An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm. Pres

Consider an endothermic reaction, X $$\to$$ Y with the activation energies Eb and Ef for the backward and forward reacti

Consider the reaction: N2 + 3H2 $$\to$$ 2NH3 carried out at constant temperature and pressure. If $$\Delta H$$ and $$\De

If the bond dissociation energies of XY, X2 and Y2 (all diatomic molecules) are in the ratio of 1:1:0.5 and $$\Delta H_f

The solubility product of a salt having general formula MX2, in water is: 4 $$\times$$ 10-12 . The concentration of M2+

If $$\alpha$$ is the degree of dissociation of Na2SO4, the vant Hoff’s factor (i) used for calculating the molecular mas

The exothermic formation of ClF3 is represented by the equation: Cl2 (g) + 3F2 (g) $$\leftrightharpoons$$ 2ClF3 (g); $$

For the reaction 2NO2 (g) $$\leftrightharpoons$$ 2NO (g) + O2 (g), (Kc = 1.8 $$\times$$ 10-6 at 184oC) (R = 0.0831 kJ/(m

Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be :

What is the conjugate base of OH-?

Which one of the following species is diamagnetic in nature?

Due to the presence of an unpaired electron, free radicals are:

Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is

2 methylbutane on reacting with bromine in the presence of sunlight gives mainly

Reaction of one molecule of HBr with one molecule of 1,3-butadiene at 40oC gives predominantly

Acid catalyzed hydration of alkenes except ethene leads to the formation of

Which types of isomerism is shown by 2,3-dichlorobutane?

Benzene and toluene form nearly ideal solutions. At 20 oC, the vapour pressure of benzene is 75 torr and that of toluene

Equimolar solutions in the same solvent have

Which one of the following methods is neither meant for the synthesis nor for separation of amines?

Amongst the following the most basic compound is

An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% and N = 46.67% while rest is oxygen.

In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-

Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound if water du

The decreasing order of nucleophilicity among the nucleophiles

The reaction is fastest when $$X$$ is

A schematic plot of $$ln$$ $${K_{eq}}$$ versus inverse of temperature for a reaction is shown below The reaction must

$$p$$-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the c

The oxidation state of chromium in the final product formed the reaction between $$K{\rm I}$$ and acidified potassium di

On heating mixture of $$C{u_2}O$$ and $$C{u_2}S$$ will give :

Calomel $$\left( {H{g_2}C{l_2}} \right)$$ on reaction with ammonium hydroxide gives :

Pick out the isoelectronic structure from the following : $$\eqalign{ & \left( i \right)\,\,\,\,\,\,C{H_3}^ + \

For a spontaneous reaction the ∆G , equilibrium constant (K) and $$E_{cell}^o$$ will be respectively

Aluminium oxide may be electrolysed at 1000oC to furnish aluminium metal (Atomic mass = 27 amu; 1 Faraday = 96,500 Coulo

The highest electrical conductivity of the following aqueous solutions is of :

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Hydrogen bomb is based on the principle of

A reaction involving two different reactants can never be

The photon of hard gamma radiation knocks a proton out of $${}_{12}^{24}Mg$$ nucleus to form

t1/4 can be taken as the time taken for the concentration of a reactant to drop to $$3 \over 4$$ of its initial value. I

The lanthanide contraction is responsible for the fact that :

Which of the following factors may be regarded as the main cause of lanthanide contraction?

The oxidation state of Cr in [Cr(NH3)4Cl2]+ is :

The IUPAC name of the coordination compound K3[Fe(CN)6] is

The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is :

Which of the following compounds shows optical isomerism?

Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (At. No. Cr = 24,

Tertiary alkyl halides are practically inert to substitution by SN2 mechanism because of

Elimination of bromine from 2-bromobutane results in the formation of-

Alkyl halides react with dialkyl copper reagents to give

The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one is

Among the following acids which has the lowest pKa value?

Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 m

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of

Of the following sets which one does NOT contain isoelectronic species?

In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same ener

Which of the following oxides is amphoteric in character?

In which of the following arrangements the order is NOT according to the property indicated against it?

Lattice energy of an ionic compounds depends upon

Let $$f:( - 1,1) \to B$$, be a function defined by $$f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$, then

A real valued function f(x) satisfies the functional equation f(x - y) = f(x)f(y) - f(a - x)f(a + y) where a is given co

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is i

Suppose $$f(x)$$ is differentiable at x = 1 and $$\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) =

Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then $$\mathop {\lim }\limits_{x \to \alp

If $$f$$ is a real valued differentiable function satisfying $$\left| {f\left( x \right) - f\left( y \right)} \right|$$

Let x1, x2,...........,xn be n observations such that $$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a possibl

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :

The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a

If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals

If the cube roots of unity are 1, $$\omega \,,\,{\omega ^2}$$ then the roots of the equation $${(x - 1)^3}$$ + 8 = 0, ar

The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\,\,a > 0,} $$ is

Area of the greatest rectangle that can be inscribed in the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}}

A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$5

If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is :

The system of equations $$\matrix{ {\alpha \,x + y + z = \alpha - 1} \cr {x + \alpha y + z = \alpha - 1} \cr

If $${a_1},{a_2},{a_3},........,{a_n},.....$$ are in G.P., then the determinant $$$\Delta = \left| {\matrix{ {\log {

If $${a^2} + {b^2} + {c^2} = - 2$$ and f$$\left( x \right) = \left| {\matrix{ {1 + {a^2}x} & {\left( {1 + {b^2}

$$\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx} $$ is

If $${I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}

The area enclosed between the curve $$y = {\log _e}\left( {x + e} \right)$$ and the coordinate axes is :

The parabolas $${y^2} = 4x$$ and $${x^2} = 4y$$ divide the square region bounded by the lines $$x=4,$$ $$y=4$$ and the c

Let $$f(x)$$ be a non - negative continuous function such that the area bounded by the curve $$y=f(x),$$ $$x$$-axis and

If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$ then $$4{x^2} - 4xy\cos \alpha + {y^2}$$ is equal to :

The value of integral, $$\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \sqrt x }}} dx $$ is

The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c>0,

If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solution of the equation is :

A random variable $$X$$ has Poisson distribution with mean $$2$$. Then $$P\left( {X > 1.5} \right)$$ equals :

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consult

Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},$$ $$P\left( {A \cap B}

If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then :

Let $$a, b$$ and $$c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\,\,\w

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :

For any vector $${\overrightarrow a }$$ , the value of $${\left( {\overrightarrow a \times \widehat i} \right)^2} + {\

If a vertex of a triangle is $$(1, 1)$$ and the mid points of two sides through this vertex are $$(-1, 2)$$ and $$(3, 2)

If $$\,\omega = {z \over {z - {1 \over 3}i}}\,$$ and $$\left| \omega \right| = 1$$, then $$z$$ lies on :

If $${z_1}$$ and $${z_2}$$ are two non-zero complex numbers such that $$\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}

In a triangle $$PQR,\;\;\angle R = {\pi \over 2}.\,\,If\,\,\tan \,\left( {{P \over 2}} \right)$$ and $$ \tan \left( {{Q

If both the roots of the quadratic equation $${x^2} - 2kx + {k^2} + k - 5 = 0$$ are less than 5, then $$k$$ lies in the

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, the

If the coefficient of $${x^7}$$ in $${\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}$$ equals the coe

If $$x$$ is so small that $${x^3}$$ and higher powers of $$x$$ may be neglected, then $${{{{\left( {1 + x} \right)}^{{3

If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of $${{\rm{(1 + y )}}^m}$$ are in A

If $$x = \sum\limits_{n = 0}^\infty {{a^n},\,\,y = \sum\limits_{n = 0}^\infty {{b^n},\,\,z = \sum\limits_{n = 0}^\inft

The line parallel to the $$x$$ - axis and passing through the intersection of the lines $$ax + 2by + 3b = 0$$ and $$bx -

If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = {p^2}$$ orthogonally, then the equ

If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, =

If the pair of lines $$a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$$ lie along diameters of a circle and divide the

An ellipse has $$OB$$ as semi minor axis, $$F$$ and $$F$$' its focii and theangle $$FBF$$' is a right angle. Then the ec

Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x$$. The locus of mid point of $$PQ$$ is

The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a -

Let $$f:R \to R$$ be a differentiable function having $$f\left( 2 \right) = 6$$, $$f'\left( 2 \right) = \left( {{1 \o

If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals

If non zero numbers $$a, b, c$$ are in $$H.P.,$$ then the straight line $${x \over a} + {y \over b} + {1 \over c} = 0$$

Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12)$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$. The relati

A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of $2 \mathrm{~cm} / \ma

In a full wave rectifier circuit operating from $$50$$ $$Hz$$ mains frequency, the fundamental frequency in the ripple w

A nuclear transformation is denoted by $$X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li.$$ Which of th

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of

A photocell is illuminated by a small bright source placed $$1$$ $$m$$ away. When the same source of light is placed $${

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of w

A moving coil galvanometer has $$150$$ equal divisions. Its current sensitivity is $$10$$- divisions per milliampere and

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge $$q$$ flows through the

The resistance of hot tungsten filament is about $$10$$ times the cold resistance. What will be resistance of $$100$$ $$

An energy source will supply a constant current into the load if its internal resistance is

A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of radius $$r$$ that is perpendicular to a

A magnetic needle is kept in a non-uniform magnetic field. It experiences :

Two concentric coils each of radius equal to $$2$$ $$\pi $$ $$cm$$ are placed at right angles to each other. $$3$$ ampe

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an ele

The self inductance of the motor of an electric fan is $$10$$ $$H$$. In order to impart maximum power at $$50$$ $$Hz$$,

The phase difference between the alternating current and $$emf$$ is $${\pi \over 2}.$$ Which of the following cannot be

A circuit has a resistance of $$12$$ $$ohm$$ and an impedance of $$15$$ $$ohm$$. The power factor of the circuit will be

A coil of inductance $$300$$ $$mH$$ and resistance $$2\,\Omega $$ is connected to a source of voltage $$2$$ $$V$$. The c

Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by eye of pupil diameter $$3$$ $$mm.$$ App

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen

A thin glass (refractive index $$1.5$$) lens has optical power of $$-5$$ $$D$$ in air. Its optical power in a liquid med

If $${I_0}$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its int

When an unpolarized light of intensity $${{I_0}}$$ is incident on a polarizing sheet, the intensity of the light which d

One conducting $$U$$ tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than $$248

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

In the circuit, the galvanometer $$G$$ shows zero deflection. If the batteries $$A$$ and $$B$$ have negligible internal

Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \rig

The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$d$$ below

If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is

A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is

A block is kept on a frictionless inclined surface with angle of inclination $$'\,\alpha \,'.$$ The incline is given an

The block of mass $$M$$ moving on the frictionless horizontal surface collides with the spring of spring constant $$k$$

A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass. After collision the

Which of the following is incorrect regarding the first law of thermodynamics?

A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio $${{Cp} \over {{C_v}}}$$ of t

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $$'\,\,\overrightarrow F \,\,

A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delt

The figure shows a system of two concentric spheres of radii $${r_1}$$ and $${r_2}$$ are kept at temperatures $${T_1}$$

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

The function $${\sin ^2}\left( {\omega t} \right)$$ represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscilla

If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is

When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, so

A parallel plate capacitor is made by stacking $$n$$ equally spaced plates connected alternatively. If the capacitance b

Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$

Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ apart with their axes coinciding. The char

A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta $$ with a large charged conducting sheet

A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a small coil of resistance wire embedded i

Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current of $$'i'$$ $$A$$ in the same direction.

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

Two sources of equal $$emf$$ are connected to an external resistance $$R.$$ The internal resistance of the two sources

A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm

Out of the following pair, which one does NOT have identical dimensions is

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The ave

The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is

A bullet fired into a fixed target loses half of its velocity after penetrating $$3$$ $$cm.$$ How much further it will p

A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parachute opens, it decelerates at $$2\,\,m/{

A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to s

Consider a car moving on a straight road with a speed of $$100$$ $$m/s$$. The distance at which car can be stopped is $$

A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. What will be its initial acceleration if

An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular sp

The upper half of an inclined plane with inclination $$\phi $$ is perfectly smooth while the lower half is rough. A body

A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of height $$100$$ $$m$$. It rolls down a smoo

A body of mass $$m$$ is accelerated uniformly from rest to a speed $$v$$ in a time $$T.$$ The instantaneous power delive

The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the pl

A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass

Average density of the earth