JEE Advanced 2007 · 08 Apr 2007 · Paper 2

Q1.In the experiment to determine the speed of sound using a resonance column,
(A) prongs of the tuning fork are kept in a vertical plane
(B) prongs of the tuning fork are kept in a horizontal plane
(C) in one of the two resonances observed, the length of the resonating air column i …

Q2.A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The s …

Q3.A particle moves in the X-Y plane under the influence of a force such that its linear momentum is $\vec{p}(t)=A[\hat{i}\cos (kt)-\hat{j}\sin (kt)]$, where $A$ and $k$ are constants. The angle between the force and the momentum is

Q4.A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is

Q6.A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Q7.Positive and negative point charges of equal magnitude are kept at $\left(0,0,\frac{a}{2}\right)$ and $\left(0,0,\frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a,0,0)$ to $(0,a,0)$ is

Q8.A magnetic field $\vec{B}=B_0\hat{j}$ exists in the region $a<x<2a$ and $\vec{B}=-B_0\hat{j}$, in the region $2a<x<3a$, where $B_0$ is a positive constant. A positive point charge moving with a velocity $\vec{v}=v_0\hat{i}$, where $v_0$ is a positive constant, ent …

Q9.Electrons with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

Q10.STATEMENT-1
If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.

Q11.STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
because
STATEMENT-2
For every action there is an equal and opposite reaction.

Q12.STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.
because
STATEMENT-2
In the above sit …

Q13.STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to th …

Q2.Among the following metal carbonyls, the C-O bond order is lowest in

Q3.A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The met …

Q4.Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is

Q5.The number of stereoisomers obtained by bromination of trans-2-butene is

Q6.Among the following, the least stable resonance structure is

Q7.A positron is emitted from ${}_{11}^{23}\mathrm{Na}$. The ratio of the atomic mass and atomic number of the resulting nuclide is

Q8.For the process ${\mathrm{H}}_2\mathrm{O}(l)(1\mathrm{bar},373\mathrm{K})\to {\mathrm{H}}_2\mathrm{O}(g)(1$ bar, $373\mathrm{K})$, the correct set of thermodynamic parameters is

Q9.Consider a reaction $\mathrm{aG}+\mathrm{bH}\to$ Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall o …

Q10.STATEMENT-1 : Alkali metals dissolve in liquid ammonia to give blue solutions.
because
STATEMENT-2 : Alkali metals in liquid ammonia give solvated species of the type ${\left[\mathrm{M}{\left({\mathrm{NH}}_3\right)}_{\mathrm{n}}\right]}^{+}(\mathrm{M}=$ alkali metals).

Q11.STATEMENT-1 : Glucose gives a reddish-brown precipitate with Fehling's solution.
because
STATEMENT-2 : Reaction of glucose with Fehling's solution gives CuO and gluconic acid.

Q12.STATEMENT-1 : Molecules that are not superimposable on their mirror images are chiral.
because
STATEMENT-2 : All chiral molecules have chiral centres.

Q13.STATEMENT-1 : Band gap in germanium is small.
because
STATEMENT-2 : The energy spread of each germanium atomic energy level is infinitesimally small.

Q17.Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicyladehydes as depicted below.

Which on …

Q18.Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicyladehydes as depicted below.

The elec …

Q19.Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicyladehydes as depicted below.

The stru …

Q20.Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the $4\times 4$ matrix given in the ORS.
| (A) …

Q21.Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the $4\times 4$ matrix given in the ORS.
| (A) …

Q22.Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
| (A) simple cubi …

Q1.Let $O(0,0),P(3,4),Q(6,0)$ be the vertices of the triangle $OPQ$. The point $R$ inside the triangle $OPQ$ is such that the triangles $OPR,PQR,OQR$ are of equal area. The coordinates of $R$ are

Q2.If $|z|=1$ and $z\ne \pm 1$, then all the values of $\frac{z}{1-z^2}$ lie on

Q3.Let $E^{\mathrm{c}}$ denote the complement of an event $E$. Let $E,F,G$ be pairwise independent events with $P(G)>0$ and $P(E\cap F\cap G)=0$. Then $P\left(E^c\cap F^c\mid G\right)$ equals

Q4.$\frac{d^{2}x}{d{y}^2}$ equals

Q5.The differential equation $\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with

Q6.Let $\vec{a},\vec{b},\vec{c}$ be unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$. Which one of the following is correct?

Q7.Let $ABCD$ be a quadrilateral with area 18, with side $AB$ parallel to the side $CD$ and $AB=2CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is

Q8.Let $f(x)=\frac{x}{{\left(1+x^n\right)}^{1/n}}$ for $n\ge 2$ and $g(x)=\underset{f\text{ occurs }n\text{ times }}{\underbrace{(f\circ f\circ \cdots \circ f)}}(x)$. Then $\int x^{n-2}g(x)dx$ equals

Q9.The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

Q10.Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5$.

STATEMENT-1 : The parametric equations of the line of intersection of the given planes are $x=3+14t,y=1+2t,z=15t$.

because

STATEMENT-2 : The vector $14\hat{i}+2\hat{j}+15\hat{k}$ is parallel to the line of …

Q11.STATEMENT-1 : The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$.

because

STATEMENT-2 : A parabola is symmetric about its axis.

Q12.Let $f(x)=2+\cos x$ for all real $x$.

STATEMENT-1 : For each real $t$, there exists a point $c$ in $[t,t+\pi ]$ such that $f^{\prime }(c)=0$.

because

STATEMENT-2 : $f(t)=f(t+2\pi )$ for each real $t$.

Q13.Lines $L_1:y-x=0$ and $L_2:2x+y=0$ intersect the line $L_3:y+2=0$ at $P$ and $Q$, respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects $L_3$ at $R$.

STATEMENT-1 : The ratio $PR:RQ$ equals $2\sqrt{2}:\sqrt{5}$. …

Q14.If a continuous function $f$ defined on the real line $\mathbf{R}$, assumes positive and negative values in $\mathbf{R}$ then the equation $f(x)=0$ has a root in $\mathbf{R}$. For example, if it is known that a continuous function $f$ on $\mathbf{R}$ is positive at …

Q15.If a continuous function $f$ defined on the real line $\mathbf{R}$, assumes positive and negative values in $\mathbf{R}$ then the equation $f(x)=0$ has a root in $\mathbf{R}$. For example, if it is known that a continuous function $f$ on $\mathbf{R}$ is positive at …

Q16.If a continuous function $f$ defined on the real line $\mathbf{R}$, assumes positive and negative values in $\mathbf{R}$ then the equation $f(x)=0$ has a root in $\mathbf{R}$. For example, if it is known that a continuous function $f$ on $\mathbf{R}$ is positive at …

Q17.Let $A_1,G_1,H_1$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $n\ge 2$, let $A_{n-1}$ and $H_{n-1}$ has arithmetic, geometric and harmonic means as $A_n,G_n,H_n$ respectively.

Which one of t …

Q20.Let $f(x)=\frac{x^2-6x+5}{x^2-5x+6}$.

Match the expressions/statements in Column I with expressions/statements in Column II and indicate your answer by darkening the appropriate bubbles in the $4\times 4$ matrix given in the ORS.
| Column I | Column II ||----------| …

Q21.Let $(x,y)$ be such that


Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the $4\times 4$ matrix given in the ORS.

| Column I …