For the reactions
2C + O₂ $$\to$$ 2CO₂; $$\Delta H$$ = -393 J
2Zn + O₂ $$\to$$ 2ZnO; $$\Delta H$$ = -412 J

If an endothermic reaction is non-spontaneous at freezing point of water and becomes feasible at its boiling point, then :

The heat required to raise the temperature of body by 1 K is called :

A heat engine absorbs heat Q₁ at temperature T₁ and heat Q₂ at temperature T₂. Work done by the engine is J (Q₁ + Q₂). This data :

Change in volume of the system does not alter which of the following equilibria?

For the reaction CO (g) + (1/2) O₂ (g) $$\leftrightharpoons$$ CO₂ (g), K_p/K_c is :

Species acting as both Bronsted acid and base is :

1 M NaCL and 1 M HCL are present in an aqueous solution. The solution is

Let the solubility of an aqueous solution of Mg(OH)₂ be x then its K_sp is :

The functional group, which is found in amino acid is

The reaction :
$${(CH)_3}C - Br\buildrel {{H_2}O} \over \longrightarrow {(CH)_3}C - OH$$

A similarity between optical and geometrical isomerism is that

In which of the following species is the underlined carbon having sp³ hybridisation?

Which of the following does not show geometrical isomerism?

Racemic mixture is formed by mixing two

Arrangement of (CH₃)₃C-, (CH₃)₂CH-, CH₃-CH₂- when attached to benzyl or an unsaturated group in increasing order of inductive effect is

Which of these will not react with acetylene ?

What is the product when acetylene reacts with hypochlorous acid ?

Freezing point of an aqueous solution is (-0.186)^oC. Elevation of boiling point of the same solution is K_b = 0.512 ^oC, K_f = 1.86 ^oC, find the increase in boiling point.

In a mixture of A and B, components show negative deviation when :

CH₃ - Mg - Br is an organometallic compound due to :

How do we differentiate between Fe³⁺ and Cr³⁺ in group III?

When primary amine reacts with chloroform in ethanoic KOH then the product is

RNA is different from DNA because RNA contains

Which of the following compounds has wrong $$IUPAC$$ name ?

The correct order of ionic radius is

The type isomerism present in nitropentammine chromium $$\left( {{\rm I}{\rm I}{\rm I}} \right)$$ chloride is :

Picric acid is :

$$C{e^{ + 3}},\,\,L{a^{ + 3}},\,\,P{m^{ + 3}}\,\,$$ and $$Y{b^{ + 3}}\,\,$$ have ionic radial in the increasing order as

Following types of compounds (as $$I, II$$ )



are studied in terms of isomerism in :

A square planar complex is formed by hybridisation of which atomic orbitals ?

For the following cell with hydrogen electrodes at two different pressure p₁ and p₂. What will be the emf for the given cell :

$$\eqalign{ & Pt({H_2})|{H^ + }(aq)|Pt({H_2}) \cr & \,\,\,\,\,{p_1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,1M\,\,\,\,\,\,\,\,\,\,\,\,{p_2} \cr} $$

When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate electrodes are :

EMF of a cell in terms of reduction potential of its left and right electrodes is :

Which of the following is a redox reaction ?

Which of the following reaction is possible at anode?

Conductivity (Seimen’s S) is directly proportional to area of the vessel and the concentration of the solution in it and is inversely proportional to the length of the vessel then, then constant of proportionality is expressed in :

$$\beta$$ - particle is emitted in radioactivity by

If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

For the reaction A + 2B $$\to$$ C, rate is given by R = [A] [B]² then the order of the reaction is

The differential rate law for the reaction H₂ + I₂ $$\to$$ 2HI is

Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively

The integrated rate equation is Rt = log C₀ - log C_t . The straight line graph is obtained by plotting

Oxidation number of Cl in CaOCl₂ (bleaching powder) is :

Which of the following statements is true?

The most stable ion is :

Which of the following ions has the maximum magnetic moment?

When KMnO₄ acts as an oxidising agent and ultimately forms [MnO₄]^-2, MnO₂, Mn₂O₃, Mn⁺² then the number of electrons transferred in each case respectively is :

Most common oxidation states of Ce (cerium) are :

What is B?

Number of atoms in 558.5 gram Fe (at. wt. of Fe = 55.85 g mol^-1) is

With increase of temperature, which of these changes?

In a compound C, H and N atoms are present in 9 : 1 : 3.5 by weight . Molecular weight of the compound is 108 g mol^-1 . Molecular formula of compound is

Uncertainty in position of a minute particle of mass 25 g in space is 10^-5 m. What is the uncertainty in its velocity (in ms^-1) (h = 6.6 $$\times$$ 10^-34 Js)

In a hydrogen atom, if energy of an electron in ground state is -13.6 eV, then that in the 2^nd excited state is

Which of the following are arranged in an increasing order of their bond strengths?

Hybridisation of underline atom changes in

In which of the following species the interatomic bond angle is 109^o28' ?

Acetylene does not react with :

For a cell given below


$$ \begin{aligned} \mathrm{Ag}^{+}+\mathrm{e}^{-} & \longrightarrow \mathrm{Ag}; E^{\circ}=x \\\\ \mathrm{Cu}^{2+}+2 e^{-} & \longrightarrow \mathrm{Cu}{;} E^{\circ}=y \end{aligned} $$

$$ E^{\circ} \text { cell is } $$ :

If $$f\left( 1 \right) = 1,{f'}\left( 1 \right) = 2,$$ then
$$\mathop {\lim }\limits_{x \to 1} {{\sqrt {f\left( x \right)} - 1} \over {\sqrt x - 1}}$$ is

$$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}$$ is

The domain of $${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {{x \over 3}} \right)} \right]$$ is

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

$$f$$ is defined in $$\left[ { - 5,5} \right]$$ as

$$f\left( x \right) = x$$ if $$x$$ is rational

$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = - x$$ if $$x$$ is irrational. Then

If f(x + y) = f(x).f(y) $$\forall $$ x, y and f(5) = 2, f'(0) = 3, then
f'(5) is

$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$

Let $$f(2) = 4$$ and $$f'(x) = 4.$$

Then $$\mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \over {x - 2}}$$ is given by

f(x) and g(x) are two differentiable functions on [0, 2] such that

f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3, g(2) = 9

then f(x) - g(x) at x = $${3 \over 2}$$ is

$$\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}$$, $$n \in N$$, ( [x] denotes the greatest integer less than or equal to x )

A triangle with vertices $$\left( {4,0} \right),\left( { - 1, - 1} \right),\left( {3,5} \right)$$ is :

Locus of mid point of the portion between the axes of

$$x$$ $$cos$$ $$\alpha + y\,\sin \alpha = p$$ where $$p$$ is constant is :

The period of $${\sin ^2}\theta $$ is

$$\int_{ - \pi }^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} dx$$ is

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :

If $$y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},$$ then $$\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}$$ is

$${\cot ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) - {\tan ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) = x,$$ then sin x is equal to :

The maximum distance from origin of a point on the curve
$$x = a\sin t - b\sin \left( {{{at} \over b}} \right)$$
$$y = a\cos t - b\cos \left( {{{at} \over b}} \right),$$ both $$a,b > 0$$ is

If $$a>0$$ and discriminant of $$\,a{x^2} + 2bx + c$$ is $$-ve$$, then
$$\left| {\matrix{ a & b & {ax + b} \cr b & c & {bx + c} \cr {ax + b} & {bx + c} & 0 \cr } } \right|$$ is equal to

$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ then $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]$$ equals

If $$y=f(x)$$ makes +$$ve$$ intercept of $$2$$ and $$0$$ unit on $$x$$ and $$y$$ axes and encloses an area of $$3/4$$ square unit with the axes then $$\int\limits_0^2 {xf'\left( x \right)dx} $$ is

The area bounded by the curves $$y = \ln x,y = \ln \left| x \right|,y = \left| {\ln {\mkern 1mu} x} \right|$$ and $$y = \left| {\ln \left| x \right|} \right|$$ is :

$$\int\limits_0^{10\pi } {\left| {\sin x} \right|dx} $$ is

$$\int\limits_0^2 {\left[ {{x^2}} \right]dx} $$ is

$$A$$ and $$B$$ are events such that $$P\left( {A \cup B} \right) = 3/4$$,$$P\left( {A \cap B} \right) = 1/4,$$
$$P\left( {\overline A } \right) = 2/3$$ then $$P\left( {\overline A \cap B} \right)$$ is :

The solution of the equation $$\,{{{d^2}y} \over {d{x^2}}} = {e^{ - 2x}}$$

The order and degree of the differential equation
$$\,{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \over {d{x^3}}}$$ are

A problem in mathematics is given to three students $$A,B,C$$ and their respective probability of solving the problem is $${1 \over 2},{1 \over 3}$$ and $${1 \over 4}.$$ Probability that the problem is solved is :

If the vectors $$\overrightarrow c ,\overrightarrow a = x\widehat i + y\widehat j + z\widehat k$$ and $$\widehat b = \widehat j$$ are such that $$\overrightarrow a ,\overrightarrow c $$ and $$\overrightarrow b $$ form a right handed system then $${\overrightarrow c }$$ is :

$$\overrightarrow a = 3\widehat i - 5\widehat j$$ and $$\overrightarrow b = 6\widehat i + 3\widehat j$$ are two vectors and $$\overrightarrow c $$ is a vector such that $$\overrightarrow c = \overrightarrow a \times \overrightarrow b $$ then $$\left| {\overrightarrow a } \right|:\left| {\overrightarrow b } \right|:\left| {\overrightarrow c } \right|$$ =

If $$\left| {\overrightarrow a } \right| = 5,\left| {\overrightarrow b } \right| = 4,\left| {\overrightarrow c } \right| = 3$$ thus what will be the value of $$\left| {\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a } \right|,$$ given that $$\overrightarrow a + \overrightarrow b + \overrightarrow c = 0$$ :

If $$\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2$$ and the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$\pi /6$$ then $${\left( {\overrightarrow a \times \overrightarrow b } \right)^2}$$ is equal to :

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :

Which one is not periodic?

Product of real roots of equation $${t^2}{x^2} + \left| x \right| + 9 = 0$$

Difference between the corresponding roots of $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ is same and $$a \ne b,$$ then

The locus of the centre of a circle which touches the circle $$\left| {z - {z_1}} \right| = a$$ and$$\left| {z - {z_2}} \right| = b\,$$ externally

($$z,\,{z_1}\,\& \,{z_2}\,$$ are complex numbers) will be :

If $$a,\,b,\,c$$ are distinct $$ + ve$$ real numbers and $${a^2} + {b^2} + {c^2} = 1$$ then $$ab + bc + ca$$ is

If $$\alpha \ne \beta $$ but $${\alpha ^2} = 5\alpha - 3$$ and $${\beta ^2} = 5\beta - 3$$ then the equation having $$\alpha /\beta $$ and $$\beta /\alpha \,\,$$ as its roots is

If $$\left| {z - 4} \right| < \left| {z - 2} \right|$$, its solution is given by :

z and w are two nonzero complex numbers such that $$\,\left| z \right| = \left| w \right|$$ and Arg z + Arg w =$$\pi $$ then z equals

If $$p$$ and $$q$$ are the roots of the equation $${x^2} + px + q = 0,$$ then

The positive integer just greater than $${\left( {1 + 0.0001} \right)^{10000}}$$ is

The sum of integers from 1 to 100 that are divisible by 2 or 5 is :

The coefficients of $${x^p}$$ and $${x^q}$$ in the expansion of $${\left( {1 + x} \right)^{p + q}}$$ are

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :

Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :

Fifth term of a GP is 2, then the product of its 9 terms is

If 1, $${\log _9}\,\,({3^{1 - x}} + 2),\,\,{\log _3}\,\,({4.3^x} - 1)$$ are in A.P. then x equals

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is

l, m, n are the $${p^{th}}$$, $${q^{th}}$$ and $${r^{th}}$$ term of a G.P all positive, $$then\,\left| {\matrix{ {\log \,l} & p & 1 \cr {\log \,m} & q & 1 \cr {\log \,n} & r & 1 \cr } } \right|\,equals$$

If the chord y = mx + 1 of the circle $${x^2}\, + \,{y^2} = 1$$ subtends an angle of measure $${45^ \circ }$$ at the major segment of the circle then value of m is :

If the vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ from the sides $B C, C A$ and $A B$ respectively of a triangle $A B C$, then :

Which of the following are not electromagnetic waves?

If $$13.6$$ $$eV$$ energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $$n=2$$ is

If two mirrors are kept at $${60^ \circ }$$ to each other, then the number of images formed by them is

If $${\theta _1},$$ is the inversion temperature, $${\theta _n}$$ is the neutral temperature, $${\theta _c}$$ is the temperature of the cold junction, then

On moving a charge of $$20$$ coulomb by $$2$$ $$cm,$$ $$2$$ $$J$$ of work is done, then the potential differences between the points is

If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a

length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wave produced on it is

Capacitance (in $$F$$) of a spherical conductor with radius $$1$$ $$m$$ is

If in a circular coil $$A$$ of radius $$R,$$ current $$I$$ is flowing and in another coil $$B$$ of radius $$2R$$ a current $$2I$$ is flowing, then the ratio of the magnetic fields $${B_A}$$ and $${B_B}$$, produced by them will be

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

If an electron and a proton having same momentum enter perpendicular to a magnetic field, then

The power factor of $$AC$$ circuit having resistance $$(R)$$ and inductance $$(L)$$ connected in series and an angular velocity $$\omega $$ is

In a transformer, number of turns in the primary coil are $$140$$ and that in the secondary coil are $$280.$$ If current in primary coil is $$4A,$$ then that in the secondary coil is

Wires $$1$$ and $$2$$ carrying currents $$i{}_1$$ and $$i{}_2$$ respectively are inclined at an angle $$\theta $$ to each other. What is the force on a small element $$dl$$ of wire $$2$$ at a distance of $$r$$ from wire $$1$$ (as shown in figure) due to the magnetic field of wire $$1$$?

Electromagnetic waves are transverse in nature is evident by

Which of the following is used in optical fibres?

An astronomical telescope has a large aperture to

Wavelength of light used in an optical instrument are $${\lambda _1} = 4000\mathop A\limits^ \circ $$ and $${\lambda _2} = 5000\mathop A\limits^ \circ ,$$ then ratio of their respective resolving powers (corresponding to $${\lambda _1}$$ and $${\lambda _2}$$ ) is :

The inductance between $$A$$ and $$D$$ is

A conducting square loop of side $$L$$ and resistance $$R$$ moves in its plane with a uniform velocity $$v$$ perpendicular to one of its sides. A magnetic induction $$B$$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced $$emf$$ is

By increasing the temperature, the specific resistance of a conductor and a semiconductor

At absolute zero, Si acts as

Formation of covalent bonds in compounds exhibits

The energy band gap is maximum in

Sodium and copper have work functions $$2.3$$ $$eV$$ and $$4.5$$ $$eV$$ respectively. Then the ratio of the wavelengths is nearest to

A wire when connected to $$220$$ $$V$$ mains supply has power dissipation $${P_1}.$$ Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $${P_2}.$$ Then $${P_2}:{P_1}$$ is

1 mole of a gas with $$\gamma = 7/5$$ is mixed with $$1$$ mole of a gas with $$\gamma = 5/3,$$ then the value of $$\gamma $$ for the resulting mixture is

A spring of force constant $$800$$ $$N/m$$ has an extension of $$5$$ $$cm.$$ The work done in extending it from $$5$$ $$cm$$ to $$15$$ $$cm$$ is

Infrared radiation is detected by

Initial angular velocity of a circular disc of mass $$M$$ is $${\omega _1}.$$ Then two small spheres of mass $$m$$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

The escape velocity of a body depends upon mass as

Which of the following is more close to a black body?

The kinetic energy needed to project a body of mass $$m$$ from the earth surface (radius $$R$$) to infinity is

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

Heat given to a body which raises its temperature by $${1^ \circ }C$$ is

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

At what temperature is the $$r.m.s$$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $${47^ \circ }C?$$

In a simple harmonic oscillator, at the mean position

Moment of inertia of a circular wire of mass $$M$$ and radius $$R$$ about its diameter is

If a spring has time period $$T,$$ and is cut into $$n$$ equal parts, then the time period of each part will be

A child swinging on a swing in sitting position, stands up, then the time period of the swing will

A charged particle $$q$$ is placed at the centre $$O$$ of cube of length $$L(ABCDEFGH).$$ Another same charge $$q$$ is placed at a distance $$L$$ from $$O$$. Then the electric flux through $$ABCD$$ is

When temperature increases, the frequency of a tuning fork

If there are $$n$$ capacitors in parallel connected to $$V$$ volt source, then the energy stored is equal to

Tube $$A$$ has bolt ends open while tube $$B$$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $$A$$ and $$B$$ is

If a current is passed through a spring then the spring will

A tuning fork arrangement (pair) produces $$4$$ beats/sec with one fork of frequency $$288$$ $$cps.$$ A little wax is placed on the unknown fork and it then produces $$2$$ beats/sec. The frequency of the unknown fork is

If a charge $$q$$ is placed at the center of the line joining two equal charges $$Q$$ such that the system is in equilibrium then the value of $$q$$ is

The mass of product liberated on anode in an electrochemical cell depends on (where $$t$$ is the time period for which the current is passed).

A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ Then the equation of the unknown wave is

If in the circuit, power dissipation is $$150W,$$ then $$R$$ is

Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of mass is

Identify the pair whose dimensions are equal

A lift is moving down with acceleration $$a.$$ A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

A light string passing over a smooth light pulley connects two blocks of masses $${m_1}$$ and $${m_2}$$ (vertically). If the acceleration of the system is $$g/8$$, then the ratio of the masses is

From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If v_A and v_B are their respective velocities on reaching the ground, then

Two forces are such that the sum of their magnitudes is $$18$$ $$N$$ and their resultant is $$12$$ $$N$$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

Speeds of two identical cars are $$u $$ and $$4$$$$u $$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is :

A ball whose kinetic energy E, is projected at an angle of $$45^\circ $$ to the horizontal. The kinetic energy of the ball at the highest point of its height will be

When forces $${F_1},\,\,{F_2},\,\,{F_3}$$ are acting on a particle of mass $$m$$ such that $${F_2}$$ and $${F_3}$$ are mutually perpendicular, then the particle remains stationary. If the force $${F_1}$$ is now removed then the acceleration of the particle is

If a body looses half of its velocity on penetrating $$3$$ $$cm$$ in a wooden block, then how much will it penetrate more before coming to rest?

Three identical blocks of masses $$m=2$$ $$kg$$ are drawn by a force $$F=10.2$$ $$N$$ with an acceleration of $$0.6$$ $$m{s^{ - 2}}$$ on a frictionless surface, then what is the tension (in $$N$$) in the string between the blocks $$B$$ and $$C$$?

One end of a mass-less rope, which passes over a mass-less and friction-less pulley $$P$$ is tied to a hook $$C$$ while the other end is free. Maximum tension that the rope can bear is $$360$$ $$N.$$ With what value of maximum safe acceleration (in $$m{s^{ - 2}}$$) can a man of $$60$$ $$kg$$ climb on the rope?

The minimum velocity (in $$m{s^{ - 1}}$$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction $$0.6$$ to avoid skidding is

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

A cylinder of height $$20$$ $$m$$ is completely filled with water. The velocity of efflux of water (in $$m{s^{ - 1}}$$) through a small hole on the side wall of the cylinder near its bottom is

A particle of mass $$m$$ moves along line PC with velocity $$v$$ as shown. What is the angular momentum of the particle about P?

Two spheres of the same material have radii $$1$$ $$m$$ and $$4$$ $$m$$ and temperatures $$4000$$ $$K$$ and $$2000$$ $$K$$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

Energy required to move a body of mass $$m$$ from an orbit of radius $$2R$$ to $$3R$$ is