In which one of the following equilibria, K_p $$ \ne $$ K_C ?

Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives :

Which one of the following is likely to give a precipitate with AgNO₃ solution ?

The molar solubility of Cd(OH)₂ is 1.84 × 10^–5 M in water. The expected solubility of Cd(OH)₂ in a buffer solution of pH = 12 is :

The compound used in the treatment of lead poisoning is :

In comparison to boron, berylium has :

Consider the following reactions :

'A' is :

Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives X as the major product. Reaction of X with Hg(OAc)₂/H₂O followed by NaBH₄ gives Y as the major product. Y is :

A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol^–1) and 1.8 g of glucose (molar mass = 180 g mol^–1) in 100 mL of water at 27^oC. The osmotic pressure of the solution is :
(R = 0.08206 L atm K^–1 mol^–1)

Which of the given statements is INCORRECT about glycogen?

NO₂ required for a reaction is produced by the decomposition of N₂O₅ in CCl₄ as per the equation,
2N₂O₅(g) $$ \to $$ 4NO₂(g) + O₂(g).
The initial concentration of N₂O₅ is 3.00 mol L^–1 and it is 2.75 mol L^–1 after 30 minutes. The rate of formation of NO₂ is :

The pair that has similar atomic radii is :

The INCORRECT match in the following is :

Thermal decomposition of a Mn compound (X) at 513 K results in compound Y, MnO₂ and gaseous product. MnO₂ reacts with NaCl and concentrated H₂O₄ to give a pungent gas Z. X, Y and Z, respectively, are :

25 g of an unknown hydrocarbon upon burning produces 88 g of CO₂ and 9 g of H₂O. This unknown hydrocarbon contains :

The coordination numbers of Co and Al in [Co(Cl)(en)₂]Cl and K₃[Al(C₂O₄)₃], respectively, are : (en = ethane-1, 2-diamine)

Among the following, the energy of 2s orbital is lowest in :

The decreasing order of electrical conductivity of the following aqueous solutions is :

0.1 M Formic acid (A),

0.1 M Acetic acid (B),

0.1 M Benzoic acid (C)

What will be the major product when m-cresol is reacted with propargyl bromide (HC$$ \equiv $$C–CH₂Br) in presence of K₂CO₃ in acetone?

The IUPAC name for the following compound is :

An 'Assertion' and a 'Reason' are given below. Choose the correct answer from the following options :
Assertion (A) : Vinyl halides do not undergo nucleophilic substitution easily.
Reason (R) : Even though the intermediate carbocation is stabilized by loosely held p-electrons, the cleavage is difficult because of strong bonding.

In the following skew conformation of ethane, H'–C–C–H'' dihedral angle is :

Let A, B and C be sets such that $$\phi $$ $$ \ne $$ A $$ \cap $$ B $$ \subseteq $$ C. Then which of the following statements is not true ?

If the area (in sq. units) bounded by the parabola y² = 4$$\lambda $$x and the line y = $$\lambda $$x, $$\lambda $$ > 0, is $${1 \over 9}$$ , then $$\lambda $$ is equal to :

The general solution of the differential equation (y² – x³)dx – xydy = 0 (x $$ \ne $$ 0) is : (where c is a constant of integration)

Let $$a \in \left( {0,{\pi \over 2}} \right)$$ be fixed. If the integral

$$\int {{{\tan x + \tan \alpha } \over {\tan x - \tan \alpha }}} dx$$ = A(x) cos 2$$\alpha $$ + B(x) sin 2$$\alpha $$ + C, where C is a

constant of integration, then the functions A(x) and B(x) are respectively :

If $$\alpha $$, $$\beta $$ and $$\gamma $$ are three consecutive terms of a non-constant G.P. such that the equations $$\alpha $$x ² + 2$$\beta $$x + $$\gamma $$ = 0 and x² + x – 1 = 0 have a common root, then $$\alpha $$($$\beta $$ + $$\gamma $$) is equal to :

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60^o with the line x + y = 0. Then an equation of the line L is :

The term independent of x in the expansion of
$$\left( {{1 \over {60}} - {{{x^8}} \over {81}}} \right).{\left( {2{x^2} - {3 \over {{x^2}}}} \right)^6}$$ is equal to :

If a₁, a₂, a₃, ..... are in A.P. such that a₁ + a₇ + a₁₆ = 40, then the sum of the first 15 terms of this A.P. is :

Let f(x) = 5 – |x – 2| and g(x) = |x + 1|, x $$ \in $$ R. If f(x) attains maximum value at $$\alpha $$ and g(x) attains minimum value at $$\beta $$, then $$\mathop {\lim }\limits_{x \to -\alpha \beta } {{\left( {x - 1} \right)\left( {{x^2} - 5x + 6} \right)} \over {{x^2} - 6x + 8}}$$ is equal to :

Let z $$ \in $$ C with Im(z) = 10 and it satisfies $${{2z - n} \over {2z + n}}$$ = 2i - 1 for some natural number n. Then :

A value of $$\theta \in \left( {0,{\pi \over 3}} \right)$$, for which
$$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$$, is :

The derivative of $${\tan ^{ - 1}}\left( {{{\sin x - \cos x} \over {\sin x + \cos x}}} \right)$$, with respect to $${x \over 2}$$ , where $$\left( {x \in \left( {0,{\pi \over 2}} \right)} \right)$$ is :

$$\mathop {\lim }\limits_{x \to 0} {{x + 2\sin x} \over {\sqrt {{x^2} + 2\sin x + 1} - \sqrt {{{\sin }^2}x - x + 1} }}$$ is :

A value of $$\alpha $$ such that
$$\int\limits_\alpha ^{\alpha + 1} {{{dx} \over {\left( {x + \alpha } \right)\left( {x + \alpha + 1} \right)}}} = {\log _e}\left( {{9 \over 8}} \right)$$ is :

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $$\overrightarrow B = \left( {1.5 \times {{10}^{ - 3}}T} \right)\widehat k$$ at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is : (electron’s charge = 1.6 × 10^–19 C, mass of electron = 9.1 × 10^–31 kg)

The number density of molecules of a gas depends on their distance r from the origin as, $$n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$$. Then the total number of molecules is proportional to :

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of sound as 10^–12 W/m² ]

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l₁ = 30 cm and l₂ = 70 cm. Then, v is equal to -

A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I₀(I₀ > I_g) by connecting a shunt resistance R_A to it and (ii) into a voltmeter of range 0 to V (V = GI₀) by connecting a series resistance R_V to it. Then,

A solid sphere, of radius R acquires a terminal velocity v₁ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v₂, when falling through the same fluid, the ratio (v₁/v₂) equals :

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30^o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $$\mu $$ = 0.2. The difference between the accelerations of the blocks, in case (B) and case (A) will be : (g = 10 ms^–2)

One kg of water, at 20^oC, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 $$\Omega $$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/(kg ^oC), Latent heat of water = 2260 kJ/kg]

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, $${{{\lambda _1}} \over {{\lambda _2}}}$$, of the photons emitted in this process is :

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?

A smooth wire of length 2$$\pi $$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $$\omega $$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $$\omega $$² is equal to -

A system of three polarizers P₁, P₂, P₃ is set up such that the pass axis of P₃ is crossed with respect to that of P₁. The pass axis of P₂ is inclined at 60^o to the pass axis of P₃. When a beam of unpolarized light of intensity I0 is incident on P₁, the intensity of light transmitted by the three polarizers is I. The ratio ($${{{I_0}} \over I}$$) equals (nearly) :

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho $$(r) = kr, where r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite points, at equal distance, $$a$$ from the centre. If A and B do not experience any force, then :

Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t = $${L \over R}$$ is :

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $$\mathop A\limits^o $$). The de-Broglie wavelength of this electron is :

A transparent cube of side, made of a material of refractive index $$\mu $$₂, is immersed in a liquid of refractive index $$\mu $$₁($$\mu $$₁ < $$\mu $$₂). A ray is incident on the face AB at an angle $$\theta $$(shown in the figure). Total internal reflection takes place at point E on the face BC.
Then $$\theta $$ must satisfy :

A particle is moving with speed v = b$$\sqrt x $$ along positive x-axis. Calculate the speed of the particle at time t = $$\tau $$(assume that the particle is at origin t = 0)

In the given circuit, the charge on 4 $$\mu $$F capacitor will be :

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h₁ and h₂. Which of the following is correct ?

Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the unregulated input voltage varies between 10 V to 16 V, then what is maximum Zener current?

Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :

The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is $${1 \over 9}$$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l₁ and l₂ where, l₁ = nl₂ and n is an integer. The ratio k₁/k₂ of the corresponding force constant, k₁ and k₂ will be :

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5A. (See figure) ($$\mu $$₀ = 4$$\pi $$ × 10^–7 N-A^–2)