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 37.0^oC. As it does so, it absorbs 208J of heat. The values of q and w for the process will be :
(R = 8.314 J/mol K) ( l n 7.5 = 2.01)

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 solution with pH of 2?

A compound with molecular mass 180 is acylated with CH₃COCl to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:

An organic compound A upon reacting with $$N{H_3}$$ gives $$B.$$ On heating $$B$$ gives $$C.$$ $$C$$ in presence of $$KOH$$ reacts with $$B{r_2}$$ to given $$C{H_3}C{H_2}N{H_2}2.$$ $$A$$ is :

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 $$AgN{O_3}.$$ Oxidation of $$(A)$$ gives an acid $$\left( B \right),$$ $${C_8}{H_6}{O_4}.\,\,\left( B \right)$$ easily forms anhydride on heating. Identify the compound $$(A).$$

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 tertiary. Which alcohol reacts fastest and by what mechanism:

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 expected to have the highest $$E_{{M^{3 + }}/{M^{2 + }}}^0$$ value?

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 be:(R = 8.314 JK^–1 mol^–1 and log 2 = 0.301)

Given

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

$$E_{C{r_2}O_7^{2 - }/C{r^{3 + }}}^o$$ = 1.33 V; $$E_{Cl/C{l^ - }}^o$$ = 1.36 V

Based on the data given above, strongest oxidising agent will be :

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, due to the formation of :

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 $$E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)$$. Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be
(h = 6.62 × 10⁻³⁴ Js and c = 3.0 × 10⁸ ms⁻¹)

Experimentally it was found that a metal oxide has formula M_0.98O. Metal M, present as M²⁺ and M³⁺ in its oxide. Fraction of the metal which exists as M³⁺ would be

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

Consider the following reaction:

$$xMnO_4^- + yC_2O_4^{2-}$$ + zH⁺ $$\to$$ xMn²⁺ + 2yCO₂ + $${z \over 2}{H_2}O$$

The value's of x, y and z in the reaction are, respectively :

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $$ \times $$ B having 3 or more elements is :

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

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

At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $$x$$ is given by $${{dp} \over {dx}} = 100 - 12\sqrt x .$$ If the firm employs $$25$$ more workers, then the new level of production of items is

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

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

Statement-2 : $$\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.$$

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 having centre at $$(0,3)$$ is :

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

The term independent of $$x$$ in expansion of
$${\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right)^{10}}$$ is

Let $${T_n}$$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $${T_{n + 1}} - {T_n}$$ = 10, then the value of n is :

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 $$a\,:b\,:c\,$$ is

The number of values of $$k$$, for which the system of equations : $$$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr } $$$
has no solution, is

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

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

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

If the vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$ and $$\overrightarrow {AC} = 5\widehat i - 2\widehat j + 4\widehat k$$ are the sides of a triangle $$ABC,$$ then the length of the median through $$A$$ is :

If the lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$$ are coplanar, then $$k$$ can have :

Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of lens is $$2 \times {10^8}\,m/s,$$ the focal length of the lens is

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 gradually changed. The plate current $$I$$ of the photocell varies as follows :

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right)$$. If $$n > > 1,$$ the frequency of radiation emitted is proportional to :

The magnetic field in a travelling electromagnetic wave has a peak value of $$20$$ $$n$$$$T$$. The peak value of electric field strength is :

A diode detector is used to detect an amplitude modulated wave of $$60\% $$ modulation by using a condenser of capacity $$250$$ picofarad in parallel with a load resistance $$100$$ kilo $$ohm.$$ Find the maximum modulated frequency which could be detected by it.

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

Two coherent point sources $${S_1}$$ and $${S_2}$$ are separated by a small distance $$'d'$$ as shown. The fringes obtained on the screen will be

In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $${S_1}$$ is closed, $${S_2}$$ kept open. ($$q$$ is charge on the capacitor and $$\tau $$ $$=RC$$ is Capacitance time constant). Which of the following statement is correct ?

A metallic rod of length $$'\ell '$$ is tied to a string of length $$2$$$$\ell $$ and made to rotate with angular speed $$w$$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $$'B'$$ in the region, the $$e.m.f$$ induced across the ends of the rod is

A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $${45^ \circ }$$ relative to that of $$A$$. The intensity of the emergent light is

A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $$15$$ $$cm.$$ If a current of $$2.0$$ $$A$$ flows through the smaller loop, than the flux linked with bigger loop is

Two short bar magnets of length $$1$$ $$cm$$ each have magnetic moments $$1.20$$ $$A{m^2}$$ and $$1.00$$ $$A{m^2}$$ respectively. They are placed on a horizontal table parallel to each other with their $$N$$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $$20.0$$ $$cm.$$ The value of the resultant horizontal magnetic induction at the mid-point $$O$$ of the line joining their centres is close to $$\left( \, \right.$$ Horizontal component of earth's magnetic induction is $$3.6 \times 10.5Wb/{m^2})$$

This questions has Statement - $${\rm I}$$ and Statement - $${\rm I}$$$${\rm I}$$. Of the four choices given after the Statements, choose the one that best describes into two Statements.

Statement - $${\rm I}$$ : Higher the range, greater is the resistance of ammeter.
Statement - $${\rm I}$$$${\rm I}$$ : To increase the range of ammeter, additional shunt needs to be used across it.

The supply voltage to room is $$120V.$$ The resistance of the lead wires is $$6\Omega $$. A $$60$$ $$W$$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $$240$$ $$W$$ heater is switched on in parallel to the bulb?

Two capacitors $${C_1}$$ and $${C_2}$$ are charged to $$120$$ $$V$$ and $$200$$ $$V$$ respectively. It is found that connecting them together the potential on each one can be made zero. Then

A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric potential at the point $$O$$ lying at distance $$L$$ from the end $$A$$ is

Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and charge $${q_0} = {q \over 2}$$ is placed at the origin. If charge $${q_0}$$ is given a small displacement $$\left( {y < < a} \right)$$ along the $$y$$-axis, the net force acting on the particle is proportional to

A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. What is the fundamental frequency of steel if density and elasticity of steel are $$7.7 \times {10^3}\,kg/{m^3}$$ and $$2.2 \times {10^{11}}\,N/{m^2}$$ respectively ?

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and the cylinder have equal cross sectional area $$A$$. When the piston is in equilibrium, the volume of the gas is $${V_0}$$ and its pressure is $${P_0}.$$ The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency

The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $$T,$$ density of liquid is $$\rho $$ and $$L$$ is its latent heat of vaporization.

A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $$\sigma $$ at equilibrium position. The extension $${x_0}$$ of the spring when it is in equilibrium is:

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?

A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?

This question has statement $${\rm I}$$ and statement $${\rm I}$$$${\rm I}$$. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $${\rm I}$$: A point particle of mass $$m$$ moving with speed $$\upsilon $$ collides with stationary point particle of mass $$M.$$ If the maximum energy loss possible is given as $$f\left( {{1 \over 2}m{v^2}} \right)$$, then $$f = \left( {{m \over {M + m}}} \right).$$

Statement - $${\rm II}$$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\widehat j}$$ is along the vertical. If g = 10 m/s², the equation of its trajectory is:

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then: