A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solu

A compound with molecular mass 180 is acylated with CH3COCl to get a compound with molecular mass 390. The number of ami

An organic compound A upon reacting with $$N{H_3}$$ gives $$B.$$ On heating $$B$$ gives $$C.$$ $$C$$ in presence of $$KO

Arrange the following compounds in order of decreasing acidity :

Compound $$\left( A \right),\,{C_8}{H_9}Br,\,\,\,$$ gives a white precipitate when warmed with alcoholic $$AgN{O_3}.$$

The order of stability of the following carbocations :

Synthesis of each molecule of glucose in photosynthesis involves:

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiar

Which of the following complex species is not expected to exhibit optical isomerism?

Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is

Which of the following arrangements does not represent the correct order of the property stated against it?

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will

Given $$E_{C{r^{2 + }}/Cr}^o$$ = -0.74 V; $$E_{MnO_4^ - /M{n^{2 + }}}^o$$ = 1.51 V $$E_{C{r_2}O_7^{2 - }/C{r^{3 + }}}^o$

The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:

A solution of (–$$l$$) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small amount of SbCl5

In which of the following pairs of molecules/ions, both the species are not likely to exist?

Stability of the species Li2, $$Li_2^−$$ and $$Li_2^+$$ increases in the order of:

Which one of the following molecules is expected to exhibit diamagnetic behaviour?

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be:

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?

Energy of an electron is given by $$E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)$$. Wavelen

Experimentally it was found that a metal oxide has formula M0.98O. Metal M, present as M2+ and M3+ in its oxide. Fractio

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO2. The empirical formula of the hydrocarbon

Consider the following reaction: $$xMnO_4^- + yC_2O_4^{2-}$$ + zH+ $$\to$$ xMn2+ + 2yCO2 + $${z \over 2}{H_2}O$$ The val

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $$ \times $$ B hav

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of th

$$\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)} \over {x\tan 4x}}$$ is equ

At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. add

The area (in square units) bounded by the curves $$y = \sqrt {x,} $$ $$2y - x + 3 = 0,$$ $$x$$-axis, and lying in the f

Statement-1 : The value of the integral $$\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}} $$ is eq

If $$\int {f\left( x \right)dx = \psi \left( x \right),} $$ then $$\int {{x^5}f\left( {{x^3}} \right)dx} $$ is equal to

If $$x, y, z$$ are in A.P. and $${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$$ and $${\tan ^{ - 1}}z$$ are also in A.P., then :

If $$y = \sec \left( {{{\tan }^{ - 1}}x} \right),$$ then $${{{dy} \over {dx}}}$$ at $$x=1$$ is equal to :

The equation of the circle passing through the foci of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$, and

The $$x$$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $$(0, 1) (1,

A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching $$X$$-axis, the equation of the reflected

The term independent of $$x$$ in expansion of $${\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over

Let $${T_n}$$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $${T_

If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then

The number of values of $$k$$, for which the system of equations : $$$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \

The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \r

If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}

The expression $${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$$ can be written

If the vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$ and $$\overrightarrow {AC} = 5\widehat i - 2\wideh

If the lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over

Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of

The $${\rm I}$$-$$V$$ characteristic of an $$LED$$ is

The anode voltage of a photocell is kept fixed. The wavelength $$\lambda $$ of the light falling on the cathode is gradu

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum

The magnetic field in a travelling electromagnetic wave has a peak value of $$20$$ $$n$$$$T$$. The peak value of electri

A diode detector is used to detect an amplitude modulated wave of $$60\% $$ modulation by using a condenser of capacity

The graph between angle of deviation $$\left( \delta \right)$$ and angle of incidence $$(i)$$ for a triangular prism is

Two coherent point sources $${S_1}$$ and $${S_2}$$ are separated by a small distance $$'d'$$ as shown. The fringes obtai

In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $${S_1}$$ is closed, $${S_2}$$ kept op

A metallic rod of length $$'\ell '$$ is tied to a string of length $$2$$$$\ell $$ and made to rotate with angular speed

A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another pol

A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance b

Two short bar magnets of length $$1$$ $$cm$$ each have magnetic moments $$1.20$$ $$A{m^2}$$ and $$1.00$$ $$A{m^2}$$ res

This questions has Statement - $${\rm I}$$ and Statement - $${\rm I}$$$${\rm I}$$. Of the four choices given after the S

The supply voltage to room is $$120V.$$ The resistance of the lead wires is $$6\Omega $$. A $$60$$ $$W$$ bulb is already

Two capacitors $${C_1}$$ and $${C_2}$$ are charged to $$120$$ $$V$$ and $$200$$ $$V$$ respectively. It is found that con

A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric pote

Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and char

A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. Wh

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and

The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas.

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. W

A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertic

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and r

A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal

This question has statement $${\rm I}$$ and statement $${\rm I}$$$${\rm I}$$. Of the four choices given after the statem

A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ i

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = ti