Match List I with List II Choose the correct answer from the options given below :

Given below are two statements : Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base mixed

Given below are two statements : Statement (I) : All the following compounds react with p-toluenesulfonyl chloride. $$\m

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Which one the following compounds will readily react with dilute $$\mathrm{NaOH}$$ ?

The shape of carbocation is :

When $$\psi_{\mathrm{A}}$$ and $$\psi_{\mathrm{B}}$$ are the wave functions of atomic orbitals, then $$\sigma^*$$ is rep

The emf of cell $$\mathrm{Tl}\left|\underset{(0.001 \mathrm{M})}{\mathrm{Tl}^{+}}\right| \underset{(0.01 \mathrm{M})}{\m

The reaction; $$\frac{1}{2} \mathrm{H}_{2(\mathrm{~g})}+\mathrm{AgCl}_{(\mathrm{s})} \rightarrow \mathrm{H}_{(\mathrm{aq

The correct sequence of acidic strength of the following aliphatic acids in their decreasing order is: $$\mathrm{CH}_3 \

For a reaction $$A \xrightarrow{\mathrm{K}_1} \mathrm{~B} \xrightarrow{\mathrm{K}_2} \mathrm{C}$$ If the rate of formati

The equilibrium $$\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}$$ is shifted to the right in

Identify the correct statements about p-block elements and their compounds. (A) Non metals have higher electronegativity

Given below are two statements : Statement (I) : Fusion of $$\mathrm{MnO}_2$$ with $$\mathrm{KOH}$$ and an oxidising age

Given below are two statements : Statement (I) : $$\mathrm{S}_{\mathrm{N}} 2$$ reactions are 'stereospecific', indicatin

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IUPAC name of following hydrocarbon(X) is :

Given below are two statements : Statement (I) : Kjeldahl method is applicable to estimate nitrogen in pyridine. Stateme

Identify the incorrect statements about group 15 elements : (A) Dinitrogen is a diatomic gas which acts like an inert ga

In qualitative test for identification of presence of phosphorous, the compound is heated with an oxidising agent. Which

$$\Delta_{\text {vap }} \mathrm{H}^{\ominus}$$ for water is $$+40.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at 1 bar and $$10

Total number of aromatic compounds among the following compounds is ______.

Total number of unpaired electrons in the complex ions $$[\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}$$ and $$[\mathrm{NiCl}_4]^{

The total number of carbon atoms present in tyrosine, an amino acid, is ________.

The number of optically active compounds from the following is _________.

Two moles of benzaldehyde and one mole of acetone under alkaline conditions using aqueous $$\mathrm{NaOH}$$ after heatin

A solution is prepared by adding 1 mole ethyl alcohol in 9 mole water. The mass percent of solute in the solution is ___

Molality of an aqueous solution of urea is $$4.44 \mathrm{~m}$$. Mole fraction of urea in solution is $$x \times 10^{-3}

Wavenumber for a radiation having 5800 $$\mathop A\limits^o $$ wavelength is $$x \times 10 \mathrm{~cm}^{-1}$$ The value

Number of molecules having bond order 2 from the following molecules is _________. $$\mathrm{C}_2, \mathrm{O}_2, \mathrm

Let $$y=y(x)$$ be the solution curve of the differential equation $$\sec y \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x \sin y

If the shortest distance between the lines $$\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}$$ and $$\frac{x-2}{4}=\frac

There are three bags $$X, Y$$ and $$Z$$. Bag $$X$$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $$Y$$ contains

The area of the region in the first quadrant inside the circle $$x^2+y^2=8$$ and outside the parabola $$y^2=2 x$$ is equ

Let $$\overrightarrow{\mathrm{a}}=4 \hat{i}-\hat{j}+\hat{k}, \overrightarrow{\mathrm{b}}=11 \hat{i}-\hat{j}+\hat{k}$$ an

If the line segment joining the points $$(5,2)$$ and $$(2, a)$$ subtends an angle $$\frac{\pi}{4}$$ at the origin, then

If $$\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$$ and $$\left|\begin{array}{lll}\alpha & \mat

Let $$\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}$$. Then $$\mathrm{e}^\alph

If the system of equations $$x+4 y-z=\lambda, 7 x+9 y+\mu z=-3,5 x+y+2 z=-1$$ has infinitely many solutions, then $$(2 \

Let $$f(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $$\frac{70}{3}$$ and

For $$\mathrm{a}, \mathrm{b}>0$$, let $$f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x 0\en

Let $$A=\{2,3,6,8,9,11\}$$ and $$B=\{1,4,5,10,15\}$$. Let $$R$$ be a relation on $$A \times B$$ defined by $$(a, b) R(c,

Let $$\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{b}}=2 \hat{i}+3 \hat{j}-5 \hat{k}

The sum of all possible values of $$\theta \in[-\pi, 2 \pi]$$, for which $$\frac{1+i \cos \theta}{1-2 i \cos \theta}$$ i

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets a

If the function $$f(x)=2 x^3-9 \mathrm{ax}^2+12 \mathrm{a}^2 x+1, \mathrm{a}> 0$$ has a local maximum at $$x=\alpha$$ an

If the value of $$\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}$$ is $$\frac{a \sqrt{5

If the image of the point $$(-4,5)$$ in the line $$x+2 y=2$$ lies on the circle $$(x+4)^2+(y-3)^2=r^2$$, then $$r$$ is e

If the term independent of $$x$$ in the expansion of $$\left(\sqrt{\mathrm{a}} x^2+\frac{1}{2 x^3}\right)^{10}$$ is 105

Let $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}$$ and $$\mathrm{a}

The number of distinct real roots of the equation $$|x+1||x+3|-4|x+2|+5=0$$, is _______

If $$\int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} \mathrm{~d} x=\mathrm{A}\left(\frac{\alpha x-1}{\beta x+3}\right)^B+\mathrm

Let $$\mathrm{S}$$ be the focus of the hyperbola $$\frac{x^2}{3}-\frac{y^2}{5}=1$$, on the positive $$x$$-axis. Let $$\m

Let $$\mathrm{P}(\alpha, \beta, \gamma)$$ be the image of the point $$\mathrm{Q}(1,6,4)$$ in the line $$\frac{x}{1}=\fra

Let $$\mathrm{A}$$ be the region enclosed by the parabola $$y^2=2 x$$ and the line $$x=24$$. Then the maximum area of th

Let $$\alpha|x|=|y| \mathrm{e}^{x y-\beta}, \alpha, \beta \in \mathbf{N}$$ be the solution of the differential equation

If $$\alpha=\lim _\limits{x \rightarrow 0^{+}}\left(\frac{\mathrm{e}^{\sqrt{\tan x}}-\mathrm{e}^{\sqrt{x}}}{\sqrt{\tan x

An arithmetic progression is written in the following way The sum of all the terms of the 10th row is _________.

Let a ray of light passing through the point $$(3,10)$$ reflects on the line $$2 x+y=6$$ and the reflected ray passes th

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross secti

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in t

The position of the image formed by the combination of lenses is :

If $$\epsilon_{\mathrm{o}}$$ is the permittivity of free space and $$\mathrm{E}$$ is the electric field, then $$\epsilon

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of $$\mathrm

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the h

A diatomic gas $$(\gamma=1.4)$$ does $$100 \mathrm{~J}$$ of work in an isobaric expansion. The heat given to the gas is

If $$M_0$$ is the mass of isotope $${ }_5^{12} B, M_p$$ and $$M_n$$ are the masses of proton and neutron, then nuclear b

A given object takes $$\mathrm{n}$$ times the time to slide down $$45^{\circ}$$ rough inclined plane as it takes the tim

There are 100 divisions on the circular scale of a screw gauge of pitch $$1 \mathrm{~mm}$$. With no measuring quantity i

A capacitor has air as dielectric medium and two conducting plates of area $$12 \mathrm{~cm}^2$$ and they are $$0.6 \mat

Least count of a vernier caliper is $$\frac{1}{20 \mathrm{~N}} \mathrm{~cm}$$. The value of one division on the main sca

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in

Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square

The angle of projection for a projectile to have same horizontal range and maximum height is :

A proton and an electron have the same de Broglie wavelength. If $$\mathrm{K}_{\mathrm{p}}$$ and $$\mathrm{K}_{\mathrm{e

In a hypothetical fission reaction $${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$$ The ide

A thin circular disc of mass $$\mathrm{M}$$ and radius $$\mathrm{R}$$ is rotating in a horizontal plane about an axis pa

A coil of negligible resistance is connected in series with $$90 \Omega$$ resistor across $$120 \mathrm{~V}, 60 \mathrm{

A plane progressive wave is given by $$y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$$. The frequency of the wave is :

An alternating emf $$\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$$ volt is applied to a capacitor of $$2 \mu \mathrm{F}$

If the net electric field at point $$\mathrm{P}$$ along $$\mathrm{Y}$$ axis is zero, then the ratio of $$\left|\frac{q_2

Two slits are $$1 \mathrm{~mm}$$ apart and the screen is located $$1 \mathrm{~m}$$ away from the slits. A light of wavel

A potential divider circuit is connected with a dc source of $$20 \mathrm{~V}$$, a light emitting diode of glow in volta

An object of mass $$0.2 \mathrm{~kg}$$ executes simple harmonic motion along $$x$$ axis with frequency of $$\left(\frac{

A circular table is rotating with an angular velocity of $$\omega \mathrm{~rad} / \mathrm{s}$$ about its axis (see figur

A heater is designed to operate with a power of $$1000 \mathrm{~W}$$ in a $$100 \mathrm{~V}$$ line. It is connected in c

Small water droplets of radius $$0.01 \mathrm{~mm}$$ are formed in the upper atmosphere and falling with a terminal velo

The coercivity of a magnet is $$5 \times 10^3 \mathrm{~A} / \mathrm{m}$$. The amount of current required to be passed in

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a dista