The compound formed as a result of oxidation of ethyl benzene by KMnO₄ is :

Which one of the following conformation of cyclohexane is chiral?

Presence of a nitro group in a benzene ring

In a sautrated solution of the sparingly soluble strong electrolyte AgIO₃ (Molecular mass = 283) the equilibrium which sets in is
AgIO_3(s) $$\leftrightharpoons$$ Ag⁺(aq) + $$IO_3^-$$
If the solubility product constant K_sp of AgIO₃ at a given temperature is 1.0 $$\times$$10⁻⁸, what is the mass of AgIO₃ contained in 100 ml of its saturated solution?

The pK_a 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 :

The first and second dissociation constants of an acid H₂A are 1.0 $$\times$$ 10⁻⁵ and 5.0 $$\times$$ 10⁻¹⁰ respectively. The overall dissociation constant of the acid will be :

Identify the correct statement regarding a spontaneous process :

In conversion of lime-stone to lime,
CaCO₃(s) $$\to$$ CaO(s) + CO₂ (g) the vales of ∆H° and ∆S° are +179.1 kJ mol−1 and 160.2 J/K respectively at 298 K and 1 bar. Assuming that ∆H° do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :

The reaction of toluene with Cl₂ in presence of FeCl₃ gives predominantly

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

The stability of dihalides of $$Si,Ge,Sn$$ and $$Pb$$ increases steadily in the sequence :

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

Assuming that water vapour is an ideal gas, the internal energy change $$\left( {\Delta U} \right)$$ when $$1$$ mol of water is vapourised at $$1$$ bar pressure and $${100^ \circ }C$$ (Given : molar enthalpy of vapourisation of water at $$1$$ bar and $$373$$ $$K$$ $$ = 41\,kJ\,mo{l^{ - 1}}\,$$
and $$R = 8.3\,J\,mo{l^{ - 1}}\,{K^{ - 1}}$$ )

The secondary structure of a protein refers to

In the chemical reaction,
CH₃CH₂NH₂ + CHCl₃ + 3KOH $$\to$$ (A) + (B) + 3H₂O, the compound (A) and (B) are respectively

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

In the following sequence of reactions,
CH₃CH₂OH $$\buildrel {P + {I_2}} \over \longrightarrow $$ A $$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{ether}^{Mg}} $$ B $$\buildrel {HCHO} \over \longrightarrow $$ C $$\buildrel {{H_2}O} \over \longrightarrow $$ D
the compound ‘D’ is

Which of the following is the correct order of decreasing S_N2 reactivity?

Which one of the following has a square planar geometry?

Identify the incorrect statement among the following :

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

Which of the following nuclear reactions will generate an isotope?

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?

Consider the reaction, 2A + 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

The energies of activation for forward and reverse reactions for A₂ + B₂ $$\leftrightharpoons$$ 2AB are 180 kJ mol⁻¹ and 200 kJ mol⁻¹ respectively. The presence of catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol⁻¹. The enthalpy change of the reaction ( A₂ + B₂ $$\to$$ 2AB) in the presence of catalyst will be (in kJ mol⁻¹)

The cell, Zn | Zn²⁺ (1M) || Cu²⁺ (1M) | Cu($$E_{cell}^o$$ = 1.10V) was allowed to be completely discharged at 298 K. The relative concentration of Zn²⁺ to Cu²⁺ $$\left[ {{{\left[ {Z{n^{2 + }}} \right]} \over {\left[ {C{u^{2 + }}} \right]}}} \right]$$ is

The equivalent conductances of two strong electrolytes at infinite dilution in H₂O (where ions move freely through a solution) at 25^oC are given below:
$$ \wedge _{C{H_3}COONa}^o$$ = 91.0 S cm²/equiv
$$ \wedge _{HCl}^o$$ = 426.2 S cm²/equiv
What additional information/quantity one needs to calculate $$ \wedge ^o$$ of an aqueous solution of acetic acid?

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

A 5.25 % solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol⁻¹) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 g cm⁻³, molar mass of the substance will be

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

Which of the following hydrogen bonds is the strongest?

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

Which of the following species exhibits the diamagnetic behaviour?

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, K⁺, Ca²⁺, Mg²⁺, Be²⁺?

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

In the reaction

2Al(s) + 6HCl(aq) $$\to$$ 2Al³⁺ (aq) + 6Cl^-(aq) + 3H₂(g)

The density (in g mL^-1) of a 3.60 M sulphuric acid solution that is 29% H₂SO₄ (molar mass = 98 g mol^-1) by mass will be

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

The function $$f:R/\left\{ 0 \right\} \to R$$ given by

$$f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}}$$

can be made continuous at $$x$$ = 0 by defining $$f$$(0) as

Let $$f:R \to R$$ be a function defined by

$$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$, then which of the following is true?

The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function

$$f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)$$$$ + \log \left( {\cos x} \right)$$,

is defined, is

If sin^-1$$\left( {{x \over 5}} \right)$$ + cosec^-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$, then the value of x is :

If a line makes an angle of $$\pi /4$$ 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 :

Two aeroplanes $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ bomb a target in succession. The probabilities of $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ 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 :

The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :

Let $$I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx} $$ and $$J = \int\limits_0^1 {{{\cos x} \over {\sqrt x }}dx} .$$ Then which one of the following is true?

The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}} $$ is

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

$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} $$ equals

If $$D = \left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + x} & 1 \cr 1 & 1 & {1 + y} \cr } } \right|$$ for $$x \ne 0,y \ne 0,$$ then $$D$$ is :

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

The function $$f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)$$ is an incresing function in

If $$\widehat u$$ and $$\widehat v$$ are unit vectors and $$\theta $$ is the acute angle between them, then $$2\widehat u \times 3\widehat v$$ is a unit vector for :

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

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

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

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

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

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

If $$\,\left| {z + 4} \right|\,\, \le \,\,3\,$$, then the maximum value of $$\left| {z + 1} \right|$$ is :

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

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 neutron respectively, the nuclear binding energy of the isotope is

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

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

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

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

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

In a Young's double slit experiment the intensity at a point where the path difference is $${\lambda \over 6}$$ ( $$\lambda $$ being the wavelength of light used ) is $$I$$. If $${I_0}$$ denotes the maximum intensity, $${I \over {{I_0}}}$$ is equal to

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

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

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 the wires $$AOB$$ and $$COD$$ , will be given by

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 $$a/2$$ and $$2a$$ is

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

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

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

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

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

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
$${{electro\,\,ch\arg e\,\,on\,\,the\,\,moon} \over {electronic\,\,ch\arg e\,\,on\,\,the\,\,earth}}\,\,to\,be$$

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

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

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

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

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 $$\left( {\sqrt 2 ,\sqrt 2 } \right)$$ and $$\left( {2,0} \right)$$ respectively. The potential difference between the points $$A$$ and $$B$$ will be

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

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

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

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

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

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 length $${L_1}$$ and $${L_2}$$ and thermal conductivities $${K_1}$$ and $${K_2}$$ respectively. The temperature at the interface of the two section is

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

For the given uniform square lamina $$ABCD$$, whose center is $$O,$$

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

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

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

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 center of mass of the new disc is $$\alpha R$$ form the center of the bigger disc. The value of $$\alpha $$ is

A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a spring (massless) of spring constant $$k.$$ The block 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 block of mass $$M$$ to pull it. Find the force of the block of mass $$m.$$

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

The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is