Which one of the following statements is not true?

The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a rever

In an irreversible process taking place at constant T and P and in which only pressure-volume work is being done, the ch

The enthalpy change for a reaction does not depend upon :

The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc is :

If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respectively 414, 347, 615 and 435 kJ/mol, the

The solubility in water of a sparingly soluble salt AB2 is 1.0 $$\times$$ 10-5 mol L-1. Its solubility product number wi

Consider the reaction equilibrium 2 SO2 (g) + O2 (g) $$\leftrightharpoons$$ 2 SO3 (g); $$\Delta H^o$$ = -198 kJ One the

For the reaction equilibrium N2O4 (g) $$\leftrightharpoons$$ 2NO2 (g) the concentrations of N2O4 and NO2 at equilibrium

When rain is accompanied by a thunderstorm, the collected rain water will have a pH value :

The IUPAC name of CH3COCH(CH3)2 is

In the anion HCOO$$-$$ the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?

The general formula CnH2nO2 could be for open chain

On mixing a certain alkane with chlorine and irradiating it with ultravioletlight, it forms only one monochloroalkane. T

Butene-1 may be converted to butane by reaction with

During dehydration of alcohols to alkenes by heating with conc. H2SO4 the initiation step is

When CH2 = CH - COOH is reduced with LiAlH4, the compound obtained will be

The correct order of increasing basic nature for the bases NH3, CH3NH2 and (CH3)2 NH is

Ethyl isocyanide on hydrolysis in acidic medium generates

Complete hydrolysis of cellulose gives

Which one of the following statements is correct?

Bottles containing C6H5l and C6H5CH2I lost their original labels. They were labelled A and B for testing A and B were se

Among the following four structures $$i$$ to $$iv,$$ it is true that

The reduction in atomic size with increase in atomic number is a characteristic of elements of

The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe), respectively, $$23,24,25$$ and $$26$$.

The reaction of chloroform with alcoholic $$KOH$$ and p-toluidine forms

The reason for double helical structure of $$DNA$$ is operation of

A red solid is insolvable in water. However it becomes soluble if some $$K{\rm I}$$ is added to water. Heating the red s

A pressure cooker reduces cooking time for food because

In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf for water as 1.85, the free

If liquids A and B form an ideal solution

Standard reduction electrode potentials of three metals A,B&C are respectively +0.5 V, -3.0 V & -1.2 V. The redu

For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be 0.295 V at 25oC. The

When during electrolysis of a solution of AgNO3, 9650 coulombs of charge pass through the electroplating bath, the mass

For the redox reaction Zn(s) + Cu2+(0.1 M) $$\to$$ Zn2+(1M) + Cu(s) taking place in a cell, $$E_{cell}^o$$ is 1.10 volt

Several blocks of magnesium are fixed to the bottom of a ship to :

The radionucleide $${}_{90}^{234}Th$$ undergoes two successive $$\beta$$ -decays followed by one $$\alpha$$-decay. The a

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it rem

In respect of the equation k = Ae-Ea/RT in chemical kinetics, which one of the following statements is correct?

The rate law for a reaction between the substances A and B is given by Rate = k[A]n [B]m On doubling the concentration o

For the reaction system: 2NO(g) + O2(g) $$\to$$ 2NO2(g) volume is suddenly reduce to half its value by increasing the p

Which one of the following substances has the highest proton affinity?

For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liqu

Glass is a :

What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?

The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Whic

Which one of the following nitrates will leave behind a metal on strong heating?

Ammonia forms the complex ion [Cu(NH3)4]2+ with copper ions in alkaline solutions but not in acidic solutions. What is t

The radius of La3+ (Atomic number of La = 57) is 1.06 Å. Which one of the following given values will be closest to the

One mole of the complex compound Co(NH3)5Cl3, gives 3 moles of ions on dissolution in water. One mole of the same comple

In the coordination compound, K4[Ni(CN)4], the oxidation state of nickel is :

The pair of species having identical shapes for molecules of both species is

What volume of hydrogen gas at 273 K and 1 atm pressure will be consumed in obtaining 21.6 g of elemental boron (atomic

25 ml of a solution of barium hydroxide on titration with a 0.1 molar solution of hydrochloric acid gave a litre value o

The number of d-electrons retained in Fe2+ (At no of Fe = 26) ion is :

The orbital angular momentum for an electron revolving in an orbit is given by $$\sqrt {l(l + 1)} {h \over {2\pi }}$$. T

Which one of the following groupings represents a collection of isoelectronic species? (At. nos. : Cs : 55, Br : 35)

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following

The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximately

According to the Periodic Law of elements, the variation in properties of elements is related to their

Which one of the following is an amphoteric oxide?

An ethar is more volatile than an alcohol having the same molecular formula. This is due to

Which one of the following pairs of molecules will have permanent dipole moments for both members

Which one of the following compounds has the smallest bond angle in its molecule?

The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$$ is

The function $$f\left( x \right)$$ $$ = \log \left( {x + \sqrt {{x^2} + 1} } \right)$$, is

A function $$f$$ from the set of natural numbers to integers defined by $$$f\left( n \right) = \left\{ {\matrix{ {{{n

If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$ \in $$ R and $$f$$(1) = 7, then $$\sum\li

Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is

If $$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}$$ = k, the v

Let $$f(a) = g(a) = k$$ and their nth derivatives $${f^n}(a)$$, $${g^n}(a)$$ exist and are not equal for some n. Further

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin

If $$f(x) = \left\{ {\matrix{ {x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0

In an experiment with 15 observations on $$x$$, then following results were available: $$\sum {{x^2}} = 2830$$, $$\sum

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select

The trigonometric equation $${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$ has a solution for :

If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where $$a>0,$$ attains its maximum and minim

If $$A = \left[ {\matrix{ a & b \cr b & a \cr } } \right]$$ and $${A^2} = \left[ {\matrix{ \alpha

If $$1,$$ $$\omega ,{\omega ^2}$$ are the cube roots of unity, then $$\Delta = \left| {\matrix{ 1 & {{\omega ^

If the system of linear equations $$x + 2ay + az = 0;$$ $$x + 3by + bz = 0;\,\,x + 4cy + cz = 0;$$ has a non - zero so

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

Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)$$ be a function that satisfies $$f\left(

If $$f\left( {a + b - x} \right) = f\left( x \right)$$ then $$\int\limits_a^b {xf\left( x \right)dx} $$ is equal to

The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx} $$ is

The solution of the differential equation $$\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right){{

The degree and order of the differential equation of the family of all parabolas whose axis is $$x$$-axis, are respectiv

Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) = {{3x + 1} \over 3},$$ $$P\left( B \righ

If $$\overrightarrow a \times \overrightarrow b = \overrightarrow b \times \overrightarrow c = \overrightarrow c \t

Let $$\overrightarrow u = \widehat i + \widehat j,\,\overrightarrow v = \widehat i - \widehat j$$ and $$\overrightarro

The vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k\,\,\& \,\,\overrightarrow {AC} = 5\widehat i - 2\wi

The two lines $$x=ay+b,z=cy+d$$ and $$x = a'y + b',z = c'y + d'$$ will be perpendicular, if and only if :

The lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2}

$$\overrightarrow a \,,\overrightarrow b \,,\overrightarrow c $$ are $$3$$ vectors, such that $$\overrightarrow a + \o

A tetrahedron has vertices at $$O(0,0,0), A(1,2,1) B(2,1,3)$$ and $$C(-1,1,2).$$ Then the angle between the faces $$OAB$

If $$\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {

Consider points $$A, B, C$$ and $$D$$ with position vectors $$7\widehat i - 4\widehat j + 7\widehat k,\widehat i - 6\wi

Let $${Z_1}$$ and $${Z_2}$$ be two roots of the equation $${Z^2} + aZ + b = 0$$, Z being complex. Further , assume that

If $${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$$ then :

If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the sum of the squares of their re

The value of '$$a$$' for which one root of the quadratic equation $$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a

The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is

The real number $$x$$ when added to its inverse gives the minimum sum at $$x$$ equal :

If $$x$$ is positive, the first negative term in the expansion of $${\left( {1 + x} \right)^{27/5}}$$ is

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

The number of integral terms in the expansion of $${\left( {\sqrt 3 + \root 8 \of 5 } \right)^{256}}$$ is

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five

If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}

A square of side a lies above the $$x$$-axis and has one vertex at the origin. The side passing through the origin makes

If $${x_1},{x_2},{x_3}$$ and $${y_1},{y_2},{y_3}$$ are both in G.P. with the same common ratio, then the points $$\left(

Locus of centroid of the triangle whose vertices are $$\left( {a\cos t,a\sin t} \right),\left( {b\sin t, - b\cos t} \rig

If the equation of the locus of a point equidistant from the point $$\left( {{a_{1,}}{b_1}} \right)$$ and $$\left( {{a_{

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the c

The foci of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the hyperbola $${{{x^2}} \over {144}}

If $$f\left( y \right) = {e^y},$$ $$g\left( y \right) = y;y > 0$$ and $$F\left( t \right) = \int\limits_0^t {f\left(

If $$f\left( x \right) = {x^n},$$ then the value of $$f\left( 1 \right) - {{f'\left( 1 \right)} \over {1!}} + {{f''\lef

Let $$f\left( x \right)$$ be a polynomial function of second degree. If $$f\left( 1 \right) = f\left( { - 1} \right)$$

If $$z$$ and $$\omega $$ are two non-zero complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$Arg(z) - Arg

Which of the following atoms has the lowest ionization potential ?

The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \right)$$ are slightly different from that of

In the nuclear fusion reaction $$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$ given that the repulsive potential energy betwe

In the middle of the depletion layer of a reverse- biased $$p$$-$$n$$ junction, the

Two identical photo-cathodes receive light of frequencies $${f_1}$$ and $${f_2}$$. If the velocities of the photo electr

If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from

In an oscillating $$LC$$ circuit the maximum charge on the capacitor is $$Q$$. The charge on the capacitor when the ener

The length of a given cylindrical wire is increased by $$100\% $$. Due to the consequent decrease in diameter the change

The thermo $$e.m.f.$$ of a thermo -couple is $$25$$ $$\mu V/{}^ \circ C$$ at room temperature. A galvanometer of $$40$$

An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ t

The nagative $$Zn$$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $$0.13g$$

A $$3$$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current $

A $$220$$ volt, $$1000$$ watt bulb is connected across a $$110$$ $$volt$$ mains supply. The power consumed will be

A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\overrightarrow v $$ describe a circular path of radius

A particle of charge $$ - 16 \times {10^{ - 18}}$$ coulomb moving with velocity $$10m{s^{ - 1}}$$ along the $$x$$-axis e

A magnetic needle lying parallel to a magnetic field requires $$W$$ units of work to turn it through $${60^ \circ }.$$ T

The magnetic lines of force inside a bar magnet

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

When the current changes from $$ + 2A$$ to $$-2A$$ in $$0.05$$ second, an $$e.m.f.$$ of $$8$$ $$V$$ is inducted in a coi

The core of any transformer is laminated so as to

To demonstrate the phenomenon of interference, we require two sources which emit radiation

To get three images of a single object, one should have two plane mirrors at an angle of

The image formed by an objective of a compound microscope is

A strip of copper and another of germanium are cooled from room temperature to $$80K.$$ The resistance of

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to

Three charges $$ - {q_1}, + {q_2}$$ and $$ - {q_3}$$ are placed as shown in the figure. The $$x$$-component of the force

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the

A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $

Let $$\overrightarrow F $$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\over

The time period of satellite of earth is $$5$$ hours. If the separation between the earth and the satellite is increased

The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is

Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space wit

Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow v \,\,.$$ These forces ar

A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of frict

''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or conseq

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature.

Which of the following parameters does not characterize the thermodynamic state of mattter?

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $

A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the

Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k

The displacement of particle varies according to the relation $$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$

The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in t

A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$

A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two r

The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by $$$y = {10^{ - 4}}\,\sin \left( {600t -

A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The b

If the electric flux entering and leaving an enclosed surface respectively is $${\phi _1}$$ and $${\phi _2},$$ the elect

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of th

A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of th

The work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity $$100$$ micro-farad is

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are

The physical quantities not having same dimensions are

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a spee

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $$30^\circ $$ with

The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha $$t3 and y = βt3. The speed to the parti

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N

A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from

A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$

A block of mass $$M$$ is pulled along a horizontal frictionless surface by a rope of mass $$m.$$ If a force $$P$$ is app

A rocket with a lift-off mass $$3.5 \times {10^4}\,\,kg$$ is blasted upwards with an initial acceleration of $$10m/{s^2}

Consider the following two statements : $$A.$$ Linear momentum of a system of particles is zero $$B.$$ Kinetic energy o

A spring of spring constant $$5 \times {10^3}\,N/m$$ is stretched initially by $$5$$ $$cm$$ from the unstretched positio

A wire suspended vertically from one of its ends is stretched by attaching a weight of $$200N$$ to the lower end. The we