List of top Questions asked in JEE Main- 2013

Two charges, each equal to $q$, are kept at $x = - a$ and $x = a$ on the $x-axis$. A particle of mass m and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $y ( y << a)$ along the y-axis, the net force acting on the particle is proportional to

Electrode potentials (E$^{\circ}$) are given below : $Cu^{+}/Cu=+0.52\, V,$ $Fe^{3+}/Fe^{2+} = +0.77 \,V,$ $\frac{1}{2}I_{2}\left(s\right)/I^{-} = 40.54 \,V,$ $Ag^{+}/Ag =+ 0.88\,V.$ Based on the above potentials, strongest oxidizing agent will be :

Oxidation state of sulphur in anions $SO^{2-}_{3}. S_{2}O^{2-}_{4}$ and $S_{2}O^{2-}_{6}$ increases in the orders:

A light ray falls on a 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 :

Diameter of a plano-convex lens is $6 \,cm$ and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is

The shown p- V diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times of its initial value. If the final pressure of gas is $128$ atmospheres, the value of ?$\gamma$?of the gas is :

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of photocell varies as follows

A $12.5\, eV$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit :

A vessel contains a mixture of $1$ mole of oxygen and two moles of nitrogen at $300 \,K$. The ratio of the rotational kinetic energy per $ O_{2} $ molecule to that per $ N_{2} $ molecule is

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Higher the range, greater is the resistance of ammeter. To increase the range of ammeter, additional shunt needs to be used across it.

Compound $( A ), C_8H_9Br$ gives a white precipitate when warmed with alcoholic $AgNO_3$. Oxidation of $(A)$ gives an acid $(B)$, $C_8H_6O$ 4. $(B)$ easily forms anhydride on heating. Identify the compound $(A)$.

Formaldehyde can be distinguished from acetaldehyde by the use of :

Sodium Carbonate cannot be used in place of $(NH_4)_2CO_3$ for the identification of $Ca^{2+},\, Ba^{2+}$ and $Sr^{2+}$ ions (in group V) during mixture analysis because :

The correct set of four quantum numbers for the valence electrons of rubidium atom $(Z = 37)$ is

The molarity of a solution obtained by mixing $750\, mL$ of $0.5\, M \,HCl$ with $250\, mL$ of $2 \,M \,HCl$ will be

The order of basicity of amines in gaseous state is:

The ellipse $E_1 : \frac{x^2}{9} + \frac{y^2}{4}$ = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse $E_2$ is

The term independent of $x$ in expansion of $\bigg(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\bigg)^{10}$ is

Stability of the species $ Li_2 , Li_2^- , \, \, and \, \, Li_2^+ $ increases in the order of

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\, cm$. The area of the image is $9$ times that of the square. The focal length of the lens is :

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777,....,$ is

The maximum area of a right angled triangle with hypotenuse $h$ is :

For which of the following compounds Kjeldahl method can be used to determine the percentage of Nitrogen ?

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n =10$ then the value of $n$ is