JEE Main 2008 · 27 Apr 2008 · Offline

Q1.Electrons accelerated by potential V are diffracted from a crystal. If $\mathrm{d}=1\mathring{A}$ and $\mathrm{i}=30^{\circ },\mathrm{V}$ should be about ( …

Q2.If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance 'd' between them (see figure), de Broglie wavelength ${\lambda }_{\mathrm{dB}}$ of electrons can be calculated by the relationship (n is an inte …

Q3.In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure).

Which of the following graph can be expected to represent the number of electron …

Q4.A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11{\mathrm{kms}}^{-1}$, the escape velocity from the surface of the planet would be

Q5.A spherical solid ball of volume V is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_2\left({\rho }_2<{\rho }_1\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ …

Q6.Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resistor $R$ is

Q7.A thin rod of length 'L' is lying along the $x$-axis with its ends at $x=0$ and $x=L$. Its linear density (mass/length) varies with $x$ as $k{\left(\frac{x}{L}\right)}^n$, where $n$ can be zero or any positive number. If the position $x_{CM}$ of the centre of mass o …

Q8.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. …

Q9.The dimension of magnetic field in $\mathrm{M},\mathrm{L},\mathrm{T}$ and C (Coulomb) is given as

Q10.Consider a uniform square plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Q11.A body of mass $\mathrm{m}=3.513\mathrm{kg}$ is moving along the x-axis with a speed of $5.00{\mathrm{ms}}^{-1}$. The magnitude of its momentum is recorded as

Q12.An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Q13.A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is 'd'. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant ${\mathrm{k}}_1=3$ and thickness …

Q14.The speed of sound in oxygen $\left({\mathrm{O}}_2\right)$ at a certain temperature is $460{\mathrm{ms}}^{-1}$. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

Q15.This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - I:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
and
Statement - II
For h …

Q16.This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-I:
For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its s …

Q17.A jar filled with two non mixing liquids 1 and 2 having densities ${\rho }_1$ and ${\rho }_2$ respectively. A solid ball, made of a material of density ${\rho }_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is tr …

Q18.A working transistor with its three legs marked $\mathrm{P},\mathrm{Q}$ and R is tested using a multimeter. No conduction is found between P and Q . By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q , some resistanc …

Q19.$\Delta \mathrm{V}$ measured between B and C is

Q20.For current entering at A , the electric field at a distance ' r ' from A is

Q21.A student measures the focal length of convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance ' $v$ ' of the image pin. The graph between ' $u$ ' and ' $v$ ' plotted by the student should look like

Q22.A block of mass 0.50 kg is moving with a speed of $2.00\mathrm{m}/\mathrm{s}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Q23.A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

Q24.Suppose an electron is attracted towards the origin by a force $\mathrm{k}/\mathrm{r}$ where ' k ' is a constant and ' r ' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the ${\mathrm{n}}^{\text{th }}$ orbital of the ele …

Q25.A wave travelling along the $x$-axis is described by the equation $y(x,t)=0.005\cos (\alpha x-\beta t)$. If the wavelength and the time period of the wave are 0.08 m and 2.0 s , respectively, then $\alpha$ and $\beta$ in appropriate units are

Q26.Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area $\mathrm{A}=10{\mathrm{cm}}^2$ and length $=20\mathrm{cm}$. If one of the solenoids has 300 turns and the other 400 turns , their mutual inductance is ( …

Q27.In the circuit below, A and B represent two inputs and C represents the output. The circuit represents

Q28.A body is at rest at x=0. At t=0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x=0 moving in the positive x direction with a constant speed. The position of the first body is given by $x_1(t)$ after t …

Q29.An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

Q30.A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0\le r<\infty$, where $r$ is the distance from the centre of the shell?

Q31.A 5 V battery with internal resistance $2\Omega$ and a 2 V battery with internal resistance $1\Omega$ are connected to a $10\Omega$ resistor as shown in the figure. The current in the $10\Omega$ resistor is

Q32.A horizontal overhead power line is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (${\mu }_0=4\pi \times 10^{-7}\mathrm{T}\mathrm{m}{\mathrm{A}}^{-1}$)

Q33.Relative permittivity and permeability of a material are ${\epsilon }_{\mathrm{r}}$ and ${\mu }_{\mathrm{r}}$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

Q34.Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of -0.03 mm while measuring the diameter of a thin wire, a stude …

Q35.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${\mathrm{V}}_1$ and contains ideal gas at pressure ${\mathrm{P}}_1$ and temperature ${\mathrm{T}}_1$. The other chamber has volume $V_2$ and contains ideal gas a …

Q1.The organic chloro compound, which shows complete stereochemical inversion during a ${\mathrm{S}}_{\mathrm{N}}2$ reaction, is

Q2.Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

Q3.The coordination number and the oxidation state of the element ' E ' in the complex $\left[\mathrm{E}(\mathrm{en}{)}_2\left({\mathrm{C}}_2{\mathrm{O}}_4\right)\right]{\mathrm{NO}}_2$ (where (en) is ethylene diamine) are, respectively,

Q4.Identify the wrong statements in the following:
(1) Chlorofluorocarbons are responsible for ozone layer depletion
(2) Greenhouse effect is responsible for global warming
(3) Ozone layer does not permit infrared radiation from the sun to reach the earth
(4) Acid rains is mostly be …

Q5.Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

Q6.In the following sequence of reactions, the alkene affords the compound ' B '
${\mathrm{CH}}_3\mathrm{CH}={\mathrm{CHCH}}_3\stackrel{{\mathrm{O}}_3}{\to }\mathrm{A}\underset{\mathrm{Zn}}{\overset{{\mathrm{H}}_2\mathrm{O}}{\to }}\mathrm{B}$.
The compound B is

Q7.Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

Q8.In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of ${\Delta }_{\circ }$ be the highest?

Q9.At $80^{\circ }\mathrm{C}$, the vapour pressure of pure liquid ' $A$ ' is 520 mm Hg and that of pure liquid ' $B$ ' is 1000 mm Hg . If a mixture solution of ' A ' and ' B ' boils at $80^{\circ }\mathrm{C}$ and 1 atm pressure, the amount of ' A ' in the mixture is ( …

Q10.For a reaction $\frac{1}{2}A\to 2B$, rate of disappearance of ' $A$ ' is related to the rate of appearance of ' $B$ ' by the expression

Q11.The equilibrium constants $K_{P_1}$ and $K_{P_2}$ for the reactions $X\rightleftharpoons 2Y$ and $Z\rightleftharpoons P+Q$, respectively are in the ratio of $1:9$. If the degree of dissociation of $X$ and $Z$ be equal then the ratio of total pressure at these equilibria i …

Q12.Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: …

Q13.Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

Q14.Bakelite is obtained from phenol by reacting with

Q15.For the following three reactions $\mathrm{a},\mathrm{b}$ and c , equilibrium constants are given:
a. $\mathrm{CO}(\mathrm{g})+{\mathrm{H}}_2\mathrm{O}(\mathrm{g})\rightleftharpoons {\mathrm{CO}}_2(\mathrm{g})+{\mathrm{H}}_2(\mathrm{g});{\mathrm{K}}_1$
b. …

Q16.The absolute configuration of

is

Q17.The electrophile, $E^{\oplus }$ attacks the benzene ring to generate the intermediate $\sigma$-complex. Of the following, which $\sigma$-complex is of lowest energy?

Q18.$\alpha$-D-(+)-glucose and $\beta$-D-(+)-glucose are

Q19.Standard entropy of $X_2,Y_2$ and $X{Y}_3$ are 60,40 and $50{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$, respectively. For the reaction, $\frac{1}{2}{X}_2+\frac{3}{2}{Y}_2\to X{Y}_3,\Delta H=-30\mathrm{kJ}$, to be at equilibrium, the temperature will be

Q20.Four species are listed below
i. ${\mathrm{HCO}}_3^{-}$
ii. ${\mathrm{H}}_3{\mathrm{O}}^{+}$
iii. ${\mathrm{HSO}}_4^{-}$
iv. ${\mathrm{HSO}}_3\mathrm{F}$

Which one of the following is the correct sequence of their acid strength?

Q21.Which one of the following constitutes a group of the isoelectronic species?

Q22.Which one of the following pairs of species have the same bond order?

Q23.The ionization enthalpy of hydrogen atom is $1.312\times 10^6{\mathrm{Jmol}}^{-1}$. The energy required to excite the electron in the atom from $\mathrm{n}=1$ to $\mathrm{n}=2$ is

Q24.Which one of the following is the correct statement?

Q25.Given ${\mathrm{E}}_{{\mathrm{Cr}}^{3+}/\mathrm{Cr}}^{\circ }=-0.72\mathrm{V},{\mathrm{E}}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{\circ }=-0.42\mathrm{V}$. The potential for the cell …

Q26.Amount of oxalic acid present in a solution can be determined by its titration with ${\mathrm{KMnO}}_4$ solution in the presence of ${\mathrm{H}}_2{\mathrm{SO}}_4$. The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl

Q27.The vapour pressure of water at $20^{\circ }\mathrm{C}$ is 17.5 mm Hg. If 18 g of glucose $\left({\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6\right)$ is added to 178.2 g of water at $20^{\circ }\mathrm{C}$, the vapour pressure of the resulting solution will be

Q28.Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is

Q29.In context with the industrial preparation of hydrogen from water gas $\left(\mathrm{CO}+{\mathrm{H}}_2\right)$, which of the following is the correct statement?

Q30.In a compound atoms of element $Y$ from ccp lattice and those of element $X$ occupy $2/3^{\text{rd }}$ of tetrahedral voids. The formula of the compound will be

Q31.Gold numbers of protective colloids $\mathrm{A},\mathrm{B},\mathrm{C}$ and D are $0.50,0.01,0.10$ and 0.005, respectively. The correct order of their protective powers is

Q32.The hydrocarbon which can react with sodium in liquid ammonia is

Q33.The treatment of ${\mathrm{CH}}_3\mathrm{MgX}$ with ${\mathrm{CH}}_3\mathrm{C}\equiv \mathrm{C}-\mathrm{H}$ produces

Q34.The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

Q35.The ${\mathrm{pK}}_{\mathrm{a}}$ of a weak acid, HA, is 4.80. The ${\mathrm{pK}}_{\mathrm{b}}$ of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

Q1.AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is $60^{\circ }$. He moves away from the pole along the line $BC$ to a point $D$ such that …

Q2.It is given that the events $A$ and $B$ are such that $P(A)=\frac{1}{4},P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{3}$. Then $P(B)$ is

Q3.A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P(A\cup B)$ is

Q4.A focus of an ellipse is at the origin. The directrix is the line $x=4$ and the eccentricity is $1/2$. Then the length of the semi-major axis is

Q5.A parabola has the origin as its focus and the line $\mathrm{x}=2$ as the directrix. Then the vertex of the parabola is at

Q6.The point diametrically opposite to the point $P(1,0)$ on the circle $x^2+y^2+2x+4y-3=0$ is

Q7.Let $f:N\to Y$ be a function defined as $f(x)=4x+3$, where $Y=\{y\in N:y=4x+3$ for some $x\in N\}$. Show that $f$ is invertible and its inverse is

Q8.The conjugate of a complex number is $\frac{1}{\mathrm{i}-1}$. Then the complex number is

Q9.Let R be the real line. Consider the following subsets of the plane $\mathrm{R}\times \mathrm{R}$.
$\mathrm{S}=\{(\mathrm{x},\mathrm{y}):\mathrm{y}=\mathrm{x}+1$ and $0<\mathrm{x}<2\},\mathrm{T}=\{(\mathrm{x},\mathrm{y}):\mathrm{x}-\mathrm{y}$ is an integer $\}$. Wh …

Q10.The perpendicular bisector of the line segment joining $\mathrm{P}(1,4)$ and $\mathrm{Q}(\mathrm{k},3)$ has y-intercept -4. Then a possible value of k is

Q11.The solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition $y(1)=1$ is

Q12.The mean of the numbers $a,b,8,5,10$ is 6 and the variance is 6.80. Then which one of the following gives possible values of $a$ and $b$?

Q13.The vector $\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{j}+\hat{k}$ and bisects the angle between $\vec{b}$ and $\vec{c}$. Then which one of the following gives possible values of $\alpha$ and …

Q14.The non-zero vectors $\vec{a},\vec{b}$ and $\vec{c}$ are related by $\vec{a}=8\vec{b}$ and $\vec{c}=-7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is

Q15.The line passing through the points $(5,1,a)$ and $(3,b,1)$ crosses the yz-plane at the point $\left(0,\frac{17}{2},\frac{-13}{2}\right)$. Then

Q16.If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer k is equal to

Q17.Statement - 1: For every natural number $n\ge 2,\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots +\frac{1}{\sqrt{n}}>\sqrt{n}$.

Statement -2 : For every natural number $n\ge 2,\sqrt{n(n+1)}<n+1$.

Q18.Let A be a $2\times 2$ matrix with real entries. Let I be the $2\times 2$ identity matrix. Denote by $\mathrm{tr}(A)$, the sum of diagonal entries of $A$. Assume that $A^2=I$.
Statement -1: If $A\ne I$ and $A\ne -I$, then $\det A=-1$.
Statement -2 : If …

Q19.Statement -1: ${\sum }_{r=0}^n(r+1{)}^n{C}_r=(n+2)2^{n-1}$.

Statement-2: ${\sum }_{r=0}^n(r+1{)}^n{C}_r{x}^r=(1+x{)}^n+nx(1+x{)}^{n-1}$.

Q20.Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and $r$ be the statement "$x$ is a rational number iff $y$ is a transcendental number".
Statement $-1:r$ is equivalent to either $q$ or $p$
Statement -2 : $r$ is equivalent to …

Q21.In a shop there are five types of ice-creams available. A child buys six ice-creams.

Statement-1: The number of different ways the child can buy the six ice-creams is ${}^{10}{C}_5$.
Statement -2: The number of different ways the child can buy the six ice-creams is equal to the nu …

Q22.Let $f(x)=\{\begin{array}{ll}(x-1)\sin \left(\frac{1}{x-1}\right),& \text{ if }x\ne 1\\ 0,& \text{ if }x=1\end{array}$. Then which one of the following is true?

Q23.The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

Q24.Suppose the cubic $x^3-px+q$ has three distinct real roots where $p>0$ and $q>0$. Then which one of the following holds?

Q25.How many real solutions does the equation $x^7+14x^5+16x^3+30x-560=0$ have?

Q26.The statement $p\to (q\to p)$ is equivalent to

Q27.The value of $\cot \left({\mathrm{cosec}}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\right)$ is

Q28.The differential equation of the family of circles with fixed radius 5 units and centre on the line $y=2$ is

Q29.Let $\mathrm{I}={\int }_0^1\frac{\sin \mathrm{x}}{\sqrt{\mathrm{x}}}\mathrm{dx}$ and $\mathrm{J}={\int }_0^1\frac{\cos \mathrm{x}}{\sqrt{\mathrm{x}}}\mathrm{dx}$. Then which one of the following is true?

Q30.The area of the plane region bounded by the curves $x+2y^2=0$ and $x+3y^2=1$ is equal to

Q31.The value of $\sqrt{2}\int \frac{\sin xdx}{\sin \left(x-\frac{\pi }{4}\right)}$ is

Q32.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Q33.Let $\mathrm{a},\mathrm{b},\mathrm{c}$ be any real numbers. Suppose that there are real numbers $\mathrm{x},\mathrm{y},\mathrm{z}$ not all zero such that $\mathrm{x}=cy+bz,y=az+cx$ and $z=bx+ay$. Then $a^2+b^2+c^2+2abc$ is equal to

Q34.Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

Q35.The quadratic equations $x^2-6x+a=0$ and $x^2-cx+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4:3$. Then the common root is