The correct order of reactivity of the given chlorides with acetate in acetic acid is :

In the structure of the dichromate ion, there is a :

Which one of the following compounds contains $$\beta$$-C₁-C₄ glycosidic linkage?

The major products A and B in the following set of reactions are :

Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature? (Given Z for Nd = 60, Yb = 70, La = 57, Ce = 58)

The major product formed in the following reaction is :

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

Assertion (A) : Treatment of bromine water with propene yields 1-bromopropan-2-ol.

Reason (R) : Attack of water on bromonium ion follows Markovnikov rule and results in 1-bromopropan-2-ol.

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

The denticity of an organic ligand, biuret is :

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

Assertion (A) : Metallic character decreases and non-metallic character increases on moving from left to right in a period.

Reason (R) : It is due to increase in ionisation enthalpy and decrease in electron gain enthalpy, when one moves from left to right in a period.

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

Choose the correct name for compound given below :

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

Assertion (A) : A simple distillation can be used to separate a mixture of propanol and propanone.

Reason (R) : Two liquids with a difference of more than 20$$^\circ$$ in their boiling points can be separated by simple distillations.

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

Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression?

The structure of product C, formed by the following sequence of reactions is :

Consider the following cell reaction :

$$C{d_{(s)}} + H{g_2}S{O_{4(s)}} + {9 \over 5}{H_2}{O_{(l)}}$$ $$\rightleftharpoons$$ $$CdS{O_4}.{9 \over 5}{H_2}{O_{(s)}} + 2H{g_{(l)}}$$

The value of $$E_{cell}^0$$ is 4.315 V at 25$$^\circ$$C. If $$\Delta$$H$$^\circ$$ = $$-$$825.2 kJ mol^$$-$$1, the standard entropy change $$\Delta$$S$$^\circ$$ in J K^$$-$$1 is ___________. (Nearest integer) [Given : Faraday constant = 96487 C mol^$$-$$1]

The molarity of the solution prepared by dissolving 6.3 g of oxalic acid (H₂C₂O₄.2H₂O) in 250 mL of water in mol L^$$-$$1 is x $$\times$$ 10^$$-$$2. The value of x is _____________. (Nearest integer) [Atomic mass : H : 1.0, C : 12.0, O : 16.0]

The total number of reagents from those given blow, that can convert nitrobenzene into aniline is ___________. (Integer answer)

I. Sn $$-$$ HCl

II. Sn $$-$$ NH₄OH

III. Fe $$-$$ HCl

IV. Zn $$-$$ HCl

V. H₂ $$-$$ Pd

VI. H₂ $$-$$ Raney Nickel

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ____________. (Integer answer)

The number of hydrogen bonded water molecule(s) associated with stoichiometry CuSO₄.5H₂O is ____________.

According to the following figure, the magnitude of the enthalpy change of the reaction

A + B $$\to$$ M + N in kJ mol^$$-$$ is equal to ___________. (Integer answer)

Ge(Z = 32) in its ground state electronic configuration has x completely filled orbitals with m_l = 0. The value of x is ___________.

A₃B₂ is a sparingly soluble salt of molar mass M (g mol^$$-$$1) and solubility x g L^$$-$$1. The solubility product satisfies $${K_{sp}} = a{\left( {{x \over M}} \right)^5}$$. The value of a is _____________. (Integer answer)

The number of real roots of the equation

$${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$$ is :

Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If $$\int_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int_0^x {f(t)dt} } $$, $$0 \le x \le 1$$ and f(0) = 0, then $$\mathop {\lim }\limits_{x \to 0} {1 \over {{x^2}}}\int_0^x {f(t)dt} $$ :

Let $$\overrightarrow a $$ and $$\overrightarrow b $$ be two vectors
such that $$\left| {2\overrightarrow a + 3\overrightarrow b } \right| = \left| {3\overrightarrow a + \overrightarrow b } \right|$$ and the angle between $$\overrightarrow a $$ and $$\overrightarrow b $$ is 60$$^\circ$$. If $${1 \over 8}\overrightarrow a $$ is a unit vector, then $$\left| {\overrightarrow b } \right|$$ is equal to :

The function

$$f(x) = \left| {{x^2} - 2x - 3} \right|\,.\,{e^{\left| {9{x^2} - 12x + 4} \right|}}$$ is not differentiable at exactly :

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r², then r² $$-$$ d is equal to :

Which of the following is not correct for relation R on the set of real numbers ?

The integral $$\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$$ is equal to : (where C is a constant of integration)

If p and q are the lengths of the perpendiculars from the origin on the lines,

x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and

x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$

respectively, then k² is equal to :

cosec18$$^\circ$$ is a root of the equation :

If the following system of linear equations

2x + y + z = 5

x $$-$$ y + z = 3

x + y + az = b

has no solution, then :

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :

If the function
$$f(x) = \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \cr k & , & {x = 0} \cr {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x > 0} \cr } } \right.$$ is continuous

at x = 0, then $${1 \over a} + {1 \over b} + {4 \over k}$$ is equal to :

If $${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$$, y(0) = 1, then y(1) is equal to :

$$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}\left( {\pi {{\cos }^4}x} \right)} \over {{x^4}}}$$ is equal to :

If $${a_r} = \cos {{2r\pi } \over 9} + i\sin {{2r\pi } \over 9}$$, r = 1, 2, 3, ....., i = $$\sqrt { - 1} $$, then
the determinant $$\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|$$ is equal to :

Let [t] denote the greatest integer $$\le$$ t. Then the value of

$$8.\int\limits_{ - {1 \over 2}}^1 {([2x] + |x|)dx} $$ is ___________.

A point z moves in the complex plane such that $$\arg \left( {{{z - 2} \over {z + 2}}} \right) = {\pi \over 4}$$, then the minimum value of $${\left| {z - 9\sqrt 2 - 2i} \right|^2}$$ is equal to _______________.

If 'R' is the least value of 'a' such that the function f(x) = x² + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x² + ax + 1 is decreasing on [1, 2], then
the value of |R $$-$$ S| is ___________.

The mean of 10 numbers 7 $$\times$$ 8, 10 $$\times$$ 10, 13 $$\times$$ 12, 16 $$\times$$ 14, ....... is ____________.

If the variable line 3x + 4y = $$\alpha$$ lies between the two
circles (x $$-$$ 1)² + (y $$-$$ 1)² = 1
and (x $$-$$ 9)² + (y $$-$$ 1)² = 4, without intercepting a chord on either circle, then the sum of all the integral values of $$\alpha$$ is ___________.

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________.

If $$x\phi (x) = \int\limits_5^x {(3{t^2} - 2\phi '(t))dt} $$, x > $$-$$2, and $$\phi$$(0) = 4, then $$\phi$$(2) is __________.

If $$\left( {{{{3^6}} \over {{4^4}}}} \right)k$$ is the term, independent of x, in the binomial expansion of $${\left( {{x \over 4} - {{12} \over {{x^2}}}} \right)^{12}}$$, then k is equal to ___________.

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to _____________.

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1, 0) and (1, 1). The output Y for this sequence will be :

Two particles A and B having charges 20$$\mu$$C and $$-$$5$$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:

A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles $$\theta$$₁ and $$\theta$$₂ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles $$\theta$$₁ and $$\theta$$₂ will be equal, is :

The masses and radii of the earth and moon are (M₁, R₁) and (M₂, R₂) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :

Choose the correct waveform that can represent the voltage across R of the following circuit, assuming the diode is ideal one :

A uniform heavy rod of weight 10 kg ms^$$-$$2, cross-sectional area 100 cm² and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 10¹¹ Nm^$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

Two plane mirrors M₁ and M₂ are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M₁ and M₂ respectively. The shortest distance between the images thus formed is : (Take $$\sqrt 5 $$ = 2.3)

Match List - I with List - II.

	List - I		List - II
(a)	Torque	(i)	MLT$$^{ - 1}$$
(b)	Impulse	(ii)	MT$$^{ - 2}$$
(c)	Tension	(iii)	ML$$^{ 2}$$T$$^{ - 2}$$
(d)	Surface Tension	(iv)	MLT$$^{ - 2}$$

Choose the most appropriate answer from the option given below :

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p₀ at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)

Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, $$\theta$$ = angle, $$\rho$$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque, $$\in$$ = permittivity, E = electric field, J = current density, L = length.

Angular momentum of a single particle moving with constant speed along circular path :

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with X_L = R = X_C. Impedance of this circuit is :

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

Consider a galvanometer shunted with 5$$\Omega$$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%.

(The bulk modulus of rubber = 9.8 $$\times$$ 10⁸ Nm^$$-$$2, Density of sea water = 10³ kgm^$$-$$3, g = 9.8 m/s²)

A particle of mass 1 kg is hanging from a spring of force constant 100 Nm^$$-$$1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is $${T \over x}$$. The value of x is _____________.

A square shaped wire with resistance of each side 3$$\Omega$$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of $$\Omega$$ will be ___________.

A wire having a linear mass density 9.0 $$\times$$ 10^$$-$$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ____________ m.

The voltage drop across 15$$\Omega$$ resistance in the given figure will be ______________ V.

A block moving horizontally on a smooth surface with a speed of 40 ms^$$-$$1 splits into two equal parts. If one of the parts moves at 60 ms^$$-$$1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ___________.

The electric field in an electromagnetic wave is given by E = (50 NC^$$-$$1) sin$$\omega$$ (t $$-$$ x/c)

The energy contained in a cylinder of volume V is 5.5 $$\times$$ 10^$$-$$12 J. The value of V is _____________ cm³. (given $$\in$$₀ = 8.8 $$\times$$ 10^$$-$$12C²N^$$-$$1m^$$-$$2)

A capacitor of 50 $$\mu$$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________$$\mu$$C.

A car is moving on a plane inclined at 30$$^\circ$$ to the horizontal with an acceleration of 10 ms^$$-$$2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ______________. (Take g = 10 ms^$$-$$2)