JEE Main 2013 Question Paper with Solutions

If the vectors $\overrightarrow {AB} = 3\widehat i + 4\widehat k$ and $\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$ are the sides of a triangle $ABC,$ then the length of the median through $A$ is :

A projectile is given an initial velocity of ( i ^ + 2 j ^ ) m/s, where i ^ is along the ground and j ^ is along the vertical. If g = 10 m/s 2 , the equation of its trajectory is:

Let [ ε 0 ] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:

The above $p$ - $v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density σ at equilibrium position. The extension x 0 of the spring when it is in equilibrium is:

In which of the following pairs of molecules/ions, both the species are not likely to exist?

For gaseous state, if most probable speed is denoted by C*, average speed by C _ _ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Stability of the species Li 2 , $Li_2^−$ and $Li_2^+$ increases in the order of:

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0 o C. As it does so, it absorbs 208J of heat. The values of q and w for the process will be : (R = 8.314 J/mol K) ( l n 7.5 = 2.01)

Consider : Statement − I : $\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy. Statement − II : $\left( {p \to q} \right) \leftrightarrow \left( { \sim q \to \sim p} \right)$ is a tautology.

The expression ${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$ can be written as:

The equation of the circle passing through the foci of the ellipse x 2 16 + y 2 9 = 1 , and having centre at ( 0 , 3 ) is :

If z is a complex number of unit modulus and argument θ , then arg ( 1 + z 1 + z ― ) equals :

The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :

The supply voltage to room is $120V.$ The resistance of the lead wires is $6\Omega$ . A $60$ $W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240$ $W$ heater is switched on in parallel to the bulb?

Two short bar magnets of length $1$ $cm$ each have magnetic moments $1.20$ $A{m^2}$ and $1.00$ $A{m^2}$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0$ $cm.$ The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to $\left( \, \right.$ Horizontal component of earth's magnetic induction is $3.6 \times 10.5Wb/{m^2})$

The graph between angle of deviation ( δ ) and angle of incidence ( i ) for a triangular prism is represented by

In an L C R circuit as shown below both switches are open initially. Now switch S 1 is closed, S 2 kept open. ( q is charge on the capacitor and τ = R C is Capacitance time constant). Which of the following statement is correct ?

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

If $x, y, z$ are in A.P. and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in A.P., then :

The real number $k$ for which the equation, $2{x^3} + 3x + k = 0$ has two distinct real roots in $\left[ {0,\,1} \right]$

If the lines ${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$ and ${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$ are coplanar, then $k$ can have :

A B C D is a trapezium such that A B and C D are parallel and B C ⊥ C D . If ∠ A D B = θ , B C = p and C D = q , then AB is equal to:

The number of values of k , for which the system of equations : $ ( k + 1 ) x + 8 y = 4 k k x + ( k + 3 ) y = 3 k − 1 $ has no solution, is

Synthesis of each molecule of glucose in photosynthesis involves:

Which of the following arrangements does not represent the correct order of the property stated against it?

Compound $\left( A \right),\,{C_8}{H_9}Br,\,\,\,$ gives a white precipitate when warmed with alcoholic $AgN{O_3}.$ Oxidation of $(A)$ gives an acid $\left( B \right),$ ${C_8}{H_6}{O_4}.\,\,\left( B \right)$ easily forms anhydride on heating. Identify the compound $(A).$

An organic compound A upon reacting with N H 3 gives B . On heating B gives C . C in presence of K O H reacts with B r 2 to given C H 3 C H 2 N H 2 2. A is :

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism: