Consider the above reaction, the major product "P" formed is :

Given below are two statement : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : SO₂(g) is absorbed to a large extent than H₂(g) on activated charcoal.

Reason R : SO₂(g) has a higher critical temperature than H₂(g).

In the light of the above statements, choose the most appropriate answer from the options given below.

The correct order of first ionisation enthalpy is :

Given below are two statements :

Statement I : Hyperconjugation is a permanent effect.

Statement II : Hyperconjugation in ethyl cation $$\left( {C{H_3} - \mathop C\limits^ + {H_2}} \right)$$ involves the overlapping of $${C_{s{p^2}}} - {H_{1s}}$$ bond with empty 2p orbital of other carbon.

Choose the correct option :

Given below are two statements :

Statement I : $${[Mn{(CN)_6}]^{3 - }}$$, $${[Fe{(CN)_6}]^{3 - }}$$ and $${[Co{({C_2}{O_4})_3}]^{3 - }}$$ are d²sp³ hybridised.

Statement II : $${[MnCl)_6}{]^{3 - }}$$ and $${[Fe{F_6}]^{3 - }}$$ are paramagnetic and have 4 and 5 unpaired electrons, respectively.

In the light of the above statements, choose the correct answer from the options given below :

To an aqueous solution containing ions such as Al³⁺, Zn²⁺, Ca²⁺, Fe³⁺, Ni²⁺, Ba²⁺ and Cu²⁺ was added conc. HCl, followed by H₂S.

The total number of cations precipitated during this reaction is/are :

Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is :

$$R - CN\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(ii){H_2}O}^{(i)DIBAL - H}} R - Y$$

Consider the above reaction and identify "Y"

Consider the above reaction, and choose the correct statement :

Match List - I with List - II :

	List - I (compound)		List - II (effect/affected species)
(a)	Carbon monoxide	(i)	Carcinogenic
(b)	Sulphur dioxide	(ii)	Metabolized by pyrus plants
(c)	Polychlorinated biphenyls	(iii)	haemoglobin
(d)	Oxides of Nitrogen	(iv)	Stiffness of flower buds

Choose the correct answer from the options given below :

What is A in the following reaction?

The correct sequence of correct reagents for the following transformation is :

The equilibrium constant for the reaction

A(s) $$\rightleftharpoons$$ M(s) + $${1 \over 2}$$O₂(g)

is K_p = 4. At equilibrium, the partial pressure of O₂ is _________ atm. (Round off to the nearest integer)

When 400 mL of 0.2 M H₂SO₄ solution is mixed with 600 mL of 0.1 M NaOH solution, the increase in temperature of the final solution is __________ $$\times$$ 10^$$-$$2 K. (Round off to the nearest integer).

[Use : H⁺ (aq) + OH^$$-$$ (aq) $$\to$$ H₂O : $$\Delta$$_$$\gamma$$H = $$-$$57.1 kJ mol^$$-$$1]

Specific heat of H₂O = 4.18 J K^$$-$$1 g^$$-$$1

density of H₂O = 1.0 g cm^$$-$$3

Assume no change in volume of solution on mixing.

2SO₂(g) + O₂(g) $$\to$$ 2SO₃(g)

The above reaction is carried out in a vessel starting with partial pressure P_SO2 = 250 m bar, P_O2 = 750 m bar and P_SO3 = 0 bar. When the reaction is complete, the total pressure in the reaction vessel is _______ m bar. (Round off of the nearest integer).

10.0 mL of 0.05 M KMnO₄ solution was consumed in a titration with 10.0 mL of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is _________ $$\times$$ 10^$$-$$2 g/L.

(Round off to the nearest integer)

The total number of electrons in all bonding molecular orbitals of $$O_2^{2 - }$$ is ______________.

(Round off to the nearest integer)

3 moles of metal complex with formula Co(en)₂Cl₃ gives 3 moles of silver chloride on treatment with excess of silver nitrate. The secondary valency of Co in the complex is ___________.

(Round off to the nearest integer)

In a solvent 50% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is __________ $$\times$$ 10^$$-$$2.

(Round off to the nearest integer)

The dihedral angle in staggered form of Newman projection of 1, 1, 1-Trichloro ethane is ___________ degree. (Round off to the nearest integer)

For the first order reaction A $$\to$$ 2B, 1 mole of reactant A gives 0.2 moles of B after 100 minutes. The half life of the reaction is __________ min. (Round off to the nearest integer).

[Use : ln 2 = 0.69, ln 10 = 2.3]

Properties of logarithms : ln x^y = y ln x;

$$\ln \left( {{x \over y}} \right) = \ln x - \ln y$$

(Round off to the nearest integer)

For the cell

Cu(s) | Cu²⁺ (aq) (0.1 M) || Ag⁺(aq) (0.01 M) | Ag(s)

the cell potential E₁ = 0.3095 V

For the cell

Cu(s) | Cu²⁺ (aq) (0.01 M) || Ag⁺(aq) (0.001 M) | Ag(s)

the cell potential = ____________ $$\times$$ 10^$$-$$2 V. (Round off the nearest integer).

[Use : $${{2.303RT} \over F}$$ = 0.059]

The point P (a, b) undergoes the following three transformations successively :

(a) reflection about the line y = x.

(b) translation through 2 units along the positive direction of x-axis.

(c) rotation through angle $${\pi \over 4}$$ about the origin in the anti-clockwise direction.

If the co-ordinates of the final position of the point P are $$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$, then the value of 2a + b is equal to :

A possible value of 'x', for which the ninth term in the expansion of $${\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}} \right\}^{10}}$$ in the increasing powers of $${3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}$$ is equal to 180, is :

Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the value of $$\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}} $$ is equal to :

Let C be the set of all complex numbers. Let

S₁ = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S₂ = {z$$\in$$C : z(1 + i) + $$\overline z $$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S₁ $$\cap$$ S₂ is equal to :

If $$\tan \left( {{\pi \over 9}} \right),x,\tan \left( {{{7\pi } \over {18}}} \right)$$ are in arithmetic progression and $$\tan \left( {{\pi \over 9}} \right),y,\tan \left( {{{5\pi } \over {18}}} \right)$$ are also in arithmetic progression, then $$|x - 2y|$$ is equal to :

Let the mean and variance of the frequency distribution

$$\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr } $$

be 6 and 6.8 respectively. If x₃ is changed from 8 to 7, then the mean for the new data will be :

The area of the region bounded by y $$-$$ x = 2 and x² = y is equal to :

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

equation (x $$-$$ x³)dy = (y + yx² $$-$$ 3x⁴)dx, x > 2. If y(3) = 3, then y(4) is equal to :

The value of

$$\mathop {\lim }\limits_{x \to 0} \left( {{x \over {\root 8 \of {1 - \sin x} - \root 8 \of {1 + \sin x} }}} \right)$$ is equal to :

Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point :

Let $$\alpha = \mathop {\max }\limits_{x \in R} \{ {8^{2\sin 3x}}{.4^{4\cos 3x}}\} $$ and $$\beta = \mathop {\min }\limits_{x \in R} \{ {8^{2\sin 3x}}{.4^{4\cos 3x}}\} $$. If $$8{x^2} + bx + c = 0$$ is a quadratic equation whose roots are $$\alpha$$^1/5 and $$\beta$$^1/5, then the value of c $$-$$ b is equal to :

Let $$f:[0,\infty ) \to [0,3]$$ be a function defined by

$$f(x) = \left\{ {\matrix{ {\max \{ \sin t:0 \le t \le x\} ,} & {0 \le x \le \pi } \cr {2 + \cos x,} & {x > \pi } \cr } } \right.$$

Then which of the following is true?

Let N be the set of natural numbers and a relation R on N be defined by $$R = \{ (x,y) \in N \times N:{x^3} - 3{x^2}y - x{y^2} + 3{y^3} = 0\} $$. Then the relation R is :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5 $$ on the x-axis. Then the radius of the circle C is equal to :

Let f : (a, b) $$\to$$ R be twice differentiable function such that $$f(x) = \int_a^x {g(t)dt} $$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :

If the real part of the complex number $$z = {{3 + 2i\cos \theta } \over {1 - 3i\cos \theta }},\theta \in \left( {0,{\pi \over 2}} \right)$$ is zero, then the value of sin²3$$\theta$$ + cos²$$\theta$$ is equal to _______________.

If $$\int_0^\pi {({{\sin }^3}x){e^{ - {{\sin }^2}x}}dx = \alpha - {\beta \over e}\int_0^1 {\sqrt t {e^t}dt} } $$, then $$\alpha$$ + $$\beta$$ is equal to ____________.

The number of real roots of the equation e^4x $$-$$ e^3x $$-$$ 4e^2x $$-$$ e^x + 1 = 0 is equal to ______________.

Let y = y(x) be the solution of the differential equation dy = e^{$$\alpha$$x + y} dx; $$\alpha$$ $$\in$$ N. If y(log_e2) = log_e2 and y(0) = log_e$$\left( {{1 \over 2}} \right)$$, then the value of $$\alpha$$ is equal to _____________.

Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)¹⁰ . (11)¹¹ . (13)¹³ is equal to __________.

Let A = {n $$\in$$ N | n² $$\le$$ n + 10,000}, B = {3k + 1 | k$$\in$$ N} an dC = {2k | k$$\in$$N}, then the sum of all the elements of the set A $$\cap$$(B $$-$$ C) is equal to _____________.

If $$A = \left[ {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right]$$ and M = A + A² + A³ + ....... + A²⁰, then the sum of all the elements of the matrix M is equal to _____________.

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$$\mathop A\limits^o $$. What is the maximum kinetic energy of the emitted photoelectron?

The expected graphical representation of the variation of angle of deviation '$$\delta$$' with angle of incidence 'i' in a prism is :

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is :

[Density of water f_w = 1000 kg m^$$-$$3 and Density of air f_a = 1.2 kg m^$$-$$3, g = 10 m/s², Coefficient of viscosity of air = 1.8 $$\times$$ 10^$$-$$5 Nsm^$$-$$2]

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$$^\circ$$ C to 37$$^\circ$$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol^$$-$$1 k^$$-$$1]

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $$t = {T \over 4}s$$ starting from mean position. Assume that the initial phase of the oscillation is zero.

Match List I with List II.

	List - I		List - II
(a)	Capacitance, C	(i)	$${M^1}{L^1}{T^{ - 3}}{A^{ - 1}}$$
(b)	Permittivity of free space, $${\varepsilon _0}$$	(ii)	$${M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$$
(c)	Permeability of free space, $${\mu _0}$$	(iii)	$${M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$
(d)	Electric field, E	(iv)	$${M^1}{L^1}{T^{ - 2}}{A^{ - 2}}$$

Choose the correct answer from the options given below

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that E_mech = 8 J, the incorrect statement for this system is :


[ where K.E. = kinetic energy ]

A 100$$\Omega$$ resistance, a 0.1 $$\mu$$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

Find the truth table for the function Y of A and B represented in the following figure.

Figure A and B shown to long straight wires of circular cross-section (a and b with a < b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as :

Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :

What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?

A physical quantity 'y' is represented by the formula $$y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$$

If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 10³ km. Find the mass of Mars.

$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$$F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]$$

Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

The resistance of a conductor at 15$$^\circ$$C is 16$$\Omega$$ and at 100$$^\circ$$C is 20$$\Omega$$. What will be the temperature coefficient of resistance of the conductor?

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $$\left( {{{{I_1}} \over {{I_2}}}} \right)$$ will be x : 1. The value of x will be _____________.

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ___________ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = 6000 $$\mathop A\limits^o $$]

In the given figure the magnetic flux through the loop increases according to the relation $$\phi$$_B(t) = 10t² + 20t, where $$\phi$$_B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$$\Omega$$ resistor at t = 5 s is ___________ mA.

A particle executes simple harmonic motion represented by displacement function as

x(t) = A sin($$\omega$$t + $$\phi$$)

If the position and velocity of the particle at t = 0 s are 2 cm and 2$$\omega$$ cm s^$$-$$1 respectively, then its amplitude is $$x\sqrt 2 $$ cm where the value of x is _________________.

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $$\theta$$ with the line AB should be _________$$^\circ$$, so that the swimmer reaches point B.

For the circuit shown, the value of current at time t = 3.2 s will be _________ A.


[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m.

(Assume there is no friction between the block and the hemisphere)

The K_$$\alpha$$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be __________ keV. (Round off to the nearest integer)

[h = 4.14 $$\times$$ 10^$$-$$15 eVs, c = 3 $$\times$$ 10⁸ ms^$$-$$1]

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum range is ________ m.