The oxoacid of sulphur that does not contain bond between sulphur atoms is

The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is :

The graph between $${\left| \psi \right|^2}$$ and r (radial distance) is shown below. This represents :

The major product of the following reaction is :

During the change of O₂ to O₂^- , the incoming electron goes to the orbital :

Three complexes,
[CoCl(NH₃)₅] ²⁺(I),
[Co(NH₃)₅H₂O]³⁺ (II) and
[Co(NH₃)₆] ³⁺(III)
absorb light in the visible region. The correct order of the wavelength of light absorbed by them is :

The species that can have a trans-isomer is :
(en = ehane-1, 2-diamine, ox = oxalate)

The major product of the following reaction is :

At room temperature, a dilute solution of urea is prepared by dissolving 0.60 of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mm Hg, lowering of vapour pressure will be. (molar mass of urea = 60 g mol^–1)

The principle of column chromatography is :

A process will be spontaneous at all temperatures if :

At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O₂ for complete combustion, and 40 mL of CO₂ is formed. The formula of the hydrocarbon is :

Consider the following statements
(a) The pH of a mixture containing 400 mL of 0.1 M H₂SO₄ and 400 mL of 0.1 M NaOH will be approximately 1.3
(b) Ionic product of water is temperature dependent.
(c) A monobasic acid with Ka = 10^–5 has pH = 5. The degree of dissociation of this acid is 50 %.
(d) The Le Chatelier's principle is not applicable to common-ion effect.

The correct statements are :

A bacterial infection in an internal wound grows as N'(t) = N₀ exp(t), where the time t is in hours. A does of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $${{dN} \over {dt}} = - 5{N^2}$$. What will be the plot of $${{{N_0}} \over N}$$ vs. t after 1 hour?

The major product of the following reaction is :

Major products of the following reaction are :

The isoelectronic set of ions is :

Consider the statements S1 and S2

S1 : Conductivity always increases with decrease in the concentration of electrolyte.

S2 : Molar conductivity always increases with decrease in the concentration of electrolyte.

The correct option among the following is :

Consider the hydrated ions of Ti²⁺, V²⁺, Ti³⁺, and Sc³⁺. The correct order of their spin-only magnetic moments is :

Amylopectin is compound of :

Ethylamine (C₂H₅NH₂) can be obtained from N-ethylphatalimide on treatment with :

Increasing rate of S_N1 reaction in the following compounds is :

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is :

If $${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - x} & 1 \cr {\cos \theta } & 1 & x \cr } } \right|$$ and
$${\Delta _2} = \left| {\matrix{ x & {\sin 2\theta } & {\cos 2\theta } \cr { - \sin 2\theta } & { - x} & 1 \cr {\cos 2\theta } & 1 & x \cr } } \right|$$, $$x \ne 0$$ ;

then for all $$\theta \in \left( {0,{\pi \over 2}} \right)$$ :

If the length of the perpendicular from the point ($$\beta $$, 0, $$\beta $$) ($$\beta $$ $$ \ne $$ 0) to the line,
$${x \over 1} = {{y - 1} \over 0} = {{z + 1} \over { - 1}}$$ is $$\sqrt {{3 \over 2}} $$, then $$\beta $$ is equal to :

If y = y(x) is the solution of the differential equation
$${{dy} \over {dx}} = \left( {\tan x - y} \right){\sec ^2}x$$, $$x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$,
such that y (0) = 0, then $$y\left( { - {\pi \over 4}} \right)$$ is equal to :

If a > 0 and z = $${{{{\left( {1 + i} \right)}^2}} \over {a - i}}$$, has magnitude $$\sqrt {{2 \over 5}} $$, then $$\overline z $$ is equal to :

If $$\alpha $$ and $$\beta $$ are the roots of the quadratic equation,
x² + x sin $$\theta $$ - 2 sin $$\theta $$ = 0, $$\theta \in \left( {0,{\pi \over 2}} \right)$$, then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right).{{\left( {\alpha - \beta } \right)}^{24}}}}$$ is equal to :

All the pairs (x, y) that satisfy the inequality
$${2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1$$
also satisfy the equation

The region represented by| x – y | $$ \le $$ 2 and | x + y| $$ \le $$ 2 is bounded by a :

Let f(x) = e^x – x and g(x) = x² – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :

If a₁, a₂, a₃, ............... a_n are in A.P. and a₁ + a₄ + a₇ + ........... + a₁₆ = 114, then a₁ + a₆ + a₁₁ + a₁₆ is equal to :

If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is :

Marks	2	3	5	7
Frequency	(x + 1)2	2x - 5	x2 - 3x	x

then the mean of the marks is

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is :

If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + $$\lambda $$z = $$\mu $$, ($$\lambda $$, $$\mu $$ $$ \in $$ R), has infinitely many solutions, then the value of $$\lambda $$ + $$\mu $$ is :

Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then cos ($$\angle $$GOA) (O being the origin) is equal to :

Let f : R $$ \to $$ R be differentiable at c $$ \in $$ R and f(c) = 0. If g(x) = |f(x)| , then at x = c, g is :

The value of $$\int\limits_0^{2\pi } {\left[ {\sin 2x\left( {1 + \cos 3x} \right)} \right]} dx$$,
where [t] denotes the greatest integer function is :

If $$\int {{{dx} \over {{{\left( {{x^2} - 2x + 10} \right)}^2}}}} = A\left( {{{\tan }^{ - 1}}\left( {{{x - 1} \over 3}} \right) + {{f\left( x \right)} \over {{x^2} - 2x + 10}}} \right) + C$$

where C is a constant of integration then :

If$$f(x) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}}}} & {,x > 0} \cr } } \right.$$
is continuous at x = 0, then the ordered pair (p, q) is equal to

If a directrix of a hyperbola centred at the origin and passing through the point (4, –2$$\sqrt 3 $$ ) is 5x = 4$$\sqrt 5 $$ and its eccentricity is e, then :

If $$\mathop {\lim }\limits_{x \to 1} {{{x^4} - 1} \over {x - 1}} = \mathop {\lim }\limits_{x \to k} {{{x^3} - {k^3}} \over {{x^2} - {k^2}}}$$, then k is :

Let f(x) = x² , x $$ \in $$ R. For any A $$ \subseteq $$ R, define g (A) = { x $$ \in $$ R : f(x) $$ \in $$ A}. If S = [0,4], then which one of the following statements is not true ?

Two wires A & B are carrying currents I₁ & I₂ as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

A 25 × 10^–3 m³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O₂ molecule ?

In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be:
Given E (in eV) = 1237/$$\lambda $$ (in nm)

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A, then the input voltage and current in the primary coil are :

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :

A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is:

n moles of an ideal gas with constant volume heat capcity C_V undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let r_p, r_e and r_He be their respective radii, then

A particle of mass m is moving along a trajectory given by
x = x₀ + a cos$$\omega $$₁t
y = y₀ + b sin$$\omega $$₂t
The torque, acting on the particle about the origin, at t = 0 is :

The electric field of a plane electromagnetic wave is given by
$$\overrightarrow E = {E_0}\widehat i\cos (kz)cos(\omega t)$$
The corresponding magnetic field $$\overrightarrow B $$ is then given by

Two coaxial discs, having moments of inertia I₁ and I₁/2, are rotating with respective angular velocities $$\omega $$₁ and $$\omega $$₁/2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E_f and E_i are the final and initial total energies, then (E_f - E_i) is:

A thin disc of mass M and radius R has mass per unit area $$\sigma $$(r) = kr² where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol^–1 K^–1]

A ball is thrown upward with an initial velocity V₀ from the surface of the earth. The motion of the ball is affected by a drag force equal to m$$\gamma $$u² (where m is mass of the ball, u is its instantaneous velocity and $$\gamma $$ is a constant). Time taken by the ball to rise to its zenith is :

One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $$\mu $$₁ and that of 2 is $$\mu $$₂, then the focal length of the combination is :

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

SI. No.	R($$\Omega $$)	l(cm)
1.	1000	60
2.	100	13
3.	10	1.5
4.	1	1.0

Which of the readings is inconsistent?

A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10^–8 $$\Omega $$m) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is 1.1 × 10^–3 m/s.

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are :

Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds u₁ and u₂, respectively. The values of u₁ and u₂ are nearly :

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁, while water rises by the same amount h in a capillary tube of radius r₂. The ratio, (r₁/r₂), is then close to :

The value of acceleration due to gravity at Earth's surface is 9.8 ms^–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms^–2, is close to : (Radius of earth = 6.4 × 10⁶ m)

A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :

In the given circuit, an ideal voltmeter connected across the 10$$\Omega $$ resistance reads 2V. The internal resistance r, of each cell is:

A moving coil galvanometer allows a full scale current of 10^–4 A. A series resistance of 2 M$$\Omega $$ is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0.10 mA is :