The electrode potential of M²⁺/M of 3d-series elements shows positive value for :

Which of the following reagent is used for the following reaction ?

$$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_3 \stackrel{?}{\longrightarrow} \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO} $$

Which of the following are isostructural pairs ?

A. $$SO_4^{2 - }$$ and $$CrO_4^{2 - }$$

B. SiCl₄, and TiCl₄

C. NH₃ and NO₃^-

D. BCl₃ and BrCl₃

Consider the elements Mg, Al, S, P and Si, the correct increasing order of their first ionization enthalpy is :

Out of the following, which type of interaction is reponsible for the stabilisation of $$\alpha $$-helix structure of proteins ?

Which of the following compound gives pink colour on reaction with phthalic anhydride in conc. H₂SO₄ followed by treatment with NaOH ?

Given below are two statements :

Statement I : Colourless cupric metaborate is reduced to cuprous metaborate in a luminous flame.

Statement II : Cuprous metaborate is obtained by heating boric anhydride and copper sulphate in a non-luminous flame.

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

In the following reaction the reason why meta-nitro product also formed is :

What is the major product formed by HI on reaction with

'A' and 'B' in the following reactions are :

Identify products A and B.

What is the final product (major) 'A' in the given reaction ?

The product formed in the first step of the reaction of


with excess $$\mathrm{Mg/Et_2O}$$ ($$\mathrm{Et=C_2H_5}$$) is

Number of amphoteric compounds among the following is ________.
(A) BeO
(B) BaO
(C) Be(OH)₂
(D) Sr(OH)₂

The stepwise formation of $${\left[ {Cu{{\left( {N{H_3}} \right)}_4}} \right]^{2 + }}$$ is given below:


The value of stability constants K₁, K₂, K₃ and K₄ are 10⁴, 1.58 x 10³, 5 x 10² and 10² respectively.
The overall equilibrium constants for dissociation of $${\left[ {Cu{{\left( {N{H_3}} \right)}_4}} \right]^{2 + }}$$ is x $$ \times $$ 10^-12.
The value of x is ________. (Rounded off to the nearest integer)

A proton and a Li³⁺ nucleus are accelerated by the same potential. If $$\lambda _{Li}$$ and $$\lambda _p$$ denote the de Broglie wavelengths of Li³⁺ and proton respectively, then the value of $${{{\lambda _{Li}}} \over {{\lambda _p}}}$$ is x $$ \times $$ 10^-1.
The value of x is ______. (Rounded off to the nearest integer)
[Mass of Li³⁺ = 8.3 mass of proton]

At 1990 K and 1 atm pressure, there are equal number of Cl₂, molecules and Cl atoms in the reaction mixture. The value of K_p for the reaction Cl_{2 (g)} $$ \rightleftharpoons $$ 2Cl_(g) under the above conditions is x $$ \times $$ 10^-1.
The value of x is _______. (Rounded off to the nearest integer)

When 9.45 g of CICH₂COOH is added to 500 mL of water, its freezing point drops by 0.5°C. The dissociation constant of CICH₂COOH is x $$ \times $$ 10^-3.
The value of x is ________. (Rounded off to the nearest integer)
[K_f(H20) = 1.86 K kg mol^-1]

4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the solution in M is x $$ \times $$ 10^-1.
The value of x is _______. (Rounded off to the nearest integer)

The reaction of sulphur in alkaline medium is given below:


The values of 'a' is _______. (Integer answer)

For the reaction A_(g) $$ \to $$ B_(g) the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The value of $$\Delta $$_rG for the reaction at 300 K and 1 atm in J mol^-1 is – xR, where x is _______. (Rounded off to the nearest integer)
[R = 8.31 J mol^–1K^-1 and ln 10 = 2.3)

Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k' value of 3.3 $$ \times $$ 10^-4 s^-1 at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is ______.
(Rounded off to the nearest integer)

If $$\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \right) + c$$, where c is a constant of integration, then the ordered pair (a, b) is equal to :

If f : R $$ \to $$ R is a function defined by f(x)= [x - 1] $$\cos \left( {{{2x - 1} \over 2}} \right)\pi $$, where [.] denotes the greatest integer function, then f is :

The population P = P(t) at time 't' of a certain species follows the differential equation

$${{dP} \over {dt}}$$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :

Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) = $${{x - {1 \over 2}} \over {x - 1}}$$. Then the composition function f(g(x)) is :

The function
f(x) = $${{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$$ :

$$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$$ is equal to :

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is :

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $${1 \over 4}$$. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then, which of these stones is / are on the path of the man?

Let p and q be two positive numbers such that p + q = 2 and p⁴+q⁴ = 272. Then p and q are roots of the equation :

The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the parabola y² = 9x, is :

If $${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$ satisfies the equation t² - 9t + 8 = 0, then the value of
$${{2\sin x} \over {\sin x + \sqrt 3 \cos x}}\left( {0 < x < {\pi \over 2}} \right)$$ is :

The locus of the mid-point of the line segment joining the focus of the parabola y² = 4ax to a moving point of the parabola, is another parabola whose directrix is :

The system of linear equations
3x - 2y - kz = 10
2x - 4y - 2z = 6
x+2y - z = 5m
is inconsistent if :

Let P = $$\left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where $$\alpha $$ $$ \in $$ R. Suppose Q = [ q_ij] is a matrix satisfying PQ = kl₃ for some non-zero k $$ \in $$ R.
If q₂₃ = $$ - {k \over 8}$$ and |Q| = $${{{k^2}} \over 2}$$, then a² + k² is equal to ______.

The minimum value of $$\alpha $$ for which the
equation $${4 \over {\sin x}} + {1 \over {1 - \sin x}} = \alpha $$ has at least one solution in $$\left( {0,{\pi \over 2}} \right)$$ is .......

If the least and the largest real values of a, for which the
equation z + $$\alpha $$|z – 1| + 2i = 0 (z $$ \in $$ C and i = $$\sqrt { - 1} $$) has a solution, are p and q respectively; then 4(p² + q²) is equal to __________.

$$\mathop {\lim }\limits_{n \to \infty } \tan \left\{ {\sum\limits_{r = 1}^n {{{\tan }^{ - 1}}\left( {{1 \over {1 + r + {r^2}}}} \right)} } \right\}$$ is equal to ______.

Let  A = {n $$ \in $$ N: n is a 3-digit number}

       B = {9k + 2: k $$ \in $$ N}

and C = {9k + $$l$$: k $$ \in $$ N} for some $$l ( 0 < l < 9)$$

If the sum of all the elements of the set A $$ \cap $$ (B $$ \cup $$ C) is 274 $$ \times $$ 400, then $$l$$ is equal to ________.

If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is ________.

If $$\int\limits_{ - a}^a {\left( {\left| x \right| + \left| {x - 2} \right|} \right)} dx = 22$$, (a > 2) and [x] denotes the greatest integer $$ \le $$ x, then$$\int\limits_{ - a}^a {\left( {x + \left[ x \right]} \right)} dx$$ is equal to _________.

Let M be any 3 $$ \times $$ 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of M^TM is seven, is ________.

Let B_i (i = 1, 2, 3) be three independent events in a sample space. The probability that only B₁ occur is $$\alpha $$, only B₂ occurs is $$\beta $$ and only B₃ occurs is $$\gamma $$. Let p be the probability that none of the events B_i occurs and these 4 probabilities satisfy the equations $$\left( {\alpha - 2\beta } \right)p = \alpha \beta $$ and $$\left( {\beta - 3\gamma } \right)p = 2\beta \gamma $$ (All the probabilities are assumed to lie in the interval (0, 1)).
Then $${{P\left( {{B_1}} \right)} \over {P\left( {{B_3}} \right)}}$$ is equal to ________.

A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillations will be :

A current through a wire depends on time as

i = $$\alpha$$₀t + $$\beta$$t²

where $$\alpha$$₀ = 20 A/s and $$\beta$$ = 8 As^$$-$$2. Find the charge crossed through a section of the wire in 15 s.

Match List I with List II.

	List I		List II
(a)	Isothermal	(i)	Pressure constant
(b)	Isochoric	(ii)	Temperature constant
(c)	Adiabatic	(iii)	Volume constant
(d)	Isobaric	(iv)	Heat content is constant

Choose the correct answer from the options given below :

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A $$ \to $$ B : Isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂ = 2V₁ and pressure charges from P₁ to P₂

B $$ \to $$ C : Isobaric compression at pressure P₂ to initial volume V₁.

C $$ \to $$ A : Isochoric change leading to change of pressure from P₂ to P₁.

Total workdone in the complete cycle ABCA is :

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$$\alpha$$'. The metal sheet is heated uniformly, by a small temperature $$\Delta$$T, so that its new temperature is T + $$\Delta$$T. Calculate the increase in the volume of the metal box.

A cell E₁ of emf 6V and internal resistance 2$$\Omega$$ is connected with another cell E₂ of emf 4V and internal resistance 8$$\Omega$$ (as shown in the figure). The potential difference across points X and Y is :

The focal length f is related to the radius of curvature r of the spherical convex mirror by :

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :

Consider two satellites S₁ and S₂ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S₁ to the angular velocity of satellite S₂ is :

If Y, K and $$\eta $$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.

The transitions A, B and C respectively represent :

The work done by a gas molecule in an isolated system is

given by, $$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. $$\alpha$$ and $$\beta$$ are constants. Then the dimensions of $$\beta$$ will be :

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as;

I₁ = M.I. of thin circular ring about its diameter,

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.

Then :

An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30$$^\circ$$ in clockwise direction, the intensity of emerging light will be _________ Lumens.

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$$^\circ$$ with the original direction. The ratio of velocities of the balls after collision is x : y, where x is __________.

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ $$\times$$ 10⁷ m/s.

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu$$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are ___________.

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms^$$-$$2]

In connection with the circuit drawn below, the value of current flowing through 2 k$$\Omega$$ resistor is _________ $$\times$$ 10^$$-$$4 A.

Given below are two statements :

Statement I : Two photons having equal linear momenta have equal wavelengths.

Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.

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