The correct option(s) to distinguish nitrate salts of $$M{n^{2 + }}$$ and $$C{u^{2 + }}$$ taken separately is (are)

For a reaction, $$A\,\,\rightleftharpoons\,\,P,$$ the plots of $$\left[ A \right]$$ and $$\left[ P \right]$$ with time a

Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air

The total number of compounds having at least one bridging oxo group among the molecules given below is _________. $${N

The correct option(s) regarding the complex $${\left[ {Co\left( {en} \right){{\left( {N{H_3}} \right)}_3}\left( {{H_2}O

To measure the quantity of $$MnC{l_2}$$ dissolved in an aqueous solution, it was completely converted to $$KMn{O_4}$$ u

The surface of copper gets tarnished by the formation of copper oxide. $${N_2}$$ gas was passed to prevent the oxide for

The Fischer presentation of $$D$$-glucose is given below. The correct structure(s) of $$\beta $$-$$L$$-glucopyranose i

In the following reaction sequence, the amount of $$D$$ (in g) formed from $$10$$ moles of acetophenone is ___________.

Aniline reacts with mixed acid (conc. $$HN{O_3}$$ and conc. $${H_2}S{O_4}$$) at $$288$$ $$K$$ to give P $$\left( {51\% }

For a first order reaction $$A\left( g \right) \to 2B\left( g \right) + C\left( g \right)$$ at constant volume and $$300

Match each set of hybrid orbitals from LIST - A with complex(es) given in LIST - B .tg {border-collapse:collapse;borde

Consider the following reversible reaction, $$A\left( g \right) + B\left( g \right) \to AB\left( g \right).$$ The activ

Consider an electrochemical cell : $$A\left( s \right)\left| {{A^{n + }}\left( {aq,2M} \right)} \right|{B^{2n + }}\left

Dilution processes of different aqueous solutions, with water, are given in LIST - I. The effects of dilution of the sol

The desired product $$X$$ can be prepared by reacting the major product of the reactions in LIST-I with one or more app

LIST-I contains reactions and LIST-II contains major products. Match the reaction in LIST-I with one or more prod

For the given compound $$X,$$ the total number of optically active stereoisomers is ____________.

For any positive integer n, define $${f_n}:(0,\infty ) \to R$$ as$${f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \lef

Let T be the line passing through the points P($$-$$2, 7) and Q(2, $$-$$5). Let F1 be the set of al pairs of circles (S1

Let S be the set of all column matrices $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \rig

Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let t

Let s, t, r be non-zero complex numbers and L be the set of solutions $$z = x + iy(x,y \in R,\,i = \sqrt { - 1} )$$ of t

Let f : (0, $$\pi $$) $$ \to $$ R be a twice differentiable function such that $$\mathop {\lim }\limits_{t \to x} {{f(x)

The value of the integral$$\int_0^{1/2} {{{1 + \sqrt 3 } \over {{{({{(x + 1)}^2}{{(1 - x)}^6})}^{1/4}}}}dx} $$ is ......

Let P be a matrix of order 3 $$ \times $$ 3 such that all the entries in P are from the set {$$-$$1, 0, 1}. Then, the ma

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $$\alpha $$ is the number of one-one f

Let f : R $$ \to $$ R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation $${{dy

Let f : R $$ \to $$ R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(

Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicula

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respect

Let $$X = {({}^{10}{C_1})^2} + 2{({}^{10}{C_2})^2} + 3{({}^{10}{C_3})^2} + ... + 10{({}^{10}{C_{10}})^2}$$, where $${}^{

Let $${E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}$$ and $${E_2} = \left\{ \matrix{ x \in

In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4,

Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane w

Let $${f_1}:R \to R,\,{f_2}:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R,\,{f_3}:( - 1,{e^{\pi /2}} - 2) \to

A particle, of mass $${10^{ - 3}}$$ $$kg$$ and charge $$1.0$$ $$C,$$ is initially at rest. At time $$t=0,$$ the particle

Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is

An infinitely long thin non-conducting wire is parallel to the $$z$$-axis and carries a uniform line charge density $$\l

In a radioactive decay chain, $${}_{90}^{232}Th$$ nucleus decays to $${}_{82}^{212}Pb$$ nucleus. Let $${N_\alpha }$$ and

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $$f,$$

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $$500$$ $$Hz$$ is

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $$m=0.4$$ $$kg$$ is at rest

A moving coil galvanometer has $$50$$ turns and each turn has an area $$2 \times {10^{ - 4}}\,{m^2}.$$ The magnetic fiel

A ball is projected from the ground at an angle of $${45^o}$$ with the horizontal surface. It reaches a maximum height o

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial v

A steel wire of diameter $$0.5$$ $$mm$$ and Young's modulus $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ carries a load of mass

Consider a hydrogen-like ionized atom with atomic number $$Z$$ with a single electron. In the emission spectrum of this

In a photoelectric experiment a parallel beam of monochromatic light with power of $$200$$ $$W$$ is incident on a perfec

The electric field $$E$$ is measured at a point $$P(0,0,d)$$ generated due to various charge distributions and the depen

A planet of mass $$M,$$ has two natural satellites with masses $${m_1}$$ and $${m_2}.$$ The radii of their circular or

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $$PV$$-diagram be

In the List-$${\rm I}$$ below, four different paths of a particle are given as functions of time. In these functions, $

A particle of mass $$m$$ is initially at rest at the origin. It is subjected to a force and starts moving along the $$x$