Identify the product A and product B in the following set of reactions.

The molar conductivity for electrolytes $$A$$ and $$B$$ are plotted against $$C^{3 / 2}$$ as shown below. Electrolytes $

Given below are two statements : Statement (I) : The oxidation state of an element in a particular compound is the charg

$$0.05 \mathrm{M} \mathrm{~CuSO}_4$$ when treated with $$0.01 \mathrm{M} \mathrm{~K}_2 \mathrm{Cr}_2 \mathrm{O}_7$$ give

Identify major product "X" formed in the following reaction :

The $$\mathrm{F}^{-}$$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface

Identify the incorrect statements regarding primary standard of titrimetric analysis. (A) It should be purely available

What is the structure of C?

The electronic configuration of $$\mathrm{Cu}(\mathrm{II})$$ is $$3 \mathrm{~d}^9$$ whereas that of $$\mathrm{Cu}(\mathr

In which one of the following pairs the central atoms exhibit $$\mathrm{sp}^2$$ hybridization ?

Relative stability of the contributing structures is :

Correct order of basic strength of Pyrrole , Pyridine and Piperidine is :

For the given compounds, the correct order of increasing $$\mathrm{pK}_{\mathrm{a}}$$ value : Choose the correct answer

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

Methods used for purification of organic compounds are based on :

Compare the energies of following sets of quantum numbers for multielectron system. (A) $$\mathrm{n}=4,1=1$$ (B) $$\math

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed?

In the following sequence of reaction, the major products B and C respectively are :

The standard reduction potentials at $$298 \mathrm{~K}$$ for the following half cells are given below : $$\mathrm{Cr}_2

Total number of essential amino acid among the given list of amino acids is ________. Arginine, Phenylalanine, Aspartic

Number of ambidentate ligands among the following is _________. $$\mathrm{NO}_2^{-}, \mathrm{SCN}^{-}, \mathrm{C}_2 \mat

Number of colourless lanthanoid ions among the following is __________. $$\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd

The total number of species from the following in which one unpaired electron is present, is _______. $$\mathrm{N}_2, \m

Given below are two statements : Statement I : The rate law for the reaction $$A+B \rightarrow C$$ is rate $$(r)=k[A]^2[

How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects?

When equal volume of $$1 \mathrm{~M} \mathrm{~HCl}$$ and $$1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ are separately ne

The heat of solution of anhydrous $$\mathrm{CuSO}_4$$ and $$\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$$ are $$-70

Molarity $$(\mathrm{M})$$ of an aqueous solution containing $$x \mathrm{~g}$$ of anhyd. $$\mathrm{CuSO}_4$$ in $$500 \ma

If the domain of the function $$f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)$$ is $$\mathbf{R}-(\alpha, \beta)$$, then

Let three vectors ,$$\overrightarrow{\mathrm{a}}=\alpha \hat{i}+4 \hat{j}+2 \hat{k}, \overrightarrow{\mathrm{b}}=5 \hat{

Let $$f(x)=a x^3+b x^2+c x+41$$ be such that $$f(1)=40, f^{\prime}(1)=2$$ and $$f^{\prime \prime}(1)=4$$. Then $$a^2+b^2

The parabola $$y^2=4 x$$ divides the area of the circle $$x^2+y^2=5$$ in two parts. The area of the smaller part is equa

The solution of the differential equation $$(x^2+y^2) \mathrm{d} x-5 x y \mathrm{~d} y=0, y(1)=0$$, is :

Let $$|\cos \theta \cos (60-\theta) \cos (60+\theta)| \leq \frac{1}{8}, \theta \epsilon[0,2 \pi]$$. Then, the sum of all

If the sum of the series $$\frac{1}{1 \cdot(1+\mathrm{d})}+\frac{1}{(1+\mathrm{d})(1+2 \mathrm{~d})}+\ldots+\frac{1}{(1+

The coefficient of $$x^{70}$$ in $$x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}$$ is $${ }^{99} \ma

The frequency distribution of the age of students in a class of 40 students is given below. .tg {border-collapse:colla

Let a circle passing through $$(2,0)$$ have its centre at the point $$(\mathrm{h}, \mathrm{k})$$. Let $$(x_{\mathrm{c}},

Let $$\int \frac{2-\tan x}{3+\tan x} \mathrm{~d} x=\frac{1}{2}\left(\alpha x+\log _e|\beta \sin x+\gamma \cos x|\right)+

Let $$\alpha, \beta$$ be the roots of the equation $$x^2+2 \sqrt{2} x-1=0$$. The quadratic equation, whose roots are $$\

Let $$f(x)=x^2+9, g(x)=\frac{x}{x-9}$$ and $$\mathrm{a}=f \circ g(10), \mathrm{b}=g \circ f(3)$$. If $$\mathrm{e}$$ and

The shortest distance between the lines $$\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$$ and $$\frac{x-5}{3}=\frac{y-9}{-

A variable line $$\mathrm{L}$$ passes through the point $$(3,5)$$ and intersects the positive coordinate axes at the poi

The solution curve, of the differential equation $$2 y \frac{\mathrm{d} y}{\mathrm{~d} x}+3=5 \frac{\mathrm{d} y}{\mathr

Let $$\lambda, \mu \in \mathbf{R}$$. If the system of equations $$\begin{aligned} & 3 x+5 y+\lambda z=3 \\ & 7 x+11 y-9

A ray of light coming from the point $$\mathrm{P}(1,2)$$ gets reflected from the point $$\mathrm{Q}$$ on the $$x$$-axis

Let the line $$\mathrm{L}$$ intersect the lines $$x-2=-y=z-1,2(x+1)=2(y-1)=z+1$$ and be parallel to the line $$\frac{x-2

Let $$\overrightarrow{O A}=2 \vec{a}, \overrightarrow{O B}=6 \vec{a}+5 \vec{b}$$ and $$\overrightarrow{O C}=3 \vec{b}$$,

Let $$A=\{2,3,6,7\}$$ and $$B=\{4,5,6,8\}$$. Let $$R$$ be a relation defined on $$A \times B$$ by $$(a_1, b_1) R(a_2, b_

Let $$\lim _\limits{n \rightarrow \infty}\left(\frac{n}{\sqrt{n^4+1}}-\frac{2 n}{\left(n^2+1\right) \sqrt{n^4+1}}+\frac{

Let $$f:(0, \pi) \rightarrow \mathbf{R}$$ be a function given by $$f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)

The remainder when $$428^{2024}$$ is divided by 21 is __________.

If a function $$f$$ satisfies $$f(\mathrm{~m}+\mathrm{n})=f(\mathrm{~m})+f(\mathrm{n})$$ for all $$\mathrm{m}, \mathrm{n

Let the centre of a circle, passing through the points $$(0,0),(1,0)$$ and touching the circle $$x^2+y^2=9$$, be $$(h, k

The sum of the square of the modulus of the elements in the set $$\{z=\mathrm{a}+\mathrm{ib}: \mathrm{a}, \mathrm{b} \in

Let the set of all positive values of $$\lambda$$, for which the point of local minimum of the function $$(1+x(\lambda^2

Let $$A$$ be a non-singular matrix of order 3. If $$\operatorname{det}(3 \operatorname{adj}(2 \operatorname{adj}((\opera

Let $$\mathrm{a}, \mathrm{b}$$ and $$\mathrm{c}$$ denote the outcome of three independent rolls of a fair tetrahedral di

A plane EM wave is propagating along $$x$$ direction. It has a wavelength of $$4 \mathrm{~mm}$$. If electric field is in

A galvanmeter has a coil of resistance $$200 \Omega$$ with a full scale deflection at $$20 \mu \mathrm{A}$$. The value o

The dimensional formula of latent heat is :

A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac

The volume of an ideal gas $$(\gamma=1.5)$$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pre

A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $$1.42 \mathrm{~eV}$$. T

A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momen

A particle moving in a straight line covers half the distance with speed $$6 \mathrm{~m} / \mathrm{s}$$. The other half

Given below are two statements : Statement (I) : When an object is placed at the centre of curvature of a concave lens,

A sample of 1 mole gas at temperature $$T$$ is adiabatically expanded to double its volume. If adiab constant for the ga

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If th

One main scale division of a vernier caliper is equal to $$\mathrm{m}$$ units. If $$\mathrm{n}^{\text {th }}$$ division

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If th

The energy equivalent of $$1 \mathrm{~g}$$ of substance is :

The equivalent resistance between A and B is :

An astronaut takes a ball of mass $$m$$ from earth to space. He throws the ball into a circular orbit about earth at an

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of th

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

A square loop of edge length $$2 \mathrm{~m}$$ carrying current of $$2 \mathrm{~A}$$ is placed with its edges parallel t

At the centre of a half ring of radius $$\mathrm{R}=10 \mathrm{~cm}$$ and linear charge density $$4 \mathrm{n} \mathrm{~

In a Young's double slit experiment, the intensity at a point is $$\left(\frac{1}{4}\right)^{\text {th }}$$ of the maxim

If $$\vec{a}$$ and $$\vec{b}$$ makes an angle $$\cos ^{-1}\left(\frac{5}{9}\right)$$ with each other, then $$|\vec{a}+\v

Two persons pull a wire towards themselves. Each person exerts a force of $$200 \mathrm{~N}$$ on the wire. Young's modul

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $

A star has $$100 \%$$ helium composition. It starts to convert three $${ }^4 \mathrm{He}$$ into one $${ }^{12} \mathrm{C

A string is wrapped around the rim of a wheel of moment of inertia $$0.40 \mathrm{~kgm}^2$$ and radius $$10 \mathrm{~cm}

When a coil is connected across a $$20 \mathrm{~V}$$ dc supply, it draws a current of $$5 \mathrm{~A}$$. When it is conn

The current flowing through the $$1 \Omega$$ resistor is $$\frac{n}{10}$$ A. The value of $$n$$ is _______.