On passing a gas, '$$\mathrm{X}$$', through Nessler's regent, a brown precipitate is obtained. The gas '$$\mathrm{X}$$'

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Which of the following acts as a strong reducing agent? (Atomic number: $$\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{Gd}=64

Given below are two statements: Statement I : Fluorine has most negative electron gain enthalpy in its group. Statement

According to IUPAC system, the compound is named as

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The element having the highest first ionization enthalpy is

Which of the following statements are correct about $$\mathrm{Zn}, \mathrm{Cd}$$ and $$\mathrm{Hg}$$ ? A. They exhibit h

The ascending acidity order of the following H atoms is

The correct IUPAC name of $$\mathrm{K}_2 \mathrm{MnO}_4$$ is

Identify the reagents used for the following conversion

Chromatographic technique/s based on the principle of differential adsorption is / are A. Column chromatography B. Thin

Which of the following reaction is correct?

Anomalous behavior of oxygen is due to its

Which one of the following will show geometrical isomerism?

A reagent which gives brilliant red precipitate with Nickel ions in basic medium is

Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid results

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The product A formed in the following reaction is

Alkyl halide is converted into alkyl isocyanide by reaction with

The total number of molecules with zero dipole moment among $$\mathrm{CH}_4, \mathrm{BF}_3, \mathrm{H}_2 \mathrm{O}, \ma

Standard enthalpy of vapourisation for $$\mathrm{CCl}_4$$ is $$30.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$. Heat required for

If $$50 \mathrm{~mL}$$ of $$0.5 \mathrm{M}$$ oxalic acid is required to neutralise $$25 \mathrm{~mL}$$ of $$\mathrm{NaOH

The following concentrations were observed at $$500 \mathrm{~K}$$ for the formation of $$\mathrm{NH}_3$$ from $$\mathrm{

A constant current was passed through a solution of $$\mathrm{AuCl}_4^{-}$$ ion between gold electrodes. After a period

The total number of anti bonding molecular orbitals, formed from $$2 s$$ and $$2 p$$ atomic orbitals in a diatomic molec

The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is ________ $$\times 10

The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is _________.

The oxidation number of iron in the compound formed during brown ring test for NO$$_3^-$$ iron is ________.

Molality of 0.8 M H$$_2$$SO$$_4$$ solution (density 1.06 g cm$$^{-3}$$) is ________ $$\times10^{-3}$$ m.

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is e

Let $$\mathrm{A}$$ be the point of intersection of the lines $$3 x+2 y=14,5 x-y=6$$ and $$\mathrm{B}$$ be the point of i

If $$\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\co

The distance of the point $$(2,3)$$ from the line $$2 x-3 y+28=0$$, measured parallel to the line $$\sqrt{3} x-y+1=0$$,

Let a unit vector $$\hat{u}=x \hat{i}+y \hat{j}+z \hat{k}$$ make angles $$\frac{\pi}{2}, \frac{\pi}{3}$$ and $$\frac{2 \

The function $$f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}$$

If R is the smallest equivalence relation on the set $$\{1,2,3,4\}$$ such that $$\{(1,2),(1,3)\} \subset \mathrm{R}$$, t

If the mean and variance of five observations are $$\frac{24}{5}$$ and $$\frac{194}{25}$$ respectively and the mean of t

Let $$\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)$$ and $$\mathrm{R}(7,3,2)$$ be the vertices of $$\triangle \mathrm{PQR}$$. Th

$$\text { Let } y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1

If $$\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}$$ are in an A.P. and $$\log _e \mathrm{a}-\log _e 2 \ma

If $$\sin \left(\frac{y}{x}\right)=\log _e|x|+\frac{\alpha}{2}$$ is the solution of the differential equation $$x \cos \

An integer is chosen at random from the integers $$1,2,3, \ldots, 50$$. The probability that the chosen integer is a mul

Let $$\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=12 \vec{a}+4 \vec{b} \text { and } \overrightarrow{O C}=\vec{b}

The function $$f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}$$, has

If each term of a geometric progression $$a_1, a_2, a_3, \ldots$$ with $$a_1=\frac{1}{8}$$ and $$a_2 \neq a_1$$, is the

Let $$\mathrm{r}$$ and $$\theta$$ respectively be the modulus and amplitude of the complex number $$z=2-i\left(2 \tan \f

The sum of the solutions $$x \in \mathbb{R}$$ of the equation $$\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x

Let $$x=\frac{m}{n}$$ ($$m, n$$ are co-prime natural numbers) be a solution of the equation $$\cos \left(2 \sin ^{-1} x\

Let $$A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$$ and $$P=\left[\begin{array}{lll

Let O be the origin, and M and $$\mathrm{N}$$ be the points on the lines $$\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$$ a

Let the area of the region $$\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{x^2+2,2 x+2\right\}\right\}$$ be A

Let the set $$C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$$. Then $$\sum_\limits{(x, y) \in C}(x+y)$$

Let the slope of the line $$45 x+5 y+3=0$$ be $$27 r_1+\frac{9 r_2}{2}$$ for some $$r_1, r_2 \in \mathbb{R}$$. Then $$\l

Let $$\alpha, \beta$$ be the roots of the equation $$x^2-\sqrt{6} x+3=0$$ such that $$\operatorname{Im}(\alpha)>\operato

Let for any three distinct consecutive terms $$a, b, c$$ of an A.P, the lines $$a x+b y+c=0$$ be concurrent at the point

Let $$P(\alpha, \beta)$$ be a point on the parabola $$y^2=4 x$$. If $$P$$ also lies on the chord of the parabola $$x^2=8

Remainder when $$64^{32^{32}}$$ is divided by 9 is equal to ________.

Let $$f(x)=\sqrt{\lim _\limits{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{

If $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}$$, where $$

A small liquid drop of radius $$R$$ is divided into 27 identical liquid drops. If the surface tension is $$T$$, then the

In the given circuit, the current in resistance R$$_3$$ is :

A physical quantity $$Q$$ is found to depend on quantities $$a, b, c$$ by the relation $$Q=\frac{a^4 b^3}{c^2}$$. The pe

A stone of mass $$900 \mathrm{~g}$$ is tied to a string and moved in a vertical circle of radius $$1 \mathrm{~m}$$ makin

The truth table for this given circuit is :

A bob of mass '$$m$$' is suspended by a light string of length '$$L$$'. It is imparted a minimum horizontal velocity at

An electric field is given by $$(6 \hat{i}+5 \hat{j}+3 \hat{k}) \mathrm{N} / \mathrm{C}$$. The electric flux through a s

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to

A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length i

The temperature of a gas having $$2.0 \times 10^{25}$$ molecules per cubic meter at $$1.38 \mathrm{~atm}$$ (Given, $$\ma

If the distance between object and its two times magnified virtual image produced by a curved mirror is $$15 \mathrm{~cm

A plane electromagnetic wave of frequency $$35 \mathrm{~MHz}$$ travels in free space along the $$X$$-direction. At a par

In an a.c. circuit, voltage and current are given by: $$V=100 \sin (100 t) V$$ and $$I=100 \sin \left(100 t+\frac{\pi}{3

A particle is moving in a straight line. The variation of position '$$x$$' as a function of time '$$t$$' is given as $$x

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it d

$$N$$ moles of a polyatomic gas $$(f=6)$$ must be mixed with two moles of a monoatomic gas so that the mixture behaves a

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference b

Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated

Two sources of light emit with a power of $$200 \mathrm{~W}$$. The ratio of number of photons of visible light emitted b

Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereaft

In the given circuit, the current flowing through the resistance $$20 \Omega$$ is $$0.3 \mathrm{~A}$$, while the ammeter

In the given figure, the charge stored in $$6 \mu F$$ capacitor, when points $$A$$ and $$B$$ are joined by a connecting

In a single slit diffraction pattern, a light of wavelength 6000$$\mathop A\limits^o$$ is used. The distance between the

A body of mass $$5 \mathrm{~kg}$$ moving with a uniform speed $$3 \sqrt{2} \mathrm{~ms}^{-1}$$ in $$X-Y$$ plane along th

Hydrogen atom is bombarded with electrons accelerated through a potential difference of $$\mathrm{V}$$, which causes exc

A simple harmonic oscillator has an amplitude $$A$$ and time period $$6 \pi$$ second. Assuming the oscillation starts fr

Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections ar

A particle is moving in a circle of radius $$50 \mathrm{~cm}$$ in such a way that at any instant the normal and tangenti

A charge of $$4.0 \mu \mathrm{C}$$ is moving with a velocity of $$4.0 \times 10^6 \mathrm{~ms}^{-1}$$ along the positive

A horizontal straight wire $$5 \mathrm{~m}$$ long extending from east to west falling freely at right angle to horizonta