The increasing order of basicity of the following compounds is :

An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?

The predominant form of histamine present in human blood is (pK_a, Histidine = 6.0)

Glucose on prolonged heating with HI gives

The major product formed in the following reaction is :

Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br₂ to form product B. A and B are respectively :

Phenol on treatment with CO₂ in the presence of NaOH followed by acidification produces compound X as the major product. X on treatment with (CH₃CO)₂O in the presence of catalytic amount of H₂SO₄ produces:

The trans-alkenes are formed by the reduction of alkynes with

The major product of the following reaction is:

Which of the following compounds will be suitable for Kjeldahl’s method for nitrogen estimation?

Consider the following reaction and statements:
[Co(NH₃)₄Br₂]⁺ + Br^- $$\to$$ [Co(NH₃)₃Br₃] + NH₃
(I) Two isomers are produced if the reactant complex ion is a cis-isomer
(II) Two isomers are produced if the reactant complex ion is a trans-isomer
(III) Only one isomer is produced if the reactant complex ion is a trans-isomer
(IV) Only one isomer is produced if the reactant complex ion is a cis – isomer
The correct statements are

The compound that does not produce nitrogen gas by the thermal decomposition is :

The oxidation states of Cr in [Cr(H₂O)₆]Cl₃, [Cr(C₆H₆)₂] and K₂[Cr(CN)₂(O)₂(O₂)(NH₃)] respectively are :

Which of the following compounds contain(s) no covalent bond(s)? KCl, PH₃, O₂, B₂H₆, H₂SO₄

How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane?
(Atomic weight of B = 10.8 u)

Which of the following salts is the most basic in aqueous solution?

At 518^oC the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr, was 1.00 Torr s^–1 when 5% had reacted and 0.5 Torr s^–1 when 33% had reacted. The order of the reaction is

Which of the following are Lewis acids?

An aqueous solution contains 0.10 M H₂S and 0.20 M HCl. If the equilibrium constants for the formation of HS^– from H₂S is 1.0 $$\times$$ 10^–7 and that of S^2- from HS^– ions is 1.2 $$\times$$ 10^–13 then the concentration of S^2- ions in aqueous solution is :

An aqueous solution contains an unknown concentration of Ba²⁺. When 50 mL of a 1 M solution of Na₂SO₄ is added, BaSO₄ just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO₄ is 1 $$\times$$ 10^–10. What is the original concentration of Ba²⁺?

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction?

The combustion of benzene(l) gives CO₂(g) and H₂O(l). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol^–1 at 25^oC; heat of combustion (in kJ mol^–1) of benzene at constant pressure will be :
(R = 8.314 JK^–1 mol^–1)

According to molecular orbital theory, which of the following will not be a viable molecule?

Total number of lone pair of electrons in $${\rm I}_3^ - $$ ion is

The ratio of mass percent of C and H of an organic compound (C_XH_YO_Z) is 6 : 1. If one molecule of the above compound (C_XH_YO_Z) contains half as much oxygen as required to burn one molecule of compound C_XH_Y completely to CO₂ and H₂O. The empirical formula of compound C_XH_YO_Z is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Let S = { $$x$$ $$ \in $$ R : $$x$$ $$ \ge $$ 0 and

$$2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0$$}. Then S

If $$\alpha ,\beta \in C$$ are the distinct roots of the equation
x² - x + 1 = 0, then $${\alpha ^{101}} + {\beta ^{107}}$$ is equal to :

If the system of linear equations

x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0

has a non-zero solution (x, y, z), then $${{xz} \over {{y^2}}}$$ is equal to

If $$\left| {\matrix{ {x - 4} & {2x} & {2x} \cr {2x} & {x - 4} & {2x} \cr {2x} & {2x} & {x - 4} \cr } } \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2}$$

then the ordered pair (A, B) is equal to :

Two sets A and B are as under :

A = {($$a$$, b) $$ \in $$ R $$ \times $$ R : |$$a$$ - 5| < 1 and |b - 5| < 1};

B = {($$a$$, b) $$ \in $$ R $$ \times $$ R : 4($$a$$ - 6)² + 9(b - 5)² $$ \le $$ 36 };

Then

Let $${a_1}$$, $${a_2}$$, $${a_3}$$, ......... ,$${a_{49}}$$ be in A.P. such that

$$\sum\limits_{k = 0}^{12} {{a_{4k + 1}}} = 416$$ and $${a_9} + {a_{43}} = 66$$.

$$a_1^2 + a_2^2 + ....... + a_{17}^2 = 140m$$, then m is equal to

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

If $$\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$$ and

$$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$$, then the standard deviation of the 9 items
$${x_1},{x_2},.......,{x_9}$$ is

Let $$\overrightarrow u $$ be a vector coplanar with the vectors $$\overrightarrow a = 2\widehat i + 3\widehat j - \widehat k$$ and $$\overrightarrow b = \widehat j + \widehat k$$. If $$\overrightarrow u $$ is perpendicular to $$\overrightarrow a $$ and $$\overrightarrow u .\overrightarrow b = 24$$, then $${\left| {\overrightarrow u } \right|^2}$$ is equal to

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :

Let y = y(x) be the solution of the differential equation

$$\sin x{{dy} \over {dx}} + y\cos x = 4x$$, $$x \in \left( {0,\pi } \right)$$.

If $$y\left( {{\pi \over 2}} \right) = 0$$, then $$y\left( {{\pi \over 6}} \right)$$ is equal to :

The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\sin }^2}x} \over {1 + {2^x}}}} dx$$ is

The integral

$$\int {{{{{\sin }^2}x{{\cos }^2}x} \over {{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}} dx$$

is equal to

Let g(x) = cosx², f(x) = $$\sqrt x $$ and $$\alpha ,\beta \left( {\alpha < \beta } \right)$$ be the roots of the quadratic equation 18x² - 9$$\pi $$x + $${\pi ^2}$$ = 0. Then the area (in sq. units) bounded by the curve
y = (gof)(x) and the lines $$x = \alpha $$, $$x = \beta $$ and y = 0 is :

Let S = { t $$ \in R:f(x) = \left| {x - \pi } \right|.\left( {{e^{\left| x \right|}} - 1} \right)$$$$\sin \left| x \right|$$ is not differentiable at t}, then the set S is equal to

Let $$f\left( x \right) = {x^2} + {1 \over {{x^2}}}$$ and $$g\left( x \right) = x - {1 \over x}$$,
$$x \in R - \left\{ { - 1,0,1} \right\}$$.
If $$h\left( x \right) = {{f\left( x \right)} \over {g\left( x \right)}}$$, then the local minimum value of h(x) is

For each t $$ \in R$$, let [t] be the greatest integer less than or equal to t.

Then $$\mathop {\lim }\limits_{x \to {0^ + }} x\left( {\left[ {{1 \over x}} \right] + \left[ {{2 \over x}} \right] + ..... + \left[ {{{15} \over x}} \right]} \right)$$

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10¹²/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 × 10²³ gm mole^–1)

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $$\mu $$m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

An EM wave from air enters a medium. The electric fields are

$$\overrightarrow {{E_1}} $$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and

$$\overrightarrow {{E_2}} $$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium,

where the wave number k and frequency $$\nu $$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B₁. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $${{B_2}}$$. The ratio $${{{B_1}} \over {{B_2}}}$$ is:

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r$$_\alpha$$ respectively in a uniform magnetic field B. The relation between r_e, r_p, r$$_\alpha$$ is:

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $$\Omega $$. The internal resistances of the two batteries are 1 $$\Omega $$ and 2 $$\Omega $$ respectively. The voltage across the load lies between :

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega $$. How much was the resistance on the left slot before interchanging the resistances?

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$ + \sigma $$, $$ - \sigma $$ and $$ + \sigma $$ respectively. The potential of shell B is :

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $$\times$$ 10³ kg/m³ and its Young’s modulus is 9.27 $$\times$$ 10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations ?

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

The mass of a hydrogen molecule is 3.32 $$\times$$ 10^-27 kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2 cm² at an angle of 45^o to the normal, and rebound elastically with a speed of 10³ m/s, then the pressure on the wall is nearly:

Two moles of an ideal monatomic gas occupies a volume V at 27^oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n^th power of R. If the period of rotation of the particle is T, then :

From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :

A particle is moving in a circular path of radius $$a$$ under the action of an attractive potential $$U = - {k \over {2{r^2}}}$$ Its total energy is:

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $$\left( {{dr \over r}} \right)$$ is:

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

In a collinear collision, a particle with an initial speed v₀ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

Two masses m₁ = 5 kg and m₂ = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is :

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

The reading of the ammeter for a silicon diode in the given circuit is :

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p_d; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p_c. The values of p_d and p_c are respectively :

If the series limit frequency of the Lyman series is $${\nu _L}$$, then the series limit frequency of the Pfund series is:

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $${\lambda _n}$$, $${\lambda _g}$$ be the de Broglie wavelength of the electron in the n^th state and the ground state respectively. Let $${\Lambda _n}$$ be the wavelength of the emitted photon in the transition from the n^th state to the ground state. For large n, (A, B are constants)