JEE Main 2012 · 29 Apr 2012 · Offline

Q1.A wooden wheel of radius $R$ is made of two semicircular parts (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 $2\pi \mathrm{R}$. To fit the ring on the wheel, it is heated so that …

Q2.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:

Q3.In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be

Q4.An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\overrightarrow{\mathrm{X}}$ and that of wave propagation by …

Q5.If a simple pendulum has significant amplitude (up to a factor of $1/\mathrm{e}$ of original) only in the period between $t=$ Os to $t=\tau \mathrm{s}$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardat …

Q6.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

Q7.A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This …

Q8.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 $10\mathrm{m}/{\mathrm{s}}^2$ and 6400km respectively. The required energy for this work will be ;

Q9.Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)

Q10.In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If ${\mathrm{I}}_{\mathrm{m}}$ be the maximum intensity, the resultant intensity I when they interfere at phase difference …

Q11.A liquid in a beaker has temperature $\theta (\mathrm{t})$ at time t and ${\theta }_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between ${\log }_{\mathrm{e}}\left(\theta -{\theta }_0\right)$ and t is

Q12.A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F(t)=F_0{e}^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

Q13.Two electric bulbs marked $25\mathrm{W}-220\mathrm{V}$ and $100\mathrm{W}-220\mathrm{V}$ are connected in series to a 440 V supply. Which of the bulbs will fuse?

Q14.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

Q15.A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

Q16.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: Davisson - germer experiment established the wave nature of electrons.

Statement 2: If electrons have wave nature, t …

Q17.A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5\times 10^{-2}\mathrm{N}$ (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

Q18.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 centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction B is obt …

Q19.Truth table for system of four NAND gates as shown in figure is

Q20.A radar has a power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth $=6.4\times 10^6$ m) is

Q21.Assume that a neutron breaks into a proton and an electron. The energy released during this process is (Mass of neutron $=1.6725\times 10^{-27}$ kg; mass of proton $=1.6725\times 10^{-27}$ kg; mass of electron $=9\times 10^{-31}$ kg)

Q22.A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

Q23.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.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found tha …

Q24.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

Q25.A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

Q26.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 be shifted to be in sha …

Q27.A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( n is an integer)

Q28.A spectrometer gives the following reading when used to measure the angle of a prism.

Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 …

Q29.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.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distri …

Q30.Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p,r_d$ and $r_{\alpha }$. Which one of the following relations is correct?

Q1.Which among the following will be named as dibromidobis(ethylene diamine)chromium(III) bromide ?

Q2.Which method of purification is represented by the following equation
$\mathrm{Ti}(\mathrm{s})+2{\mathrm{I}}_2(\mathrm{g})\stackrel{523\mathrm{K}}{\to }{\mathrm{TiI}}_4(\mathrm{g})\stackrel{1700\mathrm{K}}{\to }\mathrm{Ti}(\mathrm{s})+2{\mathrm{I}}_2(\mathrm{g})$

Q3.Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

Q4.The molecule having smallest bond angle is :

Q5.Which of the following compounds can be detected by Molisch's test ?

Q6.The incorrect expression among the following is :

Q7.The density of a solution prepared by dissolving 120 g of urea (mol. Mass $=60\mathrm{u}$) in 1000 g of water is $1.15\mathrm{g}/\mathrm{mL}$. The molarity of this solution is :

Q8.The species which can best serve as an initiator for the cationic polymerization is :

Q9.Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?

Q10.The standard reduction potentials for ${\mathrm{Zn}}^{2+}/\mathrm{Zn},{\mathrm{Ni}}^{2+}/\mathrm{Ni}$, and ${\mathrm{Fe}}^{2+}/\mathrm{Fe}$ are $-0.76,-0.23$ and -0.44 V respectively. The reaction $\mathrm{X}+{\mathrm{Y}}^{2+}\to {\mathrm{X}}^{2+}+\mathrm{Y}$ will be sponta …

Q11.According to Freundlich adsorption isotherm, which of the following is correct ?

Q12.The equilibrium constant $({\mathrm{K}}_{\mathrm{C}})$ for the reaction ${\mathrm{N}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2\mathrm{NO}(\mathrm{g})$ at temperature T is $4\times 10^{-4}$. The value of ${\mathrm{K}}_{\mathrm{C}}$ for the reaction, …

Q13.The compressibility factor for a real gas at high pressure is :

Q14.Which one of the following statements is correct ?

Q15.Aspirin is known as :

Q16.Ortho-Nitrophenol is less soluble in water than $\mathrm{p}-$ and $\mathrm{m}-$ Nitrophenols because :

Q17.How many chiral compounds are possible on monochlorination of 2-methyl butane ?

Q18.Very pure hydrogen ( $99.9\%$ ) can be made by which of the following processes ?

Q19.The electrons identified by quantum numbers n and I :
(a) $n=4,I=1$
(b) $\mathrm{n}=4,\mathrm{I}=0$
(c) $n=3$, I $=2$
(d) $n=3,I=1$

Can be placed in order of increasing energy as :

Q20.For a first order reaction, $(\mathrm{A})\to$ products, the concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of $A$ is 0.01 M is :

Q21.Iron exhibits +2 and +3 oxidation states. Which of the following statements about iron is incorrect ?

Q22.The pH of a 0.1 molar solution of the acid HQ is 3 . The value of the ionization constant, Ka of this acid is :

Q23.Which branched chain isomer of the hydrocarbon with molecular mass 72 u gives only one isomer of mono substituted alky halide ?

Q24.${\mathrm{K}}_{\mathrm{f}}$ for water is $1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$. If your automobile radiator holds 1.0 kg of water, how many grams of ethylene glycol $\left({\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2\right)$ must you add to get the freezing point …

Q25.What is DDT among the following :

Q26.The increasing order of the ionic radii of the given isoelectronic species is :

Q27.2-Hexyne gives trans-2-Hexene on treatment with :

Q28.Iodoform can be prepared from all except :

Q29.In which of the following pairs the two species are not isostructural ?

Q30.In the given transformation, which of the following is the most appropriate reagent ?

Q1.The equation $e^{\sin x}-e^{-\sin x}-4=0$ has

Q2.Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2\hat{b}$ and $\vec{d}=5\hat{a}-4\hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

Q3.A spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the …

Q4.Statement 1: The sum of the series $1+(1+2+4)+(4+6+9)+(9+12+16)+\dots +(361+380+400)$ is 8000.

Statement 2: ${\sum }_{k=1}^n\left(k^3-(k-1{)}^3\right)=n^3$ for any natural number n.

Q5.The negation of the statement "If I become a teacher, then I will open a school" is

Q6.If the integral $\int \frac{5\tan x}{\tan x-2}dx=x+a\ln |\sin x-2\cos x|+k$, then a is equal to

Q7.Statement 1: An equation of a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$ is $y=2x+2\sqrt{3}$.
Statement 2: If the line $y=mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola $y^2=16\sqrt{3}x$ and the …

Q8.Let $A=\left(\begin{array}{lll}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right)$. If $u_1$ and $u_2$ are column matrices such that $A{u}_1=\left(\begin{array}{l}1\\ 0\\ 0\end{array}\right)$ and $A{u}_2=\left(\begin{array}{l}0\\ 1\\ 0\end{array}\right)$, t …

Q9.If n is a positive integer, then $(\sqrt{3}+1{)}^{2\mathrm{n}}-(\sqrt{3}-1{)}^{2\mathrm{n}}$ is

Q10.If 100 times the $100^{\text{th }}$ term of an AP with non zero common difference equals the 50 times its $50^{\text{th }}$ term, then the $150^{\text{th }}$ term of this AP is

Q11.In a $△PQR$, if $3\sin P+4\cos Q=6$ and $4\sin Q+3\cos P=1$, then the angle $R$ is equal to

Q12.An equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is

Q13.If the line $2x+y=k$ 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

Q14.Let ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots \dots ,{\mathrm{x}}_{\mathrm{n}}$ be n observations, and let $\overline{\mathrm{x}}$ be their arithematic mean and ${\sigma }^2$ be their variance.

Statement 1: Variance of $2x_1,2x_2,\dots \dots ,2x_n$ is …

Q15.The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt}=0.5p(t)$ -450 . If $p(0)=850$, then the time at which the population becomes zero is

Q16.Let $a,b\in R$ be such that the function $f$ given by $f(x)=\ln |x|+b{x}^2+ax,x\ne 0$ has extreme values at $x=-1$ and $x=2$.

Statement 1: f has local maximum at $\mathrm{x}=-1$ and at $\mathrm{x}=2$.
Statement 2: $\mathrm{a}=\frac{1}{2}$ and …

Q17.The area bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9y$, and the straight line $y=2$ is

Q18.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

Q19.If $f:R\to R$ is a function defined by $f(x)=[x]\cos \left(\frac{2x-1}{2}\right)\pi$, where $[x]$ denotes the greatest integer function, then f is

Q20.If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then $k$ is equal to

Q21.Three numbers are chosen at random without replacement from $\{1,2,3,\dots \dots 8\}$. The probability that their minimum is 3, given that their maximum is 6, is

Q22.If $z\ne 1$ and $\frac{z^2}{z-1}$ is real, then the point represented by the complex number $z$ lies

Q23.Let $P$ and $Q$ be $3\times 3$ matrices with $P\ne Q$. If $P^3=Q^3$ and $P^{2}Q=Q^{2}P$, then determinant of ( $P^2+Q^2$ ) is equal to

Q24.If $g(x)={\int }_0^x\cos 4tdt$, then $g(x+\pi )$ equals

Q25.The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through the point $(2,3)$ is

Q26.Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is

Q27.An ellipse is drawn by taking a diameter of the circle $(x-1{)}^2+y^2=1$ as its semiminor axis and a diameter of the circle $x^2+(y-2{)}^2=4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the elli …

Q28.Consider the function $f(x)=|x-2|+|x-5|,x\in R$.

Statement 1: $f^{\prime }(4)=0$

Statement 2: $f$ is continuous in [2, 5], differentiable in (2,5) and $f(2)=f(5)$.

Q29.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

Q30.Let ABCD be a parallelogram such that $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{q}},\overrightarrow{\mathrm{AD}}=\overrightarrow{\mathrm{p}}$ and $\angle \mathrm{BAD}$ be an acute angle. If $\overrightarrow{\mathrm{r}}$ is the vector that coincides with the altitude …