P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at

The compound(s) with TWO lone pairs of electrons on the central atom is(are)

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature

One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against

The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Den

According to the Arrhenius equation,

A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from l

The product(s) of the following reaction sequence is (are)

Positive Tollen’s test is observed for

In the following mono-bromination reaction, the number of possible chiral product(s) is (are)...

In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitative oxidise thiosulphate anions to produ

The possible number of geometrical isomers for the complex [CoL2Cl2]-(L= H2NCH2CH2O-) is (are)...

The reagent(s) that can selectively precipitate S2- from a mixture of S2- and SO42- in aqueous solution is (are) :

The crystalline form of borax has.

The increasing order of atomic radii of the following group 13 elements is

On complete hydrogenation, natural rubber produces

Among [Ni(CO)4], [NiCl4]2$$-$$, [Co(NH3)4)Cl2]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compound i

The correct statements about of the following reaction sequence is (are) Cumene (C9H12) $$\mathrel{\mathop{\kern0pt\long

Let $$S = \left\{ {x \in \left( { - \pi ,\pi } \right):x \ne 0, \pm {\pi \over 2}} \right\}.$$ The sum of all distinct

Let $$ - {\pi \over 6} < \theta < - {\pi \over {12}}.$$ Suppose $${\alpha _1}$$ and $${\beta_1}$$ are the roo

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection

Let $$m$$ be the smallest positive integer such that the coefficient of $${x^2}$$ in the expansion of $${\left( {1 + x}

Let RS be the diameter of the circle $${x^2}\, + \,{y^2} = 1$$, where S is the point (1, 0). Let P be a variable point (

The circle $${C_1}:{x^2} + {y^2} = 3,$$ with centre at $$O$$, intersects the parabola $${x^2} = 2y$$ at the point $$P$$

Let $$f:\mathbb{R} \to \mathbb{R},\,g:\mathbb{R} \to \mathbb{R}$$ and $$h:\mathbb{R} \to \mathbb{R}$$ be differentiable

In a triangle $$\Delta $$$$XYZ$$, let $$x, y, z$$ be the lengths of sides opposite to the angles $$X, Y, Z$$ respectivel

The least value of a $$ \in R$$ for which $$4a{x^2} + {1 \over x} \ge 1,$$, for all $$x>0$$. is

A solution curve of the differential equation $$\left( {{x^2} + xy + 4x + 2y + 4} \right){{dy} \over {dx}} - {y^2} = 0,

The total number of distinct $$x \in \left[ {0,1} \right]$$ for which $$\int\limits_0^x {{{{t^2}} \over {1 + {t^4}}}} dt

A computer producing factory has only two plants $${T_1}$$ and $${T_2}.$$ Plant $${T_1}$$ produces $$20$$% and plant $${

Consider a pyramid $$OPQRS$$ located in the first octant $$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$ with $$O$$ as orig

Let $$f:(0,\infty ) \to R$$ be a differentiable function such that $$f'(x) = 2 - {{f(x)} \over x}$$ for all $$x \in (0,\

Let $$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$

The total number of distinct x $$\in$$ R for which $$\left| {\matrix{ x & {{x^2}} & {1 + {x^3}} \cr {2x} & {4{x^

Let $$z = {{ - 1 + \sqrt 3 i} \over 2}$$, where $$i = \sqrt { - 1} $$, and r, s $$\in$$ {1, 2, 3}. Let $$P = \left[ {\ma

Let $$\alpha$$, $$\beta$$ $$\in$$ R be such that $$\mathop {\lim }\limits_{x \to 0} {{{x^2}\sin (\beta x)} \over {\alpha

A length-scale (l) depends on the permittivity ($$\varepsilon $$) of a dielectric material, Boltzmann constant (kB), the

A uniform wooden stick of mass 1.6 kg and length $$l$$ rests in an inclined manner on a smooth, vertical wall of height

The position vector $$\overrightarrow r $$ of a particle of mass m is given by the following equation $$$\overrightarrow

Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dr

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the meta

A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refra

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wav

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation sy

A plano-convex lens is made of material of refractive index n. When a small object is placed 30 cm away in front of the

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90$$^\circ$$ v

Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car in i

A transparent slab of thickness d has a refractive index n (z) that increases with z. Here, z is the vertical distance i

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their p

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current.

A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.Taking hc = 1.237 $

The isotope $$_5^{12}B$$ having a mass 12.014 u undergoes $$\beta $$-decay to $$_6^{12}C$$. $$_6^{12}C$$ has an excited

An infinite line charge of uniform electric charge density l lies along the axis of an electrically conducting infinite

Two inductors L1 (inductance 1mH, internal resistance 3$$\Omega$$) and L2 (inductance 2 mH, internal resistance 4$$\Omeg