JEE Advanced 2009 · 12 Apr 2009 · Paper 1

Q1.Three concentric metallic spherical shells of radii $R,2R,3R$, are given charges $Q_1,Q_2,Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, …

Q2.A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $\sqrt{3}$. The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from $0^{\circ }$. Then

Q3.A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the s …

Q4.Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $m$. The mass of the ink used to draw the outer circle is $6m$. The coordinates o …

Q5.Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are $v$ and $2v$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After makin …

Q6.The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in th …

Q8.The $x$ - $t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=4/3\mathrm{s}$ is

Q9.If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

Q10.A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm . The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) valu …

Q11.For the circuit shown in the figure

Q12.${\mathrm{C}}_{\mathrm{v}}$ and ${\mathrm{C}}_{\mathrm{p}}$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

Q13.Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ${}_1^2\mathrm{H}$, known as deuteron and denoted by D , can be thought of as a candidate for fusion reactor. The D-D reaction is …

Q14.Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ${}_1^2\mathrm{H}$, known as deuteron and denoted by D , can be thought of as a candidate for fusion reactor. The D-D reaction is …

Q16.When a particle is restricted to move along $x$-axis between $x=0$ and $x=a$, where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of sta …

Q17.When a particle is restricted to move along $x$-axis between $x=0$ and $x=a$, where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of sta …

Q19.Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let $E$ be the electric field and $V$ be the electric potential at M (potential at infinity is zero …

Q1.Given that the abundances of isotopes ${}^{54}\mathrm{Fe},{}^{56}\mathrm{Fe}$ and ${}^{57}\mathrm{Fe}$ are 5%, 90% and 5%, respectively, the atomic mass of Fe is

Q2.The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

Q3.Among the electrolytes ${\mathrm{Na}}_2{\mathrm{SO}}_4,{\mathrm{CaCl}}_2,{\mathrm{Al}}_2({\mathrm{SO}}_4{)}_3$ and ${\mathrm{NH}}_4\mathrm{Cl}$, the most effective coagulating agent for ${\mathrm{Sb}}_2{\mathrm{S}}_3$ sol is

Q4.The Henry's law constant for the solubility of ${\mathrm{N}}_2$ gas in water at 298 K is $1.0\times 10^5\mathrm{atm}$. The mole fraction of ${\mathrm{N}}_2$ in air is 0.8. The number of moles of ${\mathrm{N}}_2$ from air dissolved in 10 moles of water at 298 K and 5 atm press …

Q5.The reaction of ${\mathrm{P}}_4$ with X leads selectively to ${\mathrm{P}}_4{\mathrm{O}}_6$. The X is

Q6.The correct acidity order of the following is

(I) (see structure)
(II) (see structure)
(III) (see structure)
(IV) (see structure)

Q7.Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is

Q8.The IUPAC name of the following compound is

(see structure)

Q12.The correct statement(s) about the compound ${\mathrm{H}}_3\mathrm{C}(\mathrm{HO})\mathrm{HC}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH}){\mathrm{CH}}_3$ ($\mathbf{X}$) is(are)

Q13.$p$-Amino-$N,N$-dimethylaniline is added to a strongly acidic solution of $\mathbf{X}$. The resulting solution is treated with a few drops of aqueous solution of $\mathbf{Y}$ to yield blue coloration due to the formation of methylene blue. Treatment of the aqueous solutio …

Q16.A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.

The structure of the ca …

Q17.A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.

The structures of the p …

Q18.A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.

The structure of the pr …

Q19.Match each of the diatomic molecules in Column I with its property/properties in Column II.
| (C) ${\mathrm{O}}_2^{-}$ | (r) Undergoes reduction | …

Q20.Match each of the compounds in Column I with its characteristic reaction(s) in Column II.
| (B) ${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{OCOCH}}_3$ | (q) …

Q1.Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line

Then the value of $\mu$ for which the vector $\overrightarrow{PQ}$ is parallel to the plane $x-4y+3z=1$ is

Q2.Tangents drawn from the point $P(1,8)$ to the circle

touch the circle at the points $A$ and $B$. The equation of the circumcircle of the triangle $PAB$ is

Q3.Let $f$ be a non-negative function defined on the interval $[0,1]$. If

and $f(0)=0$, then

Q4.Let $z=x+iy$ be a complex number where $x$ and $y$ are integers. Then the area of the rectangle whose vertices are the roots of the equation

is

Q5.The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse

meets its auxiliary circle at the point $M$. Then the area of the triangle with vertices at $A,M$ and the origin $O$ is

Q6.If $\vec{a},\vec{b},\vec{c}$ and $\vec{d}$ are unit vectors such that

and $\vec{a}\cdot \vec{c}=\frac{1}{2}$,
then

Q7.Let $z=\cos \theta +i\sin \theta$. Then the value of

at $\theta =2^{\circ }$ is

Q8.The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

Q9.Area of the region bounded by the curve $y=e^x$ and lines $x=0$ and $y=e$ is

Q10.Let

If $L$ is finite, then

Q11.In a triangle $ABC$ with fixed base $BC$, the vertex $A$ moves such that

If $a,b$ and $c$ denote the lengths of the sides of the triangle opposite to the angles $A,B$ and $C$, respectively, then

Q12.If

then

Q13.Let $\mathcal{A}$ be the set of all 3 × 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices in $\mathcal{A}$ is

Q14.Let $\mathcal{A}$ be the set of all 3 × 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices $A$ in $\mathcal{A}$ for which the system of linear equations …

Q16.A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required.

The probability that $X=3$ equals

Q17.A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required.

The probability that $X\ge 3$ equals

Q18.A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required.

The conditional probability that $X\ge 6$ given $X>3$ equals