.
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C)
Statement 1 is true, Statement 2 is true but Statement 2 is not the correct explanation of Statement 1.
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D)
Statement -1 is false, Statement -2 is true.
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question_answer25) nidentical waves each of intensity \[{{\operatorname{I}}_{0}}\] interfere with each other. The ratio of maximum intensities if the interference is (i) coherent and (ii) incoherent is:
JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[{{\operatorname{n}}^{2}}\]
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B)
\[\frac{1}{\operatorname{n}}\]
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C)
\[\frac{1}{{{\operatorname{n}}^{2}}}\]
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D)
\[\operatorname{n}\]
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question_answer26) A 70 Kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the pushes the ground with a constant force F to raise himself. The center of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m. The maximum power delivered by the muscles is: (Take g=10 \[\text{m}{{\text{s}}^{\text{2}}}\]).
JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{3}}}\] Watts at the start
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B)
\[\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{3}}}\] Watts at take off
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C)
\[\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{4}}}\] Watts at the start
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D)
\[\text{6}\text{.26}\times \text{1}{{\text{0}}^{\text{4}}}\] Watts at take off
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question_answer27)
A system of four gates is set up as shown. The ?truth table? corresponding to this systemis:
JEE Main Online Paper ( Held On 23 April 2013 )
A)
| A |
B |
Y |
| 0 |
0 |
1 |
| 0 |
1 |
0 |
| 1 |
0 |
0 |
| 1 |
1 |
1 |
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B)
| A |
B |
Y |
| 0 |
0 |
0 |
| 0 |
1 |
0 |
| 1 |
0 |
1 |
| 1 |
1 |
0 |
done
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C)
| A |
B |
Y |
| 0 |
0 |
1 |
| 0 |
1 |
0 |
| 1 |
0 |
1 |
| 1 |
1 |
0 |
done
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D)
| A |
B |
Y |
| 0 |
0 |
1 |
| 0 |
1 |
1 |
| 1 |
0 |
0 |
| 1 |
1 |
0 |
done
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question_answer28) A body of mass 'm' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm. If the angular velocity is doubled, elongation in the spring is 5 cm. The original length of the spring is:
JEE Main Online Paper ( Held On 23 April 2013 )
A)
15 cm
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B)
12 cm
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C)
16 cm
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D)
10 cm
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question_answer29) Select the correct statement form the following:
JEE Main Online Paper ( Held On 23 April 2013 )
A)
Electromagnetic waves cannot travel in vacuum
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B)
Electromagnetic waves are longitudinal waves
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C)
Electromagnetic waves are produced by charge moving with uniform velocity.
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D)
Electromagnetic waves carry both energy and momentum as they processes through space.
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question_answer30) A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of \[25.5{{\operatorname{KVm}}^{-1}}\]. The density of liquid is\[1.26\times {{10}^{3}}\]. The radius of the drop is (neglect buoyancy)
JEE Main Online Paper ( Held On 23 April 2013 )
A)
\[4.3\times {{10}^{-7}}\operatorname{m}\]
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B)
\[7.8\times {{10}^{-7}}\operatorname{m}\]
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C)
\[0.078\times {{10}^{-7}}\operatorname{m}\]
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D)
\[3.4\times {{10}^{-7}}\operatorname{m}\]
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