JEE Advanced 2008 · 13 Apr 2008 · Paper 1

Q1.Students I, II and III perform an experiment for measuring the acceleration due to gravity ( $g$ ) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.
Least count f …

Q2.Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

Q3.Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

Q4.Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $60^{\circ }$ ). In the position of minimum deviation, the angle of refraction will be

Q5.An ideal gas is expanding such that $P{T}^2=$ constant . The coefficient of volume expansion of the gas is

Q6.A spherically symmetric gravitational system of particles has a mass density $\rho =\{\begin{array}{ll}{\rho }_0& \text{ for }r\le R\\ 0& \text{ for }r>R\end{array}$
where ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitati …

Q7.Two balls, having linear momenta ${\vec{p}}_1=p\hat{i}$ and ${\vec{p}}_2=-p\hat{i}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\vec{p}}_1^{\prime }$ and ${\vec{p}}_2^{\prime }$ be their final momenta. The following option(s) …

Q9.A particle of mass $m$ and charge $q$, moving with velocity $V$ enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $\ell$. Choose the correct …

Q10.In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $\lambda$. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2 . Choose the correct choice(s).

Q11.STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standar …

Q12.STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT-2
An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.

Q13.STATEMENT-1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane fi …

Q14.STATEMENT-1
The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT-2
In any steady flow of an incompressible fluid, the volume flow rate of the fl …

Q15.A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

Q16.A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

Q17.A small spherical monoatomic ideal gas bubble $\left(\gamma =\frac{5}{3}\right)$ is trapped inside a liquid of density ${\rho }_{\ell }$ (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the …

Q18.In a mixture of $\mathrm{H}-{\mathrm{He}}^{+}$gas ( ${\mathrm{He}}^{+}$is singly ionized He atom), H atoms and ${\mathrm{He}}^{+}$ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to ${\mathrm{He}}^{+}$ions (by …

Q19.In a mixture of $\mathrm{H}-{\mathrm{He}}^{+}$gas ( ${\mathrm{He}}^{+}$is singly ionized He atom), H atoms and ${\mathrm{He}}^{+}$ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to ${\mathrm{He}}^{+}$ions (by …

Q20.In a mixture of $\mathrm{H}-{\mathrm{He}}^{+}$gas ( ${\mathrm{He}}^{+}$is singly ionized He atom), H atoms and ${\mathrm{He}}^{+}$ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to ${\mathrm{He}}^{+}$ions (by …

Q21.A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ }$ to $30^{\circ }$ at point B . The block is initially at rest at A. Assume that collisions between the block and the inc …

Q22.A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ }$ to $30^{\circ }$ at point B . The block is initially at rest at A. Assume that collisions between the block and the inc …

Q1.Hyperconjugation involves overlap of the following orbitals

Q3.Aqueous solution of ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ on reaction with ${\mathrm{Cl}}_2$ gives

Q4.Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of

Q5.Under the same reaction conditions, initial concentration of $1.386\mathrm{mol}{\mathrm{dm}}^{-3}$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $\left(\frac{k_1}{k_0}\right)$ of the rate constants f …

Q6.2.5 mL of $\frac{2}{5}\mathrm{M}$ weak monoacidic base $({\mathrm{K}}_{\mathrm{b}}=1\times 10^{-12}$ at $25^{\circ }\mathrm{C})$ is titrated with $\frac{2}{15}\mathrm{M}\mathrm{HCl}$ in water at $25^{\circ }\mathrm{C}$. The concentration of …

Q7.The correct statement(s) about the compound given below is (are)

Q8.The correct statement(s) concerning the structures $\mathbf{E}$, $\mathbf{F}$ and $\mathbf{G}$ is (are)

Q9.A solution of colourless salt $\mathbf{H}$ on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) $\mathbf{H}$ is (are)

Q10.A gas described by van der Waals equation
(A) behaves similar to an ideal gas in the limit of large molar volumes
(B) behaves similar to an ideal gas in the limit of large pressures
(C) is characterised by van der Waals coefficients that are dependent on the identity of the gas b …

Q12.STATEMENT-1 : ${\mathrm{Pb}}^{4+}$ compounds are stronger oxidizing agents than ${\mathrm{Sn}}^{4+}$ compounds.
and
STATEMENT-2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.

Q13.STATEMENT-1 : The plot of atomic number ( $y$-axis) versus number of neutrons ( $x$-axis) for stable nuclei shows a curvature towards $x$-axis from the line of $45^{\circ }$ slope as the atomic number is increased.
and
STATEMENT-2 : Proton-proton electrostatic repulsions begin to …

Q14.STATEMENT-1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
and
STATEMENT-2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

Q16.In the following reaction sequence, products I, J and L are formed. K represents a reagent.

The structures of compounds $\mathbf{J}$ and $\mathbf{K}$, respectively, are

Q18.There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridization e …

Q19.There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridization e …

Q20.There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridization e …

Q21.Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of it …

Q22.Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of it …

Q23.Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of it …

Q1.Consider the two curves

Then,

Q2.If $0<x<1$, then

Q3.The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $\hat{a},\hat{b},\hat{c}$ such that

Then, the volume of the parallelopiped is

Q4.Let $a$ and $b$ be non-zero real numbers. Then, the equation

represents

Q5.Let
$g(x)=\frac{(x-1{)}^n}{\log {\cos }^m(x-1)};0<x<2,m$ and $n$ are integers, $m\ne 0,n>0$, and let $p$ be the left hand derivative of $|x-1|$ at $x=1$.
If ${\lim }_{x\to 1+}g(x)=p$, then

Q6.The total number of local maxima and local minima of the function

is

Q7.A straight line through the vertex $P$ of a triangle $PQR$ intersects the side $QR$ at the point $S$ and the circumcircle of the triangle $PQR$ at the point $T$. If $S$ is not the centre of the circumcircle, then

Q9.Let

for $n=1,2,3,\cdots$. Then,

Q10.Let $f(x)$ be a non-constant twice differentiable function defined on $(-\infty ,\infty )$ such that $f(x)=f(1-x)$ and $f^{\prime }\left(\frac{1}{4}\right)=0$. Then,

Q12.Consider three planes

Let $L_1,L_2,L_3$ be the lines of intersection of the planes $P_2$ and $P_3,P_3$ and $P_1$, and $P_1$ and $P_2$, respectively.

STATEMENT …

Q13.Consider the system of equations


STATEMENT-1 : The system of equations has no solution for $k\ne 3$.

and

STATEMENT-2 : The determinant …

Q14.Consider the system of equations
$ax+by=0,cx+dy=0$, where $a,b,c,d\in \{0,1\}$.

STATEMENT-1 : The probability that the system of equations has a unique solution is $\frac{3}{8}$.

and

STATEMENT-2 : The probability that the system of equations has a solution is 1 .

Q15.A circle $C$ of radius 1 is inscribed in an equilateral triangle $PQR$. The points of contact of $C$ with the sides $PQ,QR,RP$ are $D,E,F$, respectively. The line $PQ$ is given by the equation $\sqrt{3}x+y-6=0$ and the point $D$ is …

Q18.Consider the functions defined implicitly by the equation $y^3-3y+x=0$ on various intervals in the real line.
If $x\in (-\infty ,-2)\cup (2,\infty )$, the equation implicitly defines a unique real valued differentiable function $y=f(x)$.
If $x\in (-2,2)$, the equation implicitl …

Q19.Consider the functions defined implicitly by the equation $y^3-3y+x=0$ on various intervals in the real line.
If $x\in (-\infty ,-2)\cup (2,\infty )$, the equation implicitly defines a unique real valued differentiable function $y=f(x)$.
If $x\in (-2,2)$, the equation implicitl …

Q20.Consider the functions defined implicitly by the equation $y^3-3y+x=0$ on various intervals in the real line.
If $x\in (-\infty ,-2)\cup (2,\infty )$, the equation implicitly defines a unique real valued differentiable function $y=f(x)$.
If $x\in (-2,2)$, the equation implicitl …

Q21.Let $A,B,C$ be three sets of complex numbers as defined below


The number of elements in the set $A\cap B\cap C$ is

Q22.Let $A,B,C$ be three sets of complex numbers as defined below


Let $z$ be any point in $A\cap B\cap C$. Then, …