JEE Main 2012 Question Paper with Solutions

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

Two cars of masses m 1 and m 2 are moving in circles of radii r 1 and r 2 , respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

The mass of a spaceship is $1000$ $kg.$ It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth ) are $10\,m/{s^2}$ and $6400$ $km$ respectively. The required energy for this work will be:

A wooden wheel of radius R is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L . L is slightly less than 2 π R . To fit the ring on the wheel, it is heated so that its temperature rises by Δ T and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is α , and its Young's modulus is Y , the force that one part of the wheel applies on the other part is :

A particle of mass $m$ is at rest at the origin at time $t=0.$ It is subjected to a force $F\left( t \right) = {F_0}{e^{ - bt}}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

Which of the following on thermal decomposition yields a basic as well as an acidic oxide?

The equilibrium constant (K C ) for the reaction N 2 (g) + O 2 (g) → 2NO(g) at temperature T is 4 × 10 –4 . The value of K C for the reaction, NO(g) → 1/2N 2 (g) + 1/2O 2 (g) at the same temperature is :

The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, K a of this acid is :

The electrons identified by quantum numbers n and l : (a) n = 4, l = 1 (b) n = 4, l = 0 (c) n = 3, l = 2 (d) n = 3, l = 1 Can be placed in order of increasing energy as :

In which of the following pairs the two species are not isostructural ?

In a $\Delta PQR,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu}$ If $3{\mkern 1mu} \sin {\mkern 1mu} P + 4{\mkern 1mu} \cos {\mkern 1mu} Q = 6$ and $4\sin Q + 3\cos P = 1,$ then the angle R is equal to :

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is :

If the line 2 x + y = k passes through the point which divides the line segment joining the points ( 1 , 1 ) and ( 2 , 4 ) in the ratio 3 : 2 , then k equals :

Let x 1 , x 2 ,........., x n be n observations, and let $\overline x$ be their arithematic mean and ${\sigma ^2}$ be their variance. Statement 1 : Variance of 2x 1 , 2x 2 ,......., 2x n is 4 ${\sigma ^2}$ . Statement 2 : : Arithmetic mean of 2x 1 , 2x 2 ,......, 2x n is 4 $\overline x$ .

An object $2.4$ $m$ in front of a lens forms a sharp image on a film $12$ $cm$ behind the lens. A glass plate $1$ $cm$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R.$ The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity $\omega .$ As a result of this rotation a magnetic field of induction $B$ is obtained at the center of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and very the radius of the disc then the variation of the magnetic induction at the center of the disc will be represented by the figure :

Truth table for system of four N A N D gates as shown in figure is:

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be :

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between

If $g\left( x \right) = \int\limits_0^x {\cos 4t\,dt,}$ then $g\left( {x + \pi } \right)$ equals

The population $p$ $(t)$ at time $t$ of a certain mouse species satisfies the differential equation ${{dp\left( t \right)} \over {dt}} = 0.5\,p\left( t \right) - 450.\,\,$ If $p(0)=850,$ then the time at which the population becomes zero is :

Let $a,b \in R$ be such that the function $f$ given by $f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$ has extreme values at $x=-1$ and $x=2$ Statement-1 : $f$ has local maximum at $x=-1$ and at $x=2$ . Statement-2 : $a = {1 \over 2}$ and $b = {-1 \over 4}$

If the $\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,}$ then $a$ is equal to :

A line is drawn through the point $(1, 2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $OPQ,$ where $O$ is the origin. If the area of the triangle $OPQ$ is least, then the slope of the line $PQ$ is :

K f for water is 1.86K kg mol –1 . If your automobile radiator holds 1.0 kg of water, how many grams of ethylene glycol (C 2 H 6 O 2 ) must you add to get the freezing point of the solution lowered to –2.8 o C ?

In the given transformation, which of the following is the most appropriate reagent ?

Which of the following compounds can be detected by Molisch’s test ?

Which among the following will be named as dibromidobis (ethylene diamine) chromium(III) bromide?

The species which can best serve as an initiator for the cationic polymerization is :