The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is :

The incorrect statement among the following is :

Which one of the following compounds is non-aromatic?

According to Bohr's atomic theory :

(A) Kinetic energy of electron is $$ \propto {{{Z^2}} \over {{n^2}}}$$.

(B) The product of velocity (v) of electron and principal quantum number (n), $$'vn' \propto {Z^2}$$.

(C) Frequency of revolution of electron in an orbit is $$ \propto {{{Z^3}} \over {{n^3}}}$$.

(D) Coulombic force of attraction on the electron is $$ \propto {{{Z^3}} \over {{n^4}}}$$.

Choose the most appropriate answer from the options given below :

Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of HgSO₄ and H₂SO₄?

The correct set from the following in which both pairs are in correct order of melting point is :

What is the correct sequence of reagents used for converting nitrobenzene into m-dibromobenzene?

The calculated magnetic moments (spin only value) for species $${[FeC{l_4}]^{2 - }}$$, $${[Co{({C_2}{O_4})_3}]^{3 - }}$$ and $$MnO_4^{2 - }$$ respectively are :

Which of the following reagent is suitable for the preparation of the product in the above reaction?

What is the correct order of the following elements with respect to their density?

Match List - I and List - II.

	List I		List II
(a)	Valium	(i)	Antifertility drug
(b)	Morphine	(ii)	Pernicious anaemia
(c)	Norethindrone	(iii)	Analgesic
(d)	Vitamin $${B_{12}}$$	(iv)	Tranquilizer

The correct shape and $$I - I - I$$ bond angles respectively in $$I_3^ - $$ ion are :

The diazonium salt of which of the following compounds will form a coloured dye on reaction with $$\beta$$-Naphthol in NaOH?

Match List - I and List - II.

	List-I		List-II
(a)		(i)	$$\mathrm{Br}_{2} / \mathrm{NaOH}$$
(b)		(ii)	$$\mathrm{H}_{2} / \mathrm{Pd}-\mathrm{BaSO}_{4}$$
(c)		(iii)	$$\mathrm{Zn}(\mathrm{Hg}) / \mathrm{H}$$ Conc. $$\mathrm{HCl}$$
(d)		(iv)	$$\mathrm{Cl}_{2}$$ Red $$\mathrm{P}, \mathrm{H}_{2} \mathrm{O}$$

Choose the correct answer from the options given below :

The formula of a gaseous hydrocarbon which requires 6 times of its own volume of O₂ for complete oxidation and produces 4 times its own volume of CO₂ is C_xH_y. The value of y is _____________.

The solubility product of PbI₂ is 8.0 $$\times$$ 10^$$-$$9. The solubility of lead iodide in 0.1 molar solution of lead nitrate is x $$\times$$ 10^$$-$$6. mol/L. The value of x is __________. (Rounded off to the nearest integer) [Given $$\sqrt 2 $$ = 1.41]

1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is __________ $$\times$$ 10^$$-$$2.

Assuming ideal behaviour, the magnitude of log K for the following reaction at 25$$^\circ$$C is x $$\times$$ 10^$$-$$1. The value of x is ______________. (Integer answer)

$$3HC \equiv C{H_{(g)}} \rightleftharpoons {C_6}{H_{6(l)}}$$

[Given : $${\Delta _f}{G^o}(HC \equiv CH) = - 2.04 \times {10^5}$$ J mol^$$-$$1 ; $${\Delta _f}{G^o}({C_6}{H_6}) = - 1.24 \times {10^5}$$ J mol^$$-$$1 ; R = 8.314 J K^-1 mol^$$-$$1]

C₆H₆ freezes at 5.5$$^\circ$$C. The temperature at which a solution of 10g of C₄H₁₀ in 200g of C₆H₆ freeze is __________ $$^\circ$$C. (The molal freezing point depression constant of C₆H₆ is 5.12$$^\circ$$C/m.)

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25$$^\circ$$C. After 9 h, the fraction of sucrose remaining is f. The value of $${\log _{10}}\left( {{1 \over f}} \right)$$ is ________ $$\times$$ 10^$$-$$2. (Rounded off to the nearest integer)

[Assume : ln 10 = 2.303, ln 2 = 0.693]

The magnitude of the change in oxidising power of the $$MnO_4^ - /M{n^{2 + }}$$ couple is x $$\times$$ 10^$$-$$4 V, if the H⁺ concentration is decreased from 1M to 10^$$-$$4 M at 25$$^\circ$$C. (Assume concentration of $$MnO_4^ - $$ and $$M{n^{2 + }}$$ to be same on change in H⁺ concentration). The value of x is ___________. $$\left[ {Given\,:{{2.303RT} \over F} = 0.059} \right]$$

The total number of amines among the following which can be synthesized by Gabriel synthesis is __________.

Let A and B be 3 $$\times$$ 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A²B² $$-$$ B²A²) X = O, where X is a 3 $$\times$$ 1 column matrix of unknown variables and O is a 3 $$\times$$ 1 null matrix, has :

The value of the integral, $$\int\limits_1^3 {[{x^2} - 2x - 2]dx} $$, where [x] denotes the greatest integer less than or equal to x, is :

Let a, b$$ \in $$R. If the mirror image of the point P(a, 6, 9) with respect to the line

$${{x - 3} \over 7} = {{y - 2} \over 5} = {{z - 1} \over { - 9}}$$ is (20, b, $$-$$a$$-$$9), then | a + b |, is equal to :

For the system of linear equations:

$$x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$$,

consider the following statements :

(A) The system has unique solution if $$k \ne 2,k \ne - 2$$.

(B) The system has unique solution if k = $$-$$2

(C) The system has unique solution if k = 2

(D) The system has no solution if k = 2

(E) The system has infinite number of solutions if k $$ \ne $$ $$-$$2.

Which of the following statements are correct?

Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $$-$$ x) for all x$$ \in $$ (0, 2), f(0) = 1 and f(2) = e². Then the value of $$\int\limits_0^2 {f(x)} dx$$ is :

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $$ \ne $$ 0 for all x $$ \in $$ R. If $$\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$$ = 0, for all x$$ \in $$R, then the value of f(1) lies in the interval :

Let $$f:R \to R$$ be defined as

$$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$$

Let A = {x $$ \in $$ R : f is increasing}. Then A is equal to :

If P is a point on the parabola y = x² + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

A possible value of $$\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)$$ is :

The area of the region : $$R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $$ is :

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ($$-$$5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________

If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.

Let $$\lambda$$ be an integer. If the shortest distance between the lines

x $$-$$ $$\lambda$$ = 2y $$-$$ 1 = $$-$$2z and x = y + 2$$\lambda$$ = z $$-$$ $$\lambda$$ is $${{\sqrt 7 } \over {2\sqrt 2 }}$$, then the value of | $$\lambda$$ | is _________.

If a + $$\alpha$$ = 1, b + $$\beta$$ = 2 and $$af(x) + \alpha f\left( {{1 \over x}} \right) = bx + {\beta \over x},x \ne 0$$, then the value of the expression $${{f(x) + f\left( {{1 \over x}} \right)} \over {x + {1 \over x}}}$$ is __________.

Let $$i = \sqrt { - 1} $$. If $${{{{\left( { - 1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 - i)}^{24}}}} + {{{{\left( {1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 + i)}^{24}}}} = k$$, and $$n = [|k|]$$ be the greatest integral part of | k |. Then $$\sum\limits_{j = 0}^{n + 5} {{{(j + 5)}^2} - \sum\limits_{j = 0}^{n + 5} {(j + 5)} } $$ is equal to _________.

The number of the real roots of the equation $${(x + 1)^2} + |x - 5| = {{27} \over 4}$$ is ________.

The students S₁, S₂, ....., S₁₀ are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is ___________.

The sum of first four terms of a geometric progression (G. P.) is $${{65} \over {12}}$$ and the sum of their respective reciprocals is $${{65} \over {18}}$$. If the product of first three terms of the G.P. is 1, and the third term is $$\alpha$$, then 2$$\alpha$$ is _________.

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is :

If the source of light used in a Young's double slit experiment is changed from red to violet :

The logic circuit shown above is equivalent to :

Figure shows a circuit that contains four identical resistors with resistance R = 2.0$$\Omega$$, two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9V. The current 'i' just after the switch 'S' is closed will be :

A particle is projected with velocity v₀ along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = $$-$$ $$\alpha$$x². The distance at which the particle stops :

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

If one mole of an ideal gas at (P₁, V₁) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B $$ \to $$ C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to :

A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?

[Use $$g = {{GM} \over {{R^2}}}$$ = 9.8 ms^$$-$$2 and radius of earth, R = 6400 km.]

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

Which of the following equations represents a travelling wave?

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

Match List - I with List - II.

	List I		List II
(a)	Source of microwave frequency	(i)	Radioactive decay of nucleus
(b)	Source of infrared frequency	(ii)	Magnetron
(c)	Source of Gamma Rays	(iii)	Inner shell electrons
(d)	Source of X-rays	(iv)	Vibration of atoms and molecules
		(v)	LASER
		(vi)	RC circuit

Choose the correct answer from the options given below :

A circular hole of radius $$\left( {{a \over 2}} \right)$$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :

Zener breakdown occurs in a p $$-$$ n junction having p and n both :

The de-Broglie wavelength of a proton and $$\alpha$$-particle are equal. The ratio of their velocities is :

According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ $$\times$$ 10^$$-$$2 cm.

A cylindrical wire of radius 0.5 mm and conductivity 5 $$\times$$ 10⁷ S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x³$$\pi$$ mA. The value of x is _________.

Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)_A : (K.E.)_B will be $${{A \over 1}}$$, so the value of A will be ________.

The root mean square speed of molecules of a given mass of a gas at 27$$^\circ$$C and 1 atmosphere pressure is 200 ms^$$-$$1. The root mean square speed of molecules of the gas at 127$$^\circ$$C and 2 atmosphere pressure is $${{x \over {\sqrt 3 }}}$$ ms^$$-$$1. The value of x will be _________.

A series L-C-R circuit is designed to resonate at an angular frequency $$\omega$$₀ = 10⁵ rad/s. The circuit draws 16W power from 120V source at resonance. The value of resistance 'R' in the circuit is _________ $$\Omega$$.

A point charge of +12$$\mu$$C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ $$\times$$ 10³ Nm²/C.

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ $$\times$$ 10^$$-$$1 kg m².