For per gram of reactant, the maximum quantity of N2 gas is produced in which of the following thermal decomposition rea

The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :

Given (i)   2Fe2O3(s) $$ \to $$ 4Fe(s) + 3O2(g); $$\Delta $$rGo = + 1487.0 kJ mol-1 (ii)   2CO(g) +

$$\Delta $$fGo at 500 K for substance 'S' in liquid state and gaseous state are +100.7 kcl mol-1 and +103 kcal mol-1, re

Following four solutions are prepared by mixing different volumes of NaOH and HCl of different concentrations, pH of whi

At a certain temperature in a $$5$$ $$L$$ vessel, 2 moles of carbon monoxide and 3 moles of chlorine were allowed to rea

In KO2, the nature of oxygen species and the oxydation state of oxygen atom are, respectively :

The correct order of electron affinity is :

The correct order of spin-only magnetic moments among the following is : (Atomic number : Mn = 25, Co = 27, Ni = 28, Zn

For a first order reaction, A $$ \to $$ P, t1/2 (half-life) is 10 days The time required for $${1 \over 4}$$th conversio

Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and

The total number of possible isomers for square-planar [Pt(Cl)(NO2)(NO3)(SCN)]2- is :

Two compounds I and II are eluted by column chromatography (adsorption of I > II). Which one of following is a correc

The major product formed in the following reaction is :

On treatment of the following compound with a strong acid, the most susceptible site for bond cleavage is :

The increasing order of the acidity of the following carboxylic acids is :

Which of the following best describes the diagram below of a molecular orbital ?

When 2-butyne is treate with H2/Lindlar's catalyst, compound X is produced as the major product and when treated with N

The increasing order of diazotisation of the following compounds is :

The dipeptide, Gln-Gly, on treatment with CH3COCl followed y aqueous work up gives :

The total number of optically active compounds formed in the following reactio is :

The major product formed in the following reaction is :

If f(x) is a quadratic expression such that f (1) + f (2) = 0, and $$-$$ 1 is a root of f (x) = 0, then the other root o

Let f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$

Suppose A is any 3$$ \times $$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I3 and O = O3. If $$\a

The number of four letter words that can be formed using the letters of the word BARRACK is :

If |z $$-$$ 3 + 2i| $$ \le $$ 4 then the difference between the greatest value and the least value of |z| is :

If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then :

If  a,   b,   c  are in A.P. and  a2,  b2,  c2 are in G.P. such that a <&nbs

$$\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}$$ equals :

Let f(x) = $$\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k

If    f(x) = sin-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}}

Let f(x) be a polynomial of degree $$4$$ having extreme values at $$x = 1$$ and $$x = 2.$$ If   $$\mathop {lim}\lim

The value of integral $$\int_{{\pi \over 4}}^{{{3\pi } \over 4}} {{x \over {1 + \sin x}}dx} $$ is :

If   $${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$$    $${I_2} = \int_0^1 {{e^{ - {x^

If    $$\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}

The curve satifying the differeial equation, (x2 $$-$$ y2) dx + 2xydy = 0 and passing through the point (1, 1) is :

The sides of a rhombus ABCD are parallel to the lines, x $$-$$ y + 2 = 0 and 7x $$-$$ y + 3 = 0. If the diagonals of the

The foot of the perpendicular drawn from the origin, on the line, 3x + y = $$\lambda $$ ($$\lambda $$ $$ \ne $$ 0) is P.

Tangents drawn from the point ($$-$$8, 0) to the parabola y2 = 8x touch the parabola at $$P$$ and $$Q.$$ If F is the foc

An angle between the lines whose direction cosines are gien by the equations, $$l$$ + 3m + 5n = 0 and 5$$l$$m $$-$$ 2m

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing

If the mean of the data : 7, 8, 9, 7, 8, 7, $$\lambda $$, 8 is 8, then the variance of this data is :

If the position vectors of the vertices A, B and C of a $$\Delta $$ ABC are respectively $$4\widehat i + 7\widehat j + 8

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $${30^o}$$. T

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and th

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $$3.5$$ revolutions per second. A co

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Tak

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is : [kB =1.4 $$ \times

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. x(t) = A

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sono

A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge de

A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of

A solid ball of radius R has a charge density $$\rho $$ given by $$\rho $$ = $$\rho $$o (1 $$-$$ $${\raise0.5ex\hbox{$

A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in

A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are mo

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released

As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube

A capacitor C1 = 1.0 $$\mu $$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\th

A plane polarized light is incident on a polariser with its pass axis aking angle $$\theta $$ with x-axis, as shown in t

Truth table for the following digital circuit will be :

A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10-2 m. The magnetic field

At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two co

A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that th

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The s

If the de Broglie wavelengths associated with a proton and an $$\alpha $$-particle are equal, then the ratio of velociti

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The rat

Muon ($$\mu $$$$-$$) is a negatively charged (|q| = |e|) particle with a mass m$$\mu $$ = 200 me, where me is the mass o

A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire i