JEE Advanced 2008 · 13 Apr 2008 · Paper 2

Q1.Consider a system of three charges $\frac{q}{3}$, $\frac{q}{3}$ and $-\frac{2q}{3}$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius $R$ and angle $\mathrm{CAB}=60^{\circ }$

Q2.A radioactive sample S1 having an activity of $5\mu \mathrm{Ci}$ has twice the number of nuclei as another sample S2 which has an activity of $10\mu \mathrm{Ci}$. The half lives of S1 and S2 can be

Q3.A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10\mathrm{cm}/\mathrm{s}$. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of po …

Q4.A block (B) is attached to two unstretched springs S1 and S2 with spring constants $k$ and $4k$, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction …

Q6.A glass tube of uniform internal radius $(r)$ has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius $r$. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening t …

Q8.A parallel plate capacitor $C$ with plates of unit area and separation $d$ is filled with a liquid of dielectric constant $K=2$. The level of liquid is $\frac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed $V$, the time constant as a function of time $t$ …

Q9.A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $n_0$, $\frac{n_0}{2}$, $\frac{n_0}{6}$ and $\frac{n_0}{8}$, respectively. The angle of incidence $\theta$ for which the beam just misses entering Re …

Q10.STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities …

Q11.STATEMENT-1
It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT-2
The magnitude of frictional force depends on the nature of the two surfaces in contact.

Q12.STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\frac{Q}{4\pi {\epsilon }_{0}R}$.

Q13.STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

Q14.The nuclear charge $(Ze)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho (r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial …

Q15.The nuclear charge $(Ze)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho (r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial …

Q16.The nuclear charge $(Ze)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho (r)$ [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial …

Q17.A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance $d$ from …

Q18.A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance $d$ from …

Q19.A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two identical massless springs of spring constant $k$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance $d$ from …

Q20.Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the …

Q22.Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the $4\times 4$ matrix given in the ORS.

| Column I | Colum …

Q1.The correct stability order for the following species is
(I) (see structure)
(II) (see structure)
(III) (see structure)
(IV) (see structure)

Q2.Cellulose upon acetylation with excess acetic anhydride/${\mathrm{H}}_2{\mathrm{SO}}_4$ (catalytic) gives cellulose triacetate whose structure is

Q4.Among the following, the coloured compound is

Q5.Both $[\mathrm{Ni}(\mathrm{CO}{)}_4]$ and $[\mathrm{Ni}(\mathrm{CN}{)}_4{]}^{2-}$ are diamagnetic. The hybridisations of nickel in these complexes, respectively, are

Q6.The IUPAC name of $[\mathrm{Ni}({\mathrm{NH}}_3{)}_4][{\mathrm{NiCl}}_4]$ is

Q7.Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of ${\mathrm{H}}_2$ gas at the cathode is (1 Faraday = 96500 C mol⁻¹)

Q8.Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is

Q9.Solubility product constants (${\mathrm{K}}_{\text{sp}}$) of salts of types $\mathrm{MX}$, ${\mathrm{MX}}_2$ and ${\mathrm{M}}_3\mathrm{X}$ at temperature 'T' are $4.0\times 10^{-8}$, $3.2\times 10^{-14}$ and $2.7\times 10^{-15}$, respectively. Solubilities (mol dm …

Q10.STATEMENT-1: Aniline on reaction with ${\mathrm{NaNO}}_2/\mathrm{HCl}$ at 0 °C followed by coupling with β-naphthol gives a dark blue coloured precipitate.
and
STATEMENT-2: The colour of the compound formed in the reaction of aniline with ${\mathrm{NaNO}}_2/\mathrm{HCl}$ at 0 …

Q13.STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.
and
STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

Q14.A tertiary alcohol $\mathbf{H}$ upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J and K. Compound J upon reaction with KOH gives benzyl alcohol and a compound $\mathbf{L}$, whereas $\mathbf{K}$ on reaction with KOH gives only …

Q15.A tertiary alcohol $\mathbf{H}$ upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J and K. Compound J upon reaction with KOH gives benzyl alcohol and a compound $\mathbf{L}$, whereas $\mathbf{K}$ on reaction with KOH gives only …

Q16.A tertiary alcohol $\mathbf{H}$ upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J and K. Compound J upon reaction with KOH gives benzyl alcohol and a compound $\mathbf{L}$, whereas $\mathbf{K}$ on reaction with KOH gives only …

Q17.In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal c …

Q21.Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I
(A) $\mathrm{PbS}\to \mathrm{PbO}$
(B) …

Q22.Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I
(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital
(B) A …

Q1.A particle $P$ starts from the point $z_0=1+2i$, where $i=\sqrt{-1}$. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units in the direction …

Q2.Let the function $g:(-\infty ,\infty )\to \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ be given by $g(u)=2{\tan }^{-1}\left(e^u\right)-\frac{\pi }{2}$. Then, $g$ is

Q3.Consider a branch of the hyperbola

with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $C$ is the focus of the hyperbola nearest to the point $A$, then the area of the triangle $ABC$ is

Q4.The area of the region between the curves $y=\sqrt{\frac{1+\sin x}{\cos x}}$ and $y=\sqrt{\frac{1-\sin x}{\cos x}}$ bounded by the lines $x=0$ and $x=\frac{\pi }{4}$ is

Q5.Consider three points $P=(-\sin (\beta -\alpha ),-\cos \beta )$, $Q=(\cos (\beta -\alpha ),\sin \beta )$ and $R=(\cos (\beta -\alpha +\theta ),\sin (\beta -\theta ))$, where $0<\alpha ,\beta ,\theta <\frac{\pi }{4}$. Then,

Q6.An experiment has 10 equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of 4 outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is

Q7.Let two non-collinear unit vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point $P$ moves so that at any time $t$ the position vector $\overrightarrow{OP}$ (where $O$ is the origin) is given by $\hat{a}\cos t+\hat{b}\sin t$. When $P$ is farthest from ori …

Q8.Let

Then, for an arbitrary constant $C$, the value of $J-I$ equals

Q9.Let $g(x)=\log f(x)$ where $f(x)$ is a twice differentiable positive function on $(0,\infty )$ such that $f(x+1)=xf(x)$. Then, for $N=1,2,3\dots$,

Q10.Suppose four distinct positive numbers $a_1,a_2,a_3,a_4$ are in G.P. Let $b_1=a_1$, $b_2=b_1+a_2$, $b_3=b_2+a_3$ and $b_4=b_3+a_4$.

STATEMENT-1 : The numbers $b_1,b_2,b_3,b_4$ are neither in A.P. nor in G.P.
and
STATEMENT-2 …

Q11.Let $a,b,c,p,q$ be real numbers. Suppose $\alpha ,\beta$ are the roots of the equation $x^2+2px+q=0$ and $\alpha ,\frac{1}{\beta }$ are the roots of the equation $a{x}^2+2bx+c=0$, where ${\beta }^2\notin \{-1,0,1\}$.

STATEMENT-1 : …

Q12.Consider

where $p$ is a real number, and $C:x^2+y^2+6x-10y+30=0$.

STATEMENT-1 : If line $L_1$ is a chord of circle $C$, then line $L_2$ is not always a diameter of circle …

Q14.Consider the function $f:(-\infty ,\infty )\to (-\infty ,\infty )$ defined by


Which of the following is true?

Q16.Consider the function $f:(-\infty ,\infty )\to (-\infty ,\infty )$ defined by


Let

Which of the following is true?

Q17.Consider the lines


The unit vector perpendicular to both $L_1$ and $L_2$ is

Q18.Consider the lines


The shortest distance between $L_1$ and $L_2$ is

Q19.Consider the lines


The distance of the point $(1,1,1)$ from the plane passing through the point (-1, -2, -1) and whose normal is perpend …

Q20.Consider the lines given by

Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate …

Q22.Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $4\times 4$ matrix given in the ORS.

| C …