JEE Main 2007 · 29 Apr 2007 · Offline

Q1.The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times 10^{-2}\cos \pi t$ metres. The time at which the maximum speed first occurs is

Q2.In an a.c. circuit the voltage applied is $E=E_0\sin \omega t$. The resulting current in the circuit is $I=I_0\sin \left(\omega t-\frac{\pi }{2}\right)$. The power consumption in the circuit is given by

Q3.An electric charge $10^{-3}\mu C$ is placed at the origin $(0,0)$ of X-Y co-ordinate system. Two points A and B are situated at $(\sqrt{2},\sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points A and B will be

Q4.A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

Q5.An ideal coil of 10 H is connected in series with a resistance of $5\Omega$ and a battery of 5 V. 2 second after the connection is made the current flowing in amperes in the circuit is

Q6.A long straight wire of radius 'a' carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and 2a is

Q7.A current I flows along the length of an infinitely long, straight, thin walled pipe. Then

Q8.If $M_O$ is the mass of an oxygen isotope ${}_8{O}^{17}$, $M_p$ and $M_N$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

Q9.Which of the following transitions in hydrogen atoms emit photons of highest frequency?

Q10.A block of mass '$m$' is connected to another block of mass '$M$' by a spring (massless) of spring constant '$k$'. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force '$F$' starts acting on the bl …

Q11.Two lenses of power -15 D and +5 D are in contact with each other. The focal length of the combination is

Q12.One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths ${\ell }_1$ and ${\ell }_2$ and thermal conductivities $k_1$ and $k_2$ respectively. The temperature at the interface of the two sectio …

Q13.A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of

Q14.If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

Q15.A charged particle moves through a magnetic field perpendicular to its direction. Then

Q16.Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current $I_1$ and COD carries a current $I_2$. The magnetic field on a point lying at a distance '$d$' from $O$, in a direction perpendicular to the plane of …

Q17.The resistance of a wire is 5 ohm at $50^{\circ }C$ and 6 ohm at $100^{\circ }C$. The resistance of the wire at $0^{\circ }C$ will be

Q18.A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

Q19.If $g_E$ and $g_m$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio …

Q20.A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

Q21.A round uniform body of radius R, mass M and moment of inertia 'I', rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

Q22.Angular momentum of the particle rotating with a central force is constant due to

Q23.A 2 kg block slides on a horizontal floor with a speed of $4m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is $10,000N/m$. The spring compresses by

Q24.A particle is projected at $60^{\circ }$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

Q25.In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda }{6}$ ($\lambda$ being the wavelength of the light used) is I. If ${\mathrm{I}}_0$ denotes the maximum intensity, $\frac{\mathrm{I}}{{\mathrm{I}}_0}$ is equal to

Q26.Two springs, of force constants $k_1$ and $k_2$, are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are made four times their original values, the frequency of oscillation becomes

Q27.When a system is taken from state i to state f along the path iaf, it is found that $\mathrm{Q}=50\mathrm{cal}$ and $\mathrm{W}=20\mathrm{cal}$. Along the path ibf $Q=36\mathrm{cal}$. W along the path ibf is

Q28.A particle of mass $m$ executes simple harmonic motion with amplitude 'a' and frequency 'v'. The average kinetic energy during its motion from the position of equilibrium to the end is

Q29.In gamma ray emission from a nucleus

Q30.If in a p-n junction diode, a square input signal of 10 V is applied as shown, then the output signal across $R_L$ will be

Q31.Photon of frequency $\nu$ has a momentum associated with it. If c is the velocity of light, the momentum is

Q32.The velocity of a particle is $v=v_0+gt+f{t}^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time ($t=1$) is

Q33.For the given uniform square lamina ABCD, whose centre is O, which of the following is true? (E and F are the midpoints of AB and DC respectively.)

Q34.A point mass oscillates along the x-axis according to the law $x=x_0\cos \left(\omega t-\frac{\pi }{4}\right)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then

Q35.Charges are placed on the vertices of a square as shown. Let $\vec{E}$ be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

Q36.The half-life period of a radioactive element X is the same as the mean-life time of another radioactive element Y. Initially they have the same number of atoms. Then

Q37.A Carnot engine, having an efficiency of $\eta =\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Q38.Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

Q39.A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$, and comes out without any change in magnitude or direction of $\vec{v}$. Then

Q40.The potential at a point x (measured in $\mu$m) due to some charges situated on the x-axis is given by $V(x)=\frac{20}{x^2-4}$ volts. The electric field E at $x=4\mu$m is given by

Q1.The energies of activation for forward and reverse reactions for $A_2+B_2\rightleftharpoons 2AB$ are $180{\mathrm{kJ}\mathrm{mol}}^{-1}$ and $200{\mathrm{kJ}\mathrm{mol}}^{-1}$ respectively. The presence of catalyst lowers the activation energy of both (forward and reverse) reactions by …

Q2.The cell, $\mathrm{Zn}|{\mathrm{Zn}}^{2+}(1\mathrm{M})||{\mathrm{Cu}}^{2+}(1\mathrm{M})|\mathrm{Cu}$ (${\mathrm{E}}_{\text{cell}}^0=1.10\mathrm{V}$), was allowed to be completely discharged at 298 K. The relative concentration of ${\mathrm{Zn}}^{2+}$ to ${\mathrm{Cu}}^{2+}$ …

Q3.The pKa of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which $50\%$ of the acid is ionized is

Q4.Consider the reaction, $2\mathrm{A}+\mathrm{B}\to$ Products
When concentration of $B$ alone was doubled, the half-life did not change. When the concentration of $A$ alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is

Q5.Identify the incorrect statement among the following

Q6.Which one of the following has a square planar geometry?

Q7.Which of the following molecules is expected to rotate the plane of plane polarized light?

Q8.The secondary structure of a protein refers to

Q9.Which of the following reactions will yield 2, 2-dibromopropane?

Q10.In the chemical reaction,
${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{NH}}_2-{\mathrm{CHCl}}_3+3\mathrm{KOH}⟶(\mathrm{A})+(\mathrm{B})+3{\mathrm{H}}_2\mathrm{O}$, the compound $(\mathrm{A})$ and (B) are respectively

Q11.The reaction of toluene with ${\mathrm{Cl}}_2$ in presence of ${\mathrm{FeCl}}_3$ gives predominantly

Q12.Presence of a nitro group in a benzene ring

Q13.In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?

Q14.The actinoids exhibits more number of oxidation states in general than the lanthanoids. This is because

Q15.Equal masses of methane and oxygen are mixed in an empty container at $25^{\circ }\mathrm{C}$. The fraction of the total pressure exerted by oxygen is

Q16.A $5.25\%$ solution of a substance is isotonic with a $1.5\%$ solution of urea (molar mass $=60\mathrm{g}{\mathrm{mol}}^{-1}$) in the same solvent. If the densities of both the solutions are assumed to be equal to $1.0\mathrm{g}{\mathrm{cm}}^{-3}$, molar mass of the substance …

Q17.Assuming that water vapour is an ideal gas, the internal energy ($\Delta \mathrm{U}$) when 1 mol of water is vapourised at 1 bar pressure and $100^{\circ }\mathrm{C}$, (Given: Molar enthalpy of vapourization of water at 1 bar and …

Q18.In a saturated solution of the sparingly soluble strong electrolyte ${\mathrm{AgIO}}_3$ (Molecular mass $=283$) the equilibrium which sets in is
${\mathrm{AgIO}}_{3(\mathrm{s})}\rightleftharpoons {\mathrm{Ag}}_{(\mathrm{aq})}^{+}+{\mathrm{IO}}_{3(\mathrm{aq})}^{-}$
If the solubility …

Q19.A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

Q20.Which one of the following conformation of cyclohexane is chiral?

Q21.Which of the following is the correct order of decreasing ${\mathrm{SN}}^2$ reactivity?
($\mathrm{X}=\mathrm{a}$ halogen)

Q22.In the following sequence of reactions,

the compound 'D' is

Q23.Which of the following sets of quantum numbers represents the highest energy of an atom?

Q24.Which of the following hydrogen bonds is the strongest?

Q25.In the reaction. $2{\mathrm{Al}}_{(\mathrm{s})}+6{\mathrm{HCl}}_{(\mathrm{s})}⟶2{\mathrm{Al}}_{(\mathrm{aq})}^{3+}+6{\mathrm{Cl}}_{(\mathrm{aq})}^{-}+3{\mathrm{H}}_{2(\mathrm{g})}$,

Q26.Regular use of which of the following fertilizer increases the acidity of soil?

Q27.Identify the correct statement regarding a spontaneous process

Q28.Which of the following nuclear reactions will generate an isotope?

Q29.The equivalent conductances of two strong electrolytes at infinite dilution in ${\mathrm{H}}_2\mathrm{O}$ (where ions move freely through a solution) at $25^{\circ }\mathrm{C}$ are given below: …

Q30.Which one of the following is the strongest base in aqueous solution?

Q31.The compound formed as a result of oxidation of ethyl benzene by ${\mathrm{KMnO}}_4$ is

Q32.The IUPAC name of

is

Q33.Which of the following species exhibits the diamagnetic behaviour?

Q34.The stability of dihalides of $\mathrm{Si},\mathrm{Ge},\mathrm{Sn}$ and Pb increases steadily in the sequence

Q35.Identify the incorrect statement among the following
(1) Ozone reacts with ${\mathrm{SO}}_2$ to give ${\mathrm{SO}}_3$
(2) Silicon reacts with ${\mathrm{NaOH}}_{(\mathrm{aq})}$ in the presence of air to give ${\mathrm{Na}}_2{\mathrm{SiO}}_3$ and ${\mathrm{H}}_2\mathrm{O}$ …

Q36.The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizinig order of the polarizing power of the cationic species, …

Q37.The density (in $\mathrm{g}{\mathrm{mL}}^{-1}$ ) of a 3.60 M sulphuric acid solution that is $29\%{\mathrm{H}}_2{\mathrm{SO}}_4$ (Molar mass $=98\mathrm{g}{\mathrm{mol}}^{-1}$ ) by mass will be

Q38.The first and second dissociation constants of an acid ${\mathrm{H}}_2\mathrm{A}$ are $1.0\times 10^{-5}$ and $5.0\times 10^{-10}$ respectively. The overall dissociation constant of the acid will be

Q39.A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K . The vapour pressure of propyl alcohol is 200 mm . If the mole fraction of ethyl alcohol is 0.6 , its vapour pressure (in mm ) at the same temperature will be

Q40.In conversion of lime-stone to lime,
${\mathrm{CaCO}}_3(\mathrm{s})⟶\mathrm{CaO}(\mathrm{s})+{\mathrm{CO}}_2(\mathrm{g})$
the vales of $\Delta {\mathrm{H}}^{\circ }$ and $\Delta {\mathrm{S}}^{\circ }$ are $+179.1\mathrm{kJ}{\mathrm{mol}}^{-1}$ and …

Q1.In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

Q2.If ${\sin }^{-1}\left(\frac{x}{5}\right)+{\mathrm{cosec}}^{-1}\left(\frac{5}{4}\right)=\frac{\pi }{2}$ then a value of $x$ is

Q3.In the binomial expansion of $(a-b{)}^n,n\ge 5$, the sum of $5^{\text{th}}$ and $6^{\text{th}}$ terms is zero, then $\frac{a}{b}$ equals

Q4.The set $S=\{1,2,3,\dots ,12\}$ is to be partitioned into three sets $A,B,C$ of equal size. Thus, $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$. The number of ways to partition $S$ is

Q5.The largest interval lying in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ for which the function $\left[f(x)=4^{-x^2}+{\cos }^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)\right]$ is defined, is

Q6.A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

Q7.A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

Q8.Consider a family of circles which are passing through the point $(-1,1)$ and are tangent to $x$ axis. If $(h,k)$ are the co-ordinates of the centre of the circles, then the set of values of $k$ is given by the interval

Q9.Let $L$ be the line of intersection of the planes $2x+3y+z=1$ and $x+3y+2z=2$. If $L$ makes an angles $\alpha$ with the positive $x$-axis, then $\cos \alpha$ equals

Q10.The differential equation of all circles passing through the origin and having their centres on the x-axis is

Q11.If $p$ and $q$ are positive real numbers such that $p^2+q^2=1$, then the maximum value of $(p+q)$ is

Q12.A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that $\mathrm{AB}(=\mathrm{a})$ subtends an angle of $60^{\circ }$ at the foot of the tower, and the angle of elevation of the top of the tower from A or B is $30^{\circ }$. The …

Q13.The sum of the series
${}^{20}{\mathrm{C}}_0-{}^{20}{\mathrm{C}}_1+{}^{20}{\mathrm{C}}_2-{}^{20}{\mathrm{C}}_3+\dots -\dots +{}^{20}{\mathrm{C}}_{10}$ is

Q14.The normal to a curve at $P(x,y)$ meets the $x$-axis at $G$. If the distance of $G$ from the origin is twice the abscissa of $P$, then the curve is a

Q15.If $|z+4|\le 3$, then the maximum value of $|z+1|$ is

Q16.The resultant of two forces $PN$ and $3N$ is a force of $7N$. If the direction of $3N$ force were reversed, the resultant would be $\sqrt{19}\mathrm{N}$. The value of $P$ is

Q17.Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

Q18.If $D=\left|\begin{array}{ccc}1& 1& 1\\ 1& 1+x& 1\\ 1& 1& 1+y\end{array}\right|$ for $x\ne 0,y\ne 0$ then $D$ is

Q19.For the hyperbola $\frac{x^2}{{\cos }^2\alpha }-\frac{y^2}{{\sin }^2\alpha }=1$, which of the following remains constant when $\alpha$ varies?

Q20.If a line makes an angle of $\frac{\pi }{4}$ with the positive directions of each of $x$-axis and $y$-axis, then the angle that the line makes with the positive direction of the $z$-axis is

Q21.A value of $C$ for which the conclusion of Mean Value Theorem holds for the function $f(x)={\log }_{e}x$ on the interval $[1,3]$ is

Q22.The function $\mathrm{f}(\mathrm{x})={\tan }^{-1}(\sin \mathrm{x}+\cos \mathrm{x})$ is an increasing function in

Q23.Let $\mathrm{A}=\left[\begin{array}{ccc}5& 5\alpha & \alpha \\ 0& \alpha & 5\alpha \\ 0& 0& 5\end{array}\right]$. If $\left|{\mathrm{A}}^2\right|=25$, then $|\alpha |$ equals

Q24.The sum of the series $\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\dots$ upto infinity is

Q25.If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $2\hat{u}\times 3\hat{v}$ is a unit vector for

Q26.A particle just clears a wall of height $b$ at distance $a$ and strikes the ground at a distance $c$ from the point of projection. The angle of projection is

Q27.The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

Q28.The equation of a tangent to the parabola $y^2=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Q29.If $(2,3,5)$ is one end of a diameter of the sphere $x^2+y^2+z^2-6x-12y-2z+20=0$, then the coordinates of the other end of the diameter are

Q30.Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}$, $\bar{b}=\hat{i}-\hat{j}+2\hat{k}$ and $\bar{c}=x\hat{i}+(x-2)\hat{j}-\hat{k}$. If the vector $\bar{c}$ lies in the plane of $\bar{a}$ and $\bar{b}$, then $x$ equals

Q31.Let $A(h,k)$, $B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which 'k' can take is given by

Q32.Let $P=(-1,0)$, $Q=(0,0)$ and $R=(3,3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$

Q33.If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ is

Q34.Let $F(x)=f(x)+f\left(\frac{1}{x}\right)$, where $f(x)={\int }_1^x\frac{\log t}{1+t}dt$. Then $F(e)$ equals

Q35.Let $f:R\to R$ be a function defined by $f(x)=\text{Min}\{x+1,|x|+1\}$. Then which of the following is true?

Q36.The function $f:R\sim \{0\}\to R$ given by
$f(x)=\frac{1}{x}-\frac{2}{e^{2x}-1}$
can be made continuous at $x=0$ by defining $f(0)$ as

Q37.The solution for x of the equation
is

Q38.$\int \frac{dx}{\cos x+\sqrt{3}\sin x}$ equals

Q39.The area enclosed between the curves $y^2=x$ and $y=|x|$ is

Q40.If the difference between the roots of the equation $x^2+ax+1=0$ is less than $\sqrt{5}$, then the set of possible values of $a$ is