6.02 $$\times$$ 1020 molecules of urea are present in 100 ml of its solution. The concentration of urea solution is (Avo

To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H3PO3), the volume of 0.1 M aqueous KOH so

The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100

Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 a

The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, woul

Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 1

Which one of the following ions has the highest value of ionic radius?

Among Al2O3, SiO2, P2O3 and SO2 the correct order of acid strength is

The formation of the oxide ion O2-(g) requires first an exothermic and then an endothermic step as shown below O(g) + e

The correct order of bond angles (smallest first) in H2S, NH3, BF3 and SiH4 is

The bond order in NO is 2.5 while that in NO+ is 3. Which of the following statements is true for these two species?

The states of hybridization of boron and oxygen atoms in boric acid (H3BO3) are respectively

Which one of the following has the regular tetrahedral structure? (Atomic nos : B = 5, S = 16, Ni = 28, Xe = 54)

The maximum number of 90° angles between bond pair of electrons is observed in

As the temperature is raised from 20°C to 40°C, the average kinetic energy of neon atoms changes by a factor of which of

In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure of

An ideal gas expands in volume from 1$$\times$$10-3 m3 to 1 $$\times$$ 10-2 m3 at 300 K against a constant pressure of 1

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1 respectively. The enthalpy of fo

The conjugate base of H2PO4- is :

What is the equilibrium expression for the reaction P4 (s) + 5O2 $$\leftrightharpoons$$ P4O10 (s)?

For the reaction, CO(g) + Cl2(g) $$\leftrightharpoons$$ COCl2(g) the $${{{K_p}} \over {{K_c}}}$$ is equal to :

The equilibrium constant for the reaction N2(g) + O2(g) $$\leftrightharpoons$$ 2NO(g) at temperature T is 4 $$\times$$ 1

The molar solubility (in ol L-1) of a sparingly soluble salt MX4 is "s". The corresponding solubility product is Ksp. 's

One mole of magnesium nitride on the reaction with an excess of water gives :

Which one of the following has the minimum boiling point?

Consider the acidity of the carboxylic acids: (a) PhCOOH (b) o – NO2C6H4COOH (c) p – NO2C6H4COOH (d) m – NO2C6H4COOH

Which of the following will have meso-isomer also?

Which one the following does not have sp2 hybridized carbon?

Which of the following compound is not chiral?

Identify the correct statements regarding enzymes

Which of the following liquid pairs shows a positive deviation from Raoult’s law?

Which one of the following statements is false?

Which one of the following aqueous solutions will exhibit highest boiling point?

For which of the following parameters the structural isomers C2H5OH and CH3OCH3 would be expected to have the same value

In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to :

Consider the following Eo values $$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = 0.77 V; $$E_{S{n^{2 + }}/S{n}}^o$$ = -0.14 V Under

The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25oC. The equilibrium constant of

The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm2 mol-1 respectively. The Λ° for NaB

In a cell that utilises the reaction Zn(s) + 2H+ (aq) $$\to$$ Zn2+(aq) + H2(g) addition of H2SO4 to cathode compartment,

The $$E_{{M^{3 + }}/{M^{2 + }}}^o$$ values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V respectively. Fo

In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken

Consider the following nuclear reactions $${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$ $${}_Y^XN \to {}_B^AL + 2{\beta ^ +

The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]. The correct statement in relation to t

The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after

Which one of the following ores is best concentrated by froth – floatation method?

Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in :

Which one the following statement regarding helium is incorrect?

Which among the following factors is the most important in making fluorine the strongest oxidizing halogen?

Aluminium chloride exists as dimer, Al2Cl6 in solid state as well as in solution of non-polar solvents such as benzene.

Excess of KI reacts with CuSO4 solution and then Na2S2O3 solution is added to it. Which of the statements is incorrect f

Cerium (Z = 58) is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?

Which one of the following complexes in an outer orbital complex?

Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

Coordination compound have great importance in biological systems. In this context which of the following statements is

The coordination number of central metal atom in a complex is determined by :

The correct order of magnetic moments (spin only values in B.M.) among is : (Atomic numbers: Mn = 25; Fe = 26, Co =27)

Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN– ion towards metal spe

The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is

On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is

Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?

Acetyl bromide reacts with excess of CH3MgI followed by treatment with a saturated solution of NH4Cl given

Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?

Which base is present in RNA but not in DNA?

Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to whic

The smog is essentially caused by the presence of :

The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is

Which of the following is the strongest base ?

Amongst the following compounds, the optically active alkane having lowest molecular mass is

Rate of the reaction is fastest when $$Z$$ is

The $$IUPAC$$ name of the compound is

What type of crystal defect is indicated in the diagram below?

Among the following compounds which can be dehydrated very easily is

Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin butt

If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$. If $$sin{\mkern 1mu} \alpha + \sin \be

A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis. If the angle $$\beta \,$$, which it mak

Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ and arg zw = $$\pi $$. Then arg z equals :

If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then $${{\left( {{x \over p} + {y \over q}} \right)} \over {\left

If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on :

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$ then its ro

If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots, t

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

Let $$S(K)$$ $$ = 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.$$ Then which of the following is true

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$

The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is

Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive intege

If $${S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}

The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ....\,is\,{{n{{(n + 1

The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........$$ is

The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes who

Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2, 1} \right)$$ be vertices of a triangle $$ABC$$. If the centroid of

If the sum of the slopes of the lines given by $${x^2} - 2cxy - 7{y^2} = 0$$ is four times their product $$c$$ has the v

If one of the lines given by $$6{x^2} - xy + 4c{y^2} = 0$$ is $$3x + 4y = 0,$$ then $$c$$ equals :

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi $$, then the e

If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus o

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter

Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diamet

If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$

The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$,

If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank

The sides of a triangle are $$\sin \alpha ,\,\cos \alpha $$ and $$\sqrt {1 + \sin \alpha \cos \alpha } $$ for some $$0 &

A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

A function $$y=f(x)$$ has a second order derivative $$f''\left( x \right) = 6\left( {x - 1} \right).$$ If its graph pass

If $$2a+3b+6c=0$$, then at least one root of the equation $$a{x^2} + bx + c = 0$$ lies in the interval

The normal to the curve x = a(1 + cos $$\theta $$), $$y = a\sin \theta $$ at $$'\theta '$$ always passes through the fix

Let $$A = \left( {\matrix{ 0 & 0 & { - 1} \cr 0 & { - 1} & 0 \cr { - 1} & 0 & 0 \c

Let $$A = \left( {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr

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

If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}

$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to

$$\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}} $$ is

The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is

The value of $$I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx} $$

If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then

If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {x

The area of the region bounded by the curves $$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :

The differential equation for the family of circle $${x^2} + {y^2} - 2ay = 0,$$ where a is an arbitrary constant is :

Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$$ is

The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ suc

The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The pro

A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$$ and $$3\widehat i + \widehat j - \wide

Distance between two parallel planes $$\,2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is :

Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ be such that $$\left| {\overrightarrow u } \right| = 1,

If $${\overrightarrow a ,\overrightarrow b ,\overrightarrow c }$$ are non-coplanar vectors and $$\lambda $$ is a real nu

Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero vectors such that no two of t

Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-zero vectors such that $$\left( {\overri

The intersection of the spheres $${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$$ and $${x^2} + {y^2} + {z^2} - 3x + 3y + 4z

A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-

If the straight lines $$x=1+s,y=-3$$$$ - \lambda s,$$ $$z = 1 + \lambda s$$ and $$x = {t \over 2},y = 1 + t,z = 2 - t,$

The range of the function f(x) = $${}^{7 - x}{P_{x - 3}}$$ is

If $$f:R \to S$$, defined by $$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$, is onto, then the interval of $$S$$ is

The domain of the function $$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$

The graph of the function y = f(x) is symmetrical about the line x = 2, then

Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then

Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of

In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the standard deviation of t

Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the posit

If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetw

A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two ca

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice a

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant p

Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is

A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of sta

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for an

A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $$60$$ $$cm$$ hangs freely from the edge

A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$$ is ap

A body of mass $$' m ',$$ acceleration uniformly from rest to $$'{v_1}'$$ in time $${T}$$. The instantaneous power deliv

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle,

A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a m

One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia ab

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the fol

A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circu

If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mas

The time period of an earth satellite in circular orbit is independent of

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retardi

If two soap bubbles of different radii are connected by a tube

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio

One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gam

Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ vo

Which of the following statements is correct for any thermodynamic system ?

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of therma

The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillati

The total energy of particle, executing simple harmonic motion is

A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another

A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omeg

In forced oscillation of a particle the amplitude is maximum for a frequency $${\omega _1}$$ of the force while the ener

The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin $$ $$\left( {100t + 20x +

Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a f

A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which is fixed, with a speed $$'v'$$. It appr

Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the sys

A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. T

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the

The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resist

The total current supplied to the circuit by the battery is

Thermistors are usually made of

Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is

In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is

The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\the

The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at

A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter

The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where th

Curie temperature is the temperature above which

A current $$i$$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any poin

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the c

The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance o

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration mag

Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $${I_2}$$ in the same direction. They exe

The materials suitable for making electromagnets should have

In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components, $$L,C$$ and $$R$$ is $$50V$$. The volt

Alternating current can not be measured by $$D.C.$$ ammeter because

A coil having $$n$$ turns and resistance $$R\Omega $$ is connected with a galvanometer of resistance $$4R\Omega .$$ This

In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircle of radius $$r$$ rotates about the diam

In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, th

A metal conductor of length $$1$$ $$m$$ rotates vertically about one of its ends at angular velocity $$5$$ radians per

A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index

An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a dielectric medium with permittivity $$

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-s

The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emiss

A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a met

The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \righ

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $$2:1.$$ The ratio of their n

An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The d

When $$npn$$ transistor is used as an amplifer

A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of

The manifestation of band structure in solids is due to

For a transistor amplifier in common emitter configuration for load impedance of $$1k\,\Omega $$ $$\left( {{h_{fe}} = 50

When $$p$$-$$n$$ junction diode is forward biased then

A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at t