The third ionization enthalpy is minimum for :

A graph of vapour pressure and temperature for three different liquids X, Y, and Z is shown below : The following inferences are made :
(A) X has higher intermolecular interactions compared to Y.
(B) X has lower intermolecular interactions compared to Y.
(C) Z has lower intermolecular interactions compared to Y.
The correct inference (s) is / are :

Arrange the following compounds in increasing order of C–OH bond length :
methanol, phenol, p-ethoxyphenol

The complex that can show fac- and mer-isomers is :

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

For the Balmer series in the spectrum of H atom,
$$\overline \nu = {R_H}\left\{ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right\}$$, the correct statements among (I) to (IV) are :
(I) As wavelength decreases, the lines in the series converge
(II) The integer n₁ is equal to 2
(III) The lines of longest wavelength corresponds to n₂ = 3
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines

The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is _______.

Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is _______.
Atomic weight : Fe = 55.85; S = 32.00; O = 16.00

What would be the electrode potential for the given half cell reaction at pH = 5? ______.

2H₂O $$ \to $$ O₂ + 4H^{$$ \oplus $$} + 4e^– ; $$E_{red}^0$$ = 1.23 V

(R = 8.314 J mol^–1 K^–1 ; Temp = 298 k;

oxygen under std. atm. pressure of 1 bar)

The volume (in mL) of 0.125 M AgNO₃ required to quantitatively precipitate chloride ions in 0.3 g of [Co(NH₃)₆]Cl₃ is ________.
M_{[Co(NH3)6Cl3]} = 267.46 g/mol
M_AgNO3 = 169.87 g/mol

The decreasing order of reactivity towards dehydrohalogenation (E₁) reaction of the following compounds is :

The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :

Which of the following statement is not true for glucose?

The strength of an aqueous NaOH solution is most accurately determined by titrating :
(Note : consider that an appropriate indicator is used)

The rate of a certain biochemical reaction at physiological temperature (T) occurs 10⁶ times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at 63^oC while the other boils at 60^oC What is the best way to separate the two liquids and which one will be distilled out first ?

The major product of the following reaction is :

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

The predominant intermolecular forces present in ethyl acetate, a liquid, are:

The most suitable reagent for the given conversion is :

The least positive value of 'a' for which the equation

2x² + (a – 10)x + $${{33} \over 2}$$ = 2a has real roots is

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.

The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the sum of the diagonal elements of AA^T is 3, is

Let ƒ(x) = xcos^–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?

The shortest distance between the lines

$${{x - 3} \over 3} = {{y - 8} \over { - 1}} = {{z - 3} \over 1}$$ and

$${{x + 3} \over { - 3}} = {{y + 7} \over 2} = {{z - 6} \over 4}$$ is :

The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$ \in $$ (-1, 1), is :

If $$\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$$

where c is a constant of integration, then $$\lambda f\left( {{\pi \over 3}} \right)$$ is equal to

Let A and B be two independent events such that
P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$.
Then, which of the following is TRUE?

The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :

For which of the following ordered pairs ($$\mu $$, $$\delta $$), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = $$\mu $$
4x + 4y + 4z = $$\delta $$
is inconsistent ?

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p $$ \ne $$ 0 and q $$ \ne $$ 0. If the new mean and new s.d. become half of their original values, then q is equal to

For a > 0, let the curves C₁ : y² = ax and C₂ : x² = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C₁ and C₂, and the area of
$$\Delta $$OQR = $${1 \over 2}$$, then 'a' satisfies the equation :

If the equation, x² + bx + 45 = 0 (b $$ \in $$ R) has conjugate complex roots and they satisfy |z +1| = 2$$\sqrt {10} $$ , then :

Let two points be A(1, –1) and B(0, 2). If a point P(x', y') be such that the area of $$\Delta $$PAB = 5 sq. units and it lies on the line, 3x + y – 4$$\lambda $$ = 0, then a value of $$\lambda $$ is :

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

$$\sqrt {1 - {x^2}} {{dy} \over {dx}} + \sqrt {1 - {y^2}} = 0$$, |x| < 1.

If $$y\left( {{1 \over 2}} \right) = {{\sqrt 3 } \over 2}$$, then $$y\left( { - {1 \over {\sqrt 2 }}} \right)$$ is equal to :

$$\mathop {\lim }\limits_{x \to 0} {\left( {{{3{x^2} + 2} \over {7{x^2} + 2}}} \right)^{{1 \over {{x^2}}}}}$$ is equal to

Let ƒ(x) = (sin(tan^–1x) + sin(cot^–1x))² – 1, |x| > 1.
If $${{dy} \over {dx}} = {1 \over 2}{d \over {dx}}\left( {{{\sin }^{ - 1}}\left( {f\left( x \right)} \right)} \right)$$ and $$y\left( {\sqrt 3 } \right) = {\pi \over 6}$$, then y($${ - \sqrt 3 }$$) is equal to :

Let ƒ : R $$ \to $$ R be such that for all x $$ \in $$ R
(2^1+x + 2^1–x), ƒ(x) and (3^x + 3^–x) are in A.P.,
then the minimum value of ƒ(x) is

If a, b and c are the greatest value of ¹⁹C_p, ²⁰C_q and ²¹C_r respectively, then :

Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is:
(Graphs are schematic and not drawn to scale)

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are :

Photon with kinetic energy of 1MeV moves from south to north. It gets an acceleration of 10¹² m/s² by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is 1.6 × 10^–27 kg) :

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy T_A eV end de-Broglie wavelength $$\lambda _A$$. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is T_B = (T_A – 1.5) eV. If the de-Broglie wavelength of these photoelectrons $$\lambda _B$$ = 2$$\lambda _A$$, then the work function of metal B is :

Consider a solid sphere of radius R and mass density
$$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$ , $$0 < r \le R$$
The minimum density of a liquid in which it will float is :

In finding the electric field using Gauss Law the formula $$\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}$$ is applicable. In the formula $${{\varepsilon _0}}$$ is permittivity of free space, A is the area of Gaussian surface and q_enc is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?

The graph which depicts the results of Rutherford gold foil experiment with $$\alpha $$-particales is :
$$\theta $$ : Scattering angle
Y : Number of scattered $$\alpha $$-particles detected (Plots are schematic and not to scale)

A particle is moving along the x-axis with its coordinate with the time 't' given be
x(t) = 10 + 8t – 3t². Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t³.
At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as $$\sqrt v $$. Then v (in m/s) is ______.

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is ______.

A body A, of mass m = 0.1 kg has an initial velocity of 3$$\widehat i$$ ms^-1 . It collides elastically with another body, B of the same mass which has an initial velocity of 5$$\widehat j$$ ms^-1. After collision, A moves with a velocity $$\overrightarrow v = 4\left( {\widehat i + \widehat j} \right)$$. The energy of B after collision is written as $${x \over {10}}$$. The value of x is ___________.

Effective capacitance of parallel combination of two capacitors C₁ and C₂ is 10 μF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C₂ is 4 times that of C₁. If these capacitors are connected in series, their effective capacitance will be :

Four resistances of 15$$\Omega $$, 12$$\Omega $$, 4$$\Omega $$ and 10$$\Omega $$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10$$\Omega $$ to balance the network is _____$$\Omega $$.

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell $$. The other end is fixed. The system is given an angular speed $$\omega $$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :

Boolean relation at the output stage-Y for the following circuit is :

Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is :

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $${4 \over 3}$$ for this wavelength, will be :

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is :

The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of its eye piece ?

The dimension of stopping potential V₀ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

A thermodynamic cycle xyzx is shown on a V-T diagram. The P-V diagram that best describes this cycle is :
(Diagrams are schematic and not to scale)