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## JEE Main 2013 (Offline)

Exam Held on Sun Apr 07 2013 09:30:00 GMT+0000 (Coordinated Universal Time)
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## Chemistry

Consider the following reaction:<br><br> $$xMnO_4^- + yC_2O_4^{2-}$$ + zH<sup>+<...
A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO<sub...
Experimentally it was found that a metal oxide has formula M<sub>0.98</sub>O. Me...
Energy of an electron is given by $$E = - 2.178 \times {10^{ - 18}}J\left( {{{{... Which of the following represents the correct order of increasing first ionizati... The first ionization potential of Na is 5.1 eV. The value of electron gain entha... Which one of the following molecules is expected to exhibit diamagnetic behaviou... In which of the following pairs of molecules/ions, both the species are not like... Which of the following is the wrong statement? Stability of the species Li<sub>2</sub>,$$Li_2^−$$and$$Li_2^+$$increases in ... For gaseous state, if most probable speed is denoted by C*, average speed by$$\...
A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to...
How many litres of water must be added to 1 litre of an aqueous solution of HCl ...
A solution of (–$$l$$) – chloro –1 – phenylethane in toluene racemises slowly in...
Which of the following exists as covalent crystals in the solid state?
The coagulating power of electrolytes having ions Na<sup>+</sup>, Al<sup>3+</sup...
The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL ...
Given<br> $$E_{C{r^{2 + }}/Cr}^o$$ = -0.74 V; $$E_{MnO_4^ - /M{n^{2 + }}}^o$$ = ...
The rate of a reaction doubles when its temperature changes from 300K to 310K. A...
Which of the following arrangements does not represent the correct order of the ...
Four successive members of the first row transition elements are listed below wi...
Which of the following complex species is not expected to exhibit optical isomer...
An unknown alcohol is treated with the “Lucas reagent” to determine whether the ...
A compound with molecular mass 180 is acylated with CH<sub>3</sub>COCl to get a ...
The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas trag...
Synthesis of each molecule of glucose in photosynthesis involves:
The order of stability of the following carbocations : <br><br><img class="ques...
Compound $$\left( A \right),\,{C_8}{H_9}Br,\,\,\,$$ gives a white precipitate wh...
Arrange the following compounds in order of decreasing acidity : <br><br><img cl...
An organic compound A upon reacting with $$N{H_3}$$ gives $$B.$$ On heating $$B... ## Mathematics The expression$${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \ov...
$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \bot C... If z is a complex number of unit modulus and argument$$\theta $$, then arg$$\l...
The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two di...
The number of values of $$k$$, for which the system of equations : $$\matrix{ ... If the equations$${x^2} + 2x + 3 = 0$$and$$a{x^2} + bx + c = 0,a,\,b,\,c...
Let $${T_n}$$ be the number of all possible triangles formed by joining vertices...
The term independent of $$x$$ in expansion of <br> $${\left( {{{x + 1} \over {... The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is A ray of light along$$x + \sqrt 3 y = \sqrt 3 $$gets reflected upon reaching ... The$$x$$-coordinate of the incentre of the triangle that has the coordinates of... The circle passing through$$(1, -2)$$and touching the axis of$$x$$at$$(3, 0...
The equation of the circle passing through the foci of the ellipse $${{{x^2}} \o... <b>Given :</b> A circle,$$2{x^2} + 2{y^2} = 5$$and a parabola,$${y^2} = 4\sqr...
If $$y = \sec \left( {{{\tan }^{ - 1}}x} \right),$$ then $${{{dy} \over {dx}}}... If$$x, y, z$$are in A.P. and$${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$$and$${\tan ^...
The intercepts on $$x$$-axis made by tangents to the curve, <br>$$y = \int\limi... If$$P = \left[ {\matrix{ 1 &amp; \alpha &amp; 3 \cr 1 &amp; 3 &amp; 3 ...
If $$\int {f\left( x \right)dx = \psi \left( x \right),}$$ then $$\int {{x^5}f\... <b>Statement-1 :</b> The value of the integral <br>$$\int\limits_{\pi /6}^{\pi ...
The area (in square units) bounded by the curves $$y = \sqrt {x,} 2y - x + 3 = 0... At present, a firm is manufacturing$$2000$$items. It is estimated that the rat... A multiple choice examination has$$5$$questions. Each question has three alter... Distance between two parallel planes$$2x+y+2z=8$$and$$4x+2y+4z+5=0$$is If the lines$${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$... If the vectors$$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$and$$\over...
$$\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \co... Consider : <br><b>Statement − I :</b>$$\left( {p \wedge \sim q} \right) \wedge...
All the students of a class performed poorly in Mathematics. The teacher decided...
Let A and B be two sets containing 2 elements and 4 elements respectively. The n...

## Physics

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of...
A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j}... This question has statement$${\rm I}$$and statement$${\rm I}{\rm I}$$. Of... A hoop of radius$$r$$and mass$$m$$rotating with an angular velocity$${\omeg...
What is the minimum energy required to launch a satellite of mass $$m$$ from the...
A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$... Assume that a drop of liquid evaporates by decreases in its surface energy, so t... <img class="question-image" src="https://imagex.cdn.examgoal.net/ikaZL1Ae21HD6Ok... If a piece of metal is heated to temperature$$\theta $$and then allowed to coo... The amplitude of a damped oscillator decreases to$$0.9$$times its original mag... An ideal gas enclosed in a vertical cylindrical container supports a freely movi... A sonometer wire of length$$1.5m$$is made of steel. The tension in it pr... Two charges, each equals to$$q,$$are kept at$$x=-a$$and$$x=a$$on the$$x$$... A charge$$Q$$is uniformly distributed over a long rod$$AB$$of length$$L$$a... Two capacitors$${C_1}$$and$${C_2}$$are charged to$$120V$$and$$200$$... The supply voltage to room is$$120V.$$The resistance of the lead wires is$$6\...
This questions has Statement - $${\rm I}$$ and Statement - $${\rm I}$$$${\rm I}... Two short bar magnets of length$$1cm$$each have magnetic moments$$1.20$$... A circular loop of radius$$0.3cm$$lies center of the small loop is on the... A beam of unpolarised light of intensity$${{\rm I}_0}$$is passed through a pol... Diameter of a plano-convex lens is$$6cm$$and thickness at the center is ... A metallic rod of length$$'\ell '$$is tied to a string of length$$2\ell ...
In an $$LCR$$ circuit as shown below both switches are open initially. Now switc...
Two coherent point sources $${S_1}$$ and $${S_2}$$ are separated by a small dist...
The graph between angle of deviation $$\left( \delta \right)$$ and angle of inc...
A diode detector is used to detect an amplitude modulated wave of $$60\%$$ modu...
The magnetic field in a travelling electromagnetic wave has a peak value of $$20... In a hydrogen like atom electron make transition from an energy level with quant... The anode voltage of a photocell is kept fixed. The wavelength$$\lambda $$of t... The$${\rm I}$$-$$V$$characteristic of an$$LED is

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