According to the valence bond theory the hybridization of central metal atom is dsp² for which one of the following compounds?

The correct structure of Rhumann's Purple, the compound formed in the reaction of ninhydrin with proteins is :

The correct order of intensity of colors of the compounds is :

The species given below that does NOT show disproportionation reaction is :

An inorganic Compound 'X' on treatment with concentrated H₂SO₄ produces brown fumes and gives dark brown ring with FeSO₄ in presence of concentrated H₂SO₄. Also Compound 'X' gives precipitate 'Y', when its solution in dilute HCl is treated with H₂S gas. The precipitate 'Y' on treatment with concentrated HNO₃ followed by excess of NH₄OH further gives deep blue coloured solution, Compound 'X' is :

Among the given species the Resonance stabilised carbocations are :

In the given reaction

3-Bromo-2, 2-dimethyl butane $$\buildrel {{C_2}{H_5}OH} \over \longrightarrow \mathop {'A'}\limits_{(Major\,\Pr oduct)} $$

Product A is :

Compound A is converted to B on reaction with CHCl₃ and KOH. The compound B is toxic and can be decomposed by C. A, B and C respectively are :

Identify the incorrect statement from the following

Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

For above chemical reactions, identify the correct statement from the following :

The number of lone pairs of electrons on the central I atom in I$$_3^ - $$ is ____________.

250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl. The number of unreacted HCl molecules in the solution after complete reaction is ___________ $$\times$$ 10²¹. (Nearest integer)

(N_A = 6.022 $$\times$$ 10²³)

The Azimuthal quantum number for the valence electrons of Ga⁺ ion is ___________.

(Atomic number of Ga = 31)

The spin-only magnetic moment value for the complex [Co(CN)₆]^4$$-$$ is __________ BM.

[At. no. of Co = 27]

2SO₂(g) + O₂(g) $$\rightleftharpoons$$ 2SO₃(g)

In an equilibrium mixture, the partial pressures are

P_SO3 = 43 kPa; P_O2 = 530 Pa and P_SO2 = 45 kPa. The equilibrium constant K_P = ___________ $$\times$$ 10^$$-$$2. (Nearest integer)

The number of nitrogen atoms in a semicarbazone molecule of acetone is ______________.

To synthesize 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate ___________ equivalents of CH₃MgBr Reagent will be required. (Integer value)

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation, 10% of the virus is inactivated. The rate constant for viral inactivation is ___________ $$\times$$ 10^$$-$$3 min^$$-$$1. (Nearest integer)

[Use : ln 10 = 2.303; log₁₀ 3 = 0.477; property
of logarithm : log x^y = y log x]

An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol^$$-$$1) needed to meet this energy requirement is ____________ g.

(Use : $$\Delta$$_CH(glucose) = $$-$$2700 kJ mol^$$-$$1)

At 20$$^\circ$$ C, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The mole fraction of benzene in the vapour phase at 20$$^\circ$$ above an equimolar mixture of benzene and methyl benzene is _____________ $$\times$$ 10^$$-$$2. (Nearest integer)

Let a be a positive real number such that $$\int_0^a {{e^{x - [x]}}} dx = 10e - 9$$ where [ x ] is the greatest integer less than or equal to x. Then a is equal to:

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

The value of the integral $$\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $$ is equal to:

If $$\alpha$$ and $$\beta$$ are the distinct roots of the equation $${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$$, then the value of $${\alpha ^{96}}({\alpha ^{12}} - 1) + {\beta ^{96}}({\beta ^{12}} - 1)$$ is equal to :

Let $$A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$$, a$$\in$$R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :

If z and $$\omega$$ are two complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$\arg (z) - \arg (\omega ) = {{3\pi } \over 2}$$, then $$\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)$$ is :

(Here arg(z) denotes the principal argument of complex number z)

Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \sqrt {{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}} $$ is ($$-$$ $$\infty$$, a) $$]\cup$$ [b, c) $$\cup$$ [4, $$\infty$$), a < b < c, then the value of a + b + c is :

Let y = y(x) be the solution of the differential equation $$x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( {{y \over x}} \right) - x} \right)dx$$, $$ - 1 \le x \le 1$$, $$y\left( {{1 \over 2}} \right) = {\pi \over 6}$$. Then the area of the region bounded by the curves x = 0, $$x = {1 \over {\sqrt 2 }}$$ and y = y(x) in the upper half plane is :

Let $$A = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix, where $${a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr { - x} & , & {if\,\left| {i - j} \right| = 1} \cr {2x + 1} & , & {otherwise.} \cr } } \right.$$

Let a function f : R $$\to$$ R be defined as f(x) = det(A). Then the sum of maximum and minimum values of f on R is equal to:

The number of real roots of the equation $${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4}$$ is :

Let y = y(x) be the solution of the differential equation $${e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy = 0$$, y(1) = $$-$$1. Then the value of (y(3))² is equal to :

Let 'a' be a real number such that the function f(x) = ax² + 6x $$-$$ 15, x $$\in$$ R is increasing in $$\left( { - \infty ,{3 \over 4}} \right)$$ and decreasing in $$\left( {{3 \over 4},\infty } \right)$$. Then the function g(x) = ax² $$-$$ 6x + 15, x$$\in$$R has a :

Let a function f : R $$\to$$ R be defined as $$f(x) = \left\{ {\matrix{ {\sin x - {e^x}} & {if} & {x \le 0} \cr {a + [ - x]} & {if} & {0 < x < 1} \cr {2x - b} & {if} & {x \ge 1} \cr } } \right.$$

where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x² + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :

Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $$\theta$$, with the vector $$\overrightarrow a $$ + $$\overrightarrow b $$ + $$\overrightarrow c $$. Then 36cos²2$$\theta$$ is equal to ___________.

Let $$A = \left( {\matrix{ 1 & { - 1} & 0 \cr 0 & 1 & { - 1} \cr 0 & 0 & 1 \cr } } \right)$$ and B = 7A²⁰ $$-$$ 20A⁷ + 2I, where I is an identity matrix of order 3 $$\times$$ 3. If B = [b_ij], then b₁₃is equal to _____________.

The number of rational terms in the binomial expansion of $${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$$ is _______________.

If the shortest distance between the lines $$\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k + \lambda (\widehat i - 2\widehat j + 2\widehat k)$$, $$\lambda$$ $$\in$$ R, $$\alpha$$ > 0 and $$\overrightarrow {{r_2}} = - 4\widehat i - \widehat k + \mu (3\widehat i - 2\widehat j - 2\widehat k)$$, $$\mu$$ $$\in$$ R is 9, then $$\alpha$$ is equal to ____________.

Let T be the tangent to the ellipse E : x² + 4y² = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $$\sqrt 5 $$ is $$\alpha$$$$\sqrt 5 $$ + $$\beta$$ + $$\gamma$$ cos^$$-$$1$$\left( {{1 \over {\sqrt 5 }}} \right)$$, then |$$\alpha$$ + $$\beta$$ + $$\gamma$$| is equal to ______________.

Let a, b, c, d in arithmetic progression with common difference $$\lambda$$. If $$\left| {\matrix{ {x + a - c} & {x + b} & {x + a} \cr {x - 1} & {x + c} & {x + b} \cr {x - b + d} & {x + d} & {x + c} \cr } } \right| = 2$$, then value of $$\lambda$$² is equal to ________________.

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is ______________.

If the value of $$\mathop {\lim }\limits_{x \to 0} {(2 - \cos x\sqrt {\cos 2x} )^{\left( {{{x + 2} \over {{x^2}}}} \right)}}$$ is equal to e^a, then a is equal to __________.

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r_d and r_$$\alpha$$ be their respective radii of circular path. The value of $${{{r_d}} \over {{r_\alpha }}}$$ is equal to :

For the circuit shown below, calculate the value of I_z :

A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m². At every point the direction of current density is at an angle of 60$$^\circ$$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is :

(Resistivity of magnesium $$\rho$$ = 44 $$\times$$ 10^$$-$$8 $$\Omega$$m)

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possible speed without skidding is ____________ $$\times$$ 10³ kg m/s². [Given cos30$$^\circ$$ = 0.87, $$\mu$$_s = 0.2]

Consider a mixture of gas molecule of types A, B and C having masses m_A < m_B < m_C. The ratio of their root mean square speeds at normal temperature and pressure is :

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$$^\circ$$ C to 50$$^\circ$$ C when no work is done is ___________. (R is the universal gas constant).

A butterfly is flying with a velocity $$4\sqrt 2 $$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

A certain charge Q is divided into two parts q and (Q $$-$$ q). How should the charges Q and q be divided so that q and (Q $$-$$ q) placed at a certain distance apart experience maximum electrostatic repulsion?

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance.

The value of current in the 6 $$\Omega$$ resistance is :

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s². The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____________ N. [Take g = 10 m/s² and $$\mu$$_s = 0.2]

A nucleus of mass M emits $$\gamma$$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :

[Take 'c' as the speed of electromagnetic wave]

The radiation corresponding to 3 $$\to$$ 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 $$\times$$ 10^$$-$$4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is : (Mass of electron = 9.1 $$\times$$ 10^$$-$$31 kg)

If $$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors satisfying the relation $$\overrightarrow A $$ . $$\overrightarrow B $$ = $$\left| {\overrightarrow A \times \overrightarrow B } \right|$$. Then the value of $$\left| {\overrightarrow A - \overrightarrow B } \right|$$ will be :

The entropy of any system is given by
$$S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$$ where $$\alpha$$ and $$\beta$$ are the constants. $$\mu$$, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
[Take $$S = {{dQ} \over T}$$]
Choose the incorrect option from the following :

AC voltage V(t) = 20 sin$$\omega$$t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m². The amplitude of the oscillating displacement current for the applied AC voltage is _________. [Take $$\varepsilon $$₀ = 8.85 $$\times$$ 10^$$-$$12 F/m]

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s² and 4 m/s² respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

The value of tension in a long thin metal wire has been changed from T₁ to T₂. The lengths of the metal wire at two different values of tension T₁ and T₂ are l₁ and l₂ respectively. The actual length of the metal wire is :

A body having specific charge 8 $$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be _______________ s.

In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is _________ m. (g = 10 m/s²).

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to __________ cm.

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't₁'. When it rolls down the plane, it takes time t₂. The value of $${{{t_2}} \over {{t_1}}}$$ is $$\sqrt {{3 \over x}} $$. The value of x will be _______________.

The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$ at time t = 0 and $$y = {1 \over {1 + {{(x - 2)}^2}}}$$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.

In an LCR series circuit, an inductor 30 mH and a resistor 1 $$\Omega$$ are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 45$$^\circ$$ is $${1 \over x} \times {10^{ - 3}}$$ F. Then the value of x is ____________.

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $$\left( {{m \over M}} \right)$$ is $${1 \over x}$$. The value of 'x' will be ____________.

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ $$\pi$$J.