In the following sequence of reactions, the final product D is :

The structure of the starting compound P used in the reaction given below is :

Match List - I with List - II :


Choose the most appropriate answer from the options given below :

Match items of List-I with those of List-II :

	List - I (Property)		List - II (Example)
(a)	Diamagnetism	(i)	MnO
(b)	Ferrimagnetism	(ii)	$${O_2}$$
(c)	Paramagnetism	(iii)	NaCl
(d)	Antiferromagnetism	(iv)	$$F{e_3}{O_4}$$

Choose the most appropriate answer from the options given below :

The major product of the following reaction is :

Which of the following is not a correct statement for primary aliphatic amines?

Acidic ferric chloride solution on treatment with excess of potassium ferrocyanide gives a Prussian blue coloured colloidal species. It is :

The nature of oxides V₂O₃ and CrO is indexed as 'X' and 'Y' type respectively. The correct set of X and Y is :

Out of following isomeric forms of uracil, which one is present in RNA?

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

Assertion (A) : Synthesis of ethyl phenyl ether may be achieved by Williamson synthesis.

Reason (R) : Reaction of bromobenzene with sodium ethoxide yields ethyl phenyl ether.

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

In the following sequence of reactions the P is :

In polythionic acid, H₂S_xO₆ (x = 3 to 5) the oxidation state(s) of sulphur is/are :

In Carius method for estimation of halogens, 0.2 g of an organic compound gave 0.188 g of AgBr. The percentage of bromine in the compound is ______________. (Nearest integer)

[Atomic mass : Ag = 108, Br = 80]

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is

$$2{K_2}C{r_2}{O_7} + 8{H_2}S{O_4} + 3{C_2}{H_6}O \to 2C{r_2}{(S{O_4})_3} + 3{C_2}{H_4}{O_2} + 2{K_2}S{O_4} + 11{H_2}O$$

If the rate of appearance of Cr₂(SO₄)₃ is 2.67 mol min^$$-$$1 at a particular time, the rate of disappearance of C₂H₆O at the same time is _____________ mol min^$$-$$1. (Nearest integer)

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $${{{h^2}} \over {xma_0^2}}$$. The value of 10x is ___________. (a₀ is radius of Bohr's orbit) (Nearest integer) [Given : $$\pi$$ = 3.14]

1 kg of 0.75 molal aqueous solution of sucrose can be cooled up to $$-$$4$$^\circ$$C before freezing. The amount of ice (in g) that will be separated out is __________. (Nearest integer)

[Given : K_f(H₂O) = 1.86 K kg mol^$$-$$1]

1 mol of an octahedral metal complex with formula MCl₃ . 2L on reaction with excess of AgNO₃ gives 1 mol of AgCl. The denticity of Ligand L is ____________. (Integer answer)

The number of moles of CuO, that will be utilized in Dumas method for estimation nitrogen in a sample of 57.5 g of N, N-dimethylaminopentane is _____________ $$\times$$ 10^$$-$$2. (Nearest integer)

The number of f electrons in the ground state electronic configuration of Np (Z = 93) is ___________. (Nearest integer)

200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH. The molar heat of neutralization of this reaction is $$-$$57.1 kJ. The increase in temperature in $$^\circ$$C of the system on mixing is x $$\times$$ 10^$$-$$2. The value of x is ___________. (Nearest integer)

[Given : Specific heat of water = 4.18 J g^$$-$$1 K^$$-$$1, Density of water = 1.00 g cm^$$-$$3]

[Assume no volume change on mixing)

The number of moles of NH₃, that must be added to 2L of 0.80 M AgNO₃ in order to reduce the concentration of Ag⁺ ions to 5.0 $$\times$$ 10^$$-$$8 M (K_formation for [Ag(NH₃)₂]⁺ = 1.0 $$\times$$ 10⁸) is ____________. (Nearest integer)

[Assume no volume change on adding NH₃]

When 10 mL of an aqueous solution of KMnO₄ was titrated in acidic medium, equal volume of 0.1 M of an aqueous solution of ferrous sulphate was required for complete discharge of colour. The strength of KMnO₄ in grams per litre is __________ $$\times$$ 10^$$-$$2. (Nearest integer)

[Atomic mass of K = 39, Mn = 55, O = 16]

Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

If $${({\sin ^{ - 1}}x)^2} - {({\cos ^{ - 1}}x)^2} = a$$; 0 < x < 1, a $$\ne$$ 0, then the value of 2x² $$-$$ 1 is :

If the matrix $$A = \left( {\matrix{ 0 & 2 \cr K & { - 1} \cr } } \right)$$ satisfies $$A({A^3} + 3I) = 2I$$, then the value of K is :

If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :

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

$${{dy} \over {dx}} = 2(y + 2\sin x - 5)x - 2\cos x$$ such that y(0) = 7. Then y($$\pi$$) is equal to :

Let us consider a curve, y = f(x) passing through the point ($$-$$2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x². Then :

If $$\alpha$$, $$\beta$$ are the distinct roots of x² + bx + c = 0, then

$$\mathop {\lim }\limits_{x \to \beta } {{{e^{2({x^2} + bx + c)}} - 1 - 2({x^2} + bx + c)} \over {{{(x - \beta )}^2}}}$$ is equal to :

When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face occurs with probability $${1 \over 6} + x$$. All other faces occur with probability $${1 \over 6}$$. Note that opposite faces sum to 7 in any die. If 0 < x < $${1 \over 6}$$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is $${13 \over 96}$$, then the value of x is :

If x² + 9y² $$-$$ 4x + 3 = 0, x, y $$\in$$ R, then x and y respectively lie in the intervals :

$$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx} $$ is equal to :

A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :

Let $$\overrightarrow a = \widehat i + 5\widehat j + \alpha \widehat k$$, $$\overrightarrow b = \widehat i + 3\widehat j + \beta \widehat k$$ and $$\overrightarrow c = - \widehat i + 2\widehat j - 3\widehat k$$ be three vectors such that, $$\left| {\overrightarrow b \times \overrightarrow c } \right| = 5\sqrt 3 $$ and $${\overrightarrow a }$$ is perpendicular to $${\overrightarrow b }$$. Then the greatest amongst the values of $${\left| {\overrightarrow a } \right|^2}$$ is _____________.

The number of distinct real roots of the equation 3x⁴ + 4x³ $$-$$ 12x² + 4 = 0 is _____________.

If A = {x $$\in$$ R : |x $$-$$ 2| > 1},
B = {x $$\in$$ R : $$\sqrt {{x^2} - 3} $$ > 1},
C = {x $$\in$$ R : |x $$-$$ 4| $$\ge$$ 2} and Z is the set of all integers, then the number of subsets of the
set (A $$\cap$$ B $$\cap$$ C)^c $$\cap$$ Z is ________________.

If $$\int {{{dx} \over {{{({x^2} + x + 1)}^2}}} = a{{\tan }^{ - 1}}\left( {{{2x + 1} \over {\sqrt 3 }}} \right) + b\left( {{{2x + 1} \over {{x^2} + x + 1}}} \right) + C} $$, x > 0 where C is the constant of integration, then the value of $$9\left( {\sqrt 3 a + b} \right)$$ is equal to _____________.

If the system of linear equations

2x + y $$-$$ z = 3

x $$-$$ y $$-$$ z = $$\alpha$$

3x + 3y + $$\beta$$z = 3

has infinitely many solution, then $$\alpha$$ + $$\beta$$ $$-$$ $$\alpha$$$$\beta$$ is equal to _____________.

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is ____________.

A uniformly charged disc of radius R having surface charge density $$\sigma$$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-

Which of the following is not a dimensionless quantity?

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :

The resultant of these forces $$\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS} $$ and $$\overrightarrow {OT} $$ is approximately .......... N.

[Take $$\sqrt 3 = 1.7$$, $$\sqrt 2 = 1.4$$ Given $$\widehat i$$ and $$\widehat j$$ unit vectors along x, y axis]

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$$^\circ$$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $$-$$7$$^\circ$$C. Assuming the volume constant?

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d₁ from C and the distance of the image formed is d₂ from C, the radius of curvature of this mirror is :

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second?

Given : 1 ly = 9.46 $$\times$$ 10¹⁵ m

1 AU = 1.5 $$\times$$ 10¹¹ m

Calculate the amount of charge on capacitor of 4$$\mu$$F. The internal resistance of battery is 1$$\Omega$$ :

Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :

An ideal gas is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is :

In a photoelectric experiment, increasing the intensity of incident light :

A bar magnet is passing through a conducting loop of radius R with velocity $$\upsilon $$. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve :

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

Find the distance of the image from object O, formed by the combination of lenses in the figure :

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10^$$-$$5 m and density 1.2 $$\times$$ 10³ kgm^$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10^$$-$$5 Nsm^$$-$$2. (Neglect buoyancy due to air).

Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $$-$$ 10 $$\times$$ 10¹⁰ t) V/m The velocity of electromagnetic wave in this medium is :

(Given C = speed of light in vacuum)

Five identical cells each of internal resistance 1$$\Omega$$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.


The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :

A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown in the figure. The ratio of $${M \over m}$$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ............ .

The alternating current is given by $$i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A$$

The r.m.s. value of of this current is ................. A.

A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V₀. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : $$\sqrt y $$ where y is ................. .

First, a set of n equal resistors of 10 $$\Omega$$ each are connected in series to a battery of emf 20V and internal resistance 10$$\Omega$$. A current I is observed to flow. Then, the n resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of n is ............... .

If the velocity of a body related to displacement x is given by $$\upsilon = \sqrt {5000 + 24x} $$ m/s, then the acceleration of the body is .................... m/s².

A rod CD of thermal resistance 10.0 KW^$$-$$1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200$$^\circ$$C, 100$$^\circ$$C and 125$$^\circ$$C respectively. The heat current in CD is P watt. The value of P is ................. .

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45$$^\circ$$ and 60$$^\circ$$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $${1 \over {\sqrt x }}$$. The value of x is .................... .