An ideal gas expands in volume from 1$$\times$$10^-3 m³ to 1 $$\times$$ 10^-2 m³ at 300 K against a constant pressure of 1$$\times$$10⁵ Nm^-2. The work done is :

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1 respectively. The enthalpy of formation of carbon monoxide per mole is :

The conjugate base of H₂PO₄^- is :

What is the equilibrium expression for the reaction
P₄ (s) + 5O₂ $$\leftrightharpoons$$ P₄O₁₀ (s)?

For the reaction, CO(g) + Cl₂(g) $$\leftrightharpoons$$ COCl₂(g) the $${{{K_p}} \over {{K_c}}}$$ is equal to :

The equilibrium constant for the reaction N₂(g) + O₂(g) $$\leftrightharpoons$$ 2NO(g) at temperature T is 4 $$\times$$ 10^-4. The value of K_c for the reaction NO(g) $$\leftrightharpoons$$ $$1 \over 2$$N₂ (g) + $$1 \over 2$$O₂ (g) at the same temperature is :

The molar solubility (in ol L^-1) of a sparingly soluble salt MX₄ is "s". The corresponding solubility product is K_sp. 's' is given in term of K_sp by the relation :

Which one of the following has the minimum boiling point?

Which one the following does not have sp² hybridized carbon?

Which of the following compound is not chiral?

Consider the acidity of the carboxylic acids:
(a) PhCOOH
(b) o – NO₂C₆H₄COOH
(c) p – NO₂C₆H₄COOH
(d) m – NO₂C₆H₄COOH
Which of the following order is correct?

Which of the following will have meso-isomer also?

Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN^– ion towards metal species is :

The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is

On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is

Which of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?

Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?

Acetyl bromide reacts with excess of CH₃MgI followed by treatment with a saturated solution of NH₄Cl given

Which base is present in RNA but not in DNA?

Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?

The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is

The correct order of magnetic moments (spin only values in B.M.) among is :
(Atomic numbers: Mn = 25; Fe = 26, Co =27)

Which of the following is the strongest base ?

Amongst the following compounds, the optically active alkane having lowest molecular mass is

Rate of the reaction



is fastest when $$Z$$ is

The $$IUPAC$$ name of the compound is

Among the following compounds which can be dehydrated very easily is

Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

Consider the following nuclear reactions
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ + }$$
The number of neutrons in the element L is

Identify the correct statements regarding enzymes

For which of the following parameters the structural isomers C₂H₅OH and CH₃OCH₃ would be expected to have the same values? (Assume ideal behaviour)

Which of the following liquid pairs shows a positive deviation from Raoult’s law?

Which one of the following aqueous solutions will exhibit highest boiling point?

Which one of the following statements is false?

In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to :

Consider the following E^o values

$$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = 0.77 V;

$$E_{S{n^{2 + }}/S{n}}^o$$ = -0.14 V

Under standard conditions the potential for the reaction

Sn(s) + 2Fe³⁺(aq) $$\to$$ 2Fe²⁺(aq) + Sn²⁺(aq) is :

The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25^oC. The equilibrium constant of the reaction is (F = 96,500 C mol^-1: R = 8.314 JK^-1 mol^-1)

The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm² mol^-1 respectively. The Λ° for NaBr is

In a cell that utilises the reaction Zn(s) + 2H⁺ (aq) $$\to$$ Zn2+(aq) + H2(g) addition of H₂SO₄ to cathode compartment, will

The $$E_{{M^{3 + }}/{M^{2 + }}}^o$$ values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V respectively. For which one of these metals the change in oxidation state form +2 to +3 is easiest?

In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that the

The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in :

Which one the following statement regarding helium is incorrect?

Excess of KI reacts with CuSO₄ solution and then Na₂S₂O₃ solution is added to it. Which of the statements is incorrect for this reaction?

Cerium (Z = 58) is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?

Which one of the following complexes in an outer orbital complex?

Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect?

Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

The coordination number of central metal atom in a complex is determined by :

6.02 $$\times$$ 10²⁰ molecules of urea are present in 100 ml of its solution. The concentration of urea solution is
(Avogadro constant, N_A = 6.02 $$\times$$ 10²³ mol^-1)

To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H₃PO₃), the volume of 0.1 M aqueous KOH solution required is

The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is

Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 are respectively

The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097 $$\times$$ 10⁷ m^-1)

Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 17, Na = 11, Mg = 12, Al = 13, K = 19, Ca = 20, Sc = 21)

Which one of the following ions has the highest value of ionic radius?

Among Al₂O₃, SiO₂, P₂O₃ and SO₂ the correct order of acid strength is

The formation of the oxide ion O^2-(g) requires first an exothermic and then an endothermic step as shown below

O_(g) + e^- = $$O_{(g)}^{-}$$ $$\Delta $$H^o = -142 kJmol^-1

$$O_{(g)}^{-}$$ + e^- = $$O_{(g)}^{2-}$$ $$\Delta $$H^o = 844 kJmol^-1

This because

The correct order of bond angles (smallest first) in H₂S, NH₃, BF₃ and SiH₄ is

The bond order in NO is 2.5 while that in NO⁺ is 3. Which of the following statements is true for these two species?

The states of hybridization of boron and oxygen atoms in boric acid (H₃BO₃) are respectively

Which one of the following has the regular tetrahedral structure?
(Atomic nos : B = 5, S = 16, Ni = 28, Xe = 54)

The maximum number of 90° angles between bond pair of electrons is observed in

The graph of the function y = f(x) is symmetrical about the line x = 2, then

The range of the function f(x) = $${}^{7 - x}{P_{x - 3}}$$ is

If $$f:R \to S$$, defined by
$$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$,
is onto, then the interval of $$S$$ is

The domain of the function
$$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$

Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

If $$f(x)$$ is continuous in $$\left[ {0,{\pi \over 2}} \right]$$, then $$f\left( {{\pi \over 4}} \right)$$ is

If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then the value of $$a$$ and $$b$$, are

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?

In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the standard deviation of the observations is 2, then $$|a|$$ equals

If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}\theta } $$

then the difference between the maximum and minimum values of $${u^2}$$ is given by :

The value of $$I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx} $$ is

If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is

A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

Let $$A = \left( {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right).$$ and $$10$$ $$B = \left( {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right)$$. if $$B$$ is

the inverse of matrix $$A$$, then $$\alpha $$ is

Let $$A = \left( {\matrix{ 0 & 0 & { - 1} \cr 0 & { - 1} & 0 \cr { - 1} & 0 & 0 \cr } } \right)$$. The only correct

statement about the matrix $$A$$ is

If $${a_1},{a_2},{a_3},.........,{a_n},......$$ are in G.P., then the value of the determinant

$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|,$$ is

If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,} $$ then value of
$$(A, B)$$ is

$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to

The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$, then the equation of the ellipse is :

The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is

If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then $$A$$ is

If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {xg\left\{ {x\left( {1 - x} \right)} \right\}dx} $$
and $${I_2} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {g\left\{ {x\left( {1 - x} \right)} \right\}dx} ,$$ then the value of $${{{I_2}} \over {{I_1}}}$$ is

The area of the region bounded by the curves
$$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :

Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$$ is

The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The probability that they contradict each other when asked to speak on a fact is :

A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$$ and $$3\widehat i + \widehat j - \widehat k$$ is displaced from the point $$\widehat i + 2\widehat j + 3\widehat k$$ to the point $$\,5\widehat i + 4\widehat j + \widehat k.$$ The total work done by the forces is :

Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ be such that $$\left| {\overrightarrow u } \right| = 1,\,\,\,\left| {\overrightarrow v } \right|2,\,\,\,\left| {\overrightarrow w } \right|3.$$ If the projection $${\overrightarrow v }$$ along $${\overrightarrow u }$$ is equal to that of $${\overrightarrow w }$$ along $${\overrightarrow u }$$ and $${\overrightarrow v },$$ $${\overrightarrow w }$$ are perpendicular to each other then $$\left| {\overrightarrow u - \overrightarrow v + \overrightarrow w } \right|$$ equals :

A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-ordinates of each of the points of intersection are given by :

Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, $$m \ne n,\,\,{T_m} = {1 \over n}\,\,and\,{T_n} = {1 \over m},\,$$ then a - d equals

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$.
If $$sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}$$ and $$\cos \alpha + \cos \beta = - {{27} \over {65}}$$ then the value of $$\cos {{\alpha - \beta } \over 2}$$ :

A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.

If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta $$ equals :

Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ and arg zw = $$\pi $$. Then arg z equals :

If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then

$${{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}$$ is equal to :

If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on :

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$ then its root are

If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots,
then the value of $$'q'$$ is

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$ and $${\left( {1 - \alpha x} \right)^6}$$ is the same if $$\alpha $$ equals

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is

The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes whose sum is $$-1$$ is :

Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2, 1} \right)$$ be vertices of a triangle $$ABC$$. If the centroid of this triangle moves on the line $$2x + 3y = 1$$, then the locus of the vertex $$C$$ is the line :

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi $$, then the equation of the circle is :

If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus of its centre is :

Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diameter is :

If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$ and $${x^2} = 4ay$$, then :

Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-zero vectors such that $$\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c = {1 \over 3}\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|\overrightarrow a \,\,.$$ If $$\theta $$ is the acute angle between the vectors $${\overrightarrow b }$$ and $${\overrightarrow c },$$ then $$sin\theta $$ equals :

If the straight lines
$$x=1+s,y=-3$$$$ - \lambda s,$$ $$z = 1 + \lambda s$$ and $$x = {t \over 2},y = 1 + t,z = 2 - t,$$ with parameters $$s$$ and $$t$$ respectively, are co-planar, then $$\lambda $$ equals :

Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero vectors such that no two of these are collinear. If the vector $$\overrightarrow a + 2\overrightarrow b $$ is collinear with $$\overrightarrow c $$ and $$\overrightarrow b + 3\overrightarrow c $$ is collinear with $$\overrightarrow a $$ ($$\lambda $$ being some non-zero scalar) then $$\overrightarrow a + 2\overrightarrow b + 6\overrightarrow c $$ equals to :

Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :

The manifestation of band structure in solids is due to

An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a dielectric medium with permittivity $$ \in = 4.0.$$ Then

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is :

The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emission from this substance is approximately.

A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal $$Vs$$ the frequency, of the incident radiation gives as straight the whose slope

An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \right)$$ is $$1.1$$ $$MeV$$ and $$7$$ $$MeV$$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $$n$$) is :

When $$p$$-$$n$$ junction diode is forward biased then

A current $$i$$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the system is in equilibrium the value of $$q$$ is

A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $$ = 9.9 \times {10^{ - 15}}\,\,kg$$ and $$g = 10\,m/{s^2}$$)

The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resistance is $$P.$$ If $$S = nP$$ then the Minimum possible value of $$n$$ is

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of $${4 \over 3}$$ and $${2 \over 3}$$, then the ratio of the current passing through the wires will be

The total current supplied to the circuit by the battery is

Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is

In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is balanced against another resistance $$Y.$$ If $$X < Y$$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $$4$$ $$X$$ against $$Y$$

Thermistors are usually made of

The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at the cathode when a $$3A$$ current is passed for $$2$$ seconds will be

The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\theta ^2}$$ in volts where the ratio $$a/b$$ is $${700^ \circ }C.$$ If the cold junction is kept at $${0^ \circ }C,$$ then the neutral temperature is

The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where the symbols have their usual meanings, are respectively based on

A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter of a wire made of $$'A'$$. Then for the two wires to have the same resistance, the ratio $${l \over B}/{l \over A}$$ of their respective lengths must be

Curie temperature is the temperature above which

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $$B.$$ It is then bent into a circular loop of $$n$$ turns. The magnetic field at the center of the coil will be

The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance of $$4$$ $$cm$$ from the centre is $$54\,\mu T.$$ What will be its value at the center of loop?

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $$2s.$$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $${I_2}$$ in the same direction. They exert a force $$F$$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $$3d$$. The new value of the force between them is

The materials suitable for making electromagnets should have

Alternating current can not be measured by $$D.C.$$ ammeter because

In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components, $$L,C$$ and $$R$$ is $$50V$$. The voltage across the $$L.C$$ combination will be :

A coil having $$n$$ turns and resistance $$R\Omega $$ is connected with a galvanometer of resistance $$4R\Omega .$$ This combination is moved in time $$t$$ seconds from a magnetic field $${W_1}$$ weber to $${W_2}$$ weber. The induced current in the circuit is

In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircle of radius $$r$$ rotates about the diameter of the circle with an angular frequency $$\omega .$$ The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $$R,$$ the mean power generated per period of rotation is

A metal conductor of length $$1$$ $$m$$ rotates vertically about one of its ends at angular velocity $$5$$ radians per second. If the horizontal component of earth's magnetic field is $$0.2 \times {10^{ - 4}}T,$$ then the $$e.m.f.$$ developed between the two ends of the conductor is

In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, the inductance should be changed from $$L$$ to

A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object

A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $${45^ \circ }$$, we conclude that the refractive index $$n$$

Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a force $$F$$ when kept apart at some distance. A third spherical conductor having same radius as that $$B$$ but uncharged is brought in contact with $$B,$$ then brought in correct with $$C$$ and finally removed away from both. The new force of repulsion between $$B$$ and $$C$$ is

If two soap bubbles of different radii are connected by a tube

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $$x$$ is proportional to

A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $$60$$ $$cm$$ hangs freely from the edge of the table. The total mass of the chain is $$4$$ $$kg.$$ What is the work done in pulling the entire chain on the table?

A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$$ is applied over a particle which displaces it from its origin to the point $$\overrightarrow r = \left( {2\overrightarrow i - \overrightarrow j } \right)m.$$ The work done on the particle in joules is

A body of mass $$' m ',$$ acceleration uniformly from rest to $$'{v_1}'$$ in time $${T}$$. The instantaneous power delivered to the body as a function of time is given by

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that

A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a maximum force of $$144$$ $$N$$ on the gun. How many bullets can he fire per second at the most?

One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $${I_A}$$ and $${I_B}$$ such that

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the following will not be affected ?

A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth is

The time period of an earth satellite in circular orbit is independent of

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius $$R$$ around the sun will be proportional to

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is

One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is $$\gamma $$ for the mixture? $$\gamma $$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ volume $$\left( {{V_1},{V_2}} \right)$$ and pressure $$\left( {{P_1},{P_2}} \right)$$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Which of the following statements is correct for any thermodynamic system ?

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$$ and thickness $$x$$ and $$4x,$$ respectively, are $${T_2}$$ and $${T_1}\left( {{T_2} > {T_1}} \right).$$ The rate of heat transfer through the slab, in a steady state is $$\left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f,$$ with $$f$$ equal to

The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillation of the bob is $${t_0}$$ in air. Neglecting frictional force of water and given that the density of the bob is $$\left( {4/3} \right) \times 1000\,\,kg/{m^3}.$$ What relationship between $$t$$ and $${t_0}$$ is true

A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another spring is $${t_2}$$. If the period of oscillation with the two springs in series is $$T$$ then

The total energy of particle, executing simple harmonic motion is

A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omega _0}.$$ An external force $$F(t)$$ proportional to $$\cos \,\omega t\left( {\omega \ne {\omega _0}} \right)$$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin $$ $$\left( {100t + 20x + {\pi \over 4}} \right)$$ $$m$$ where $$t$$ is in second and $$x$$ in meter. The speed of the wave is

A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which is fixed, with a speed $$'v'$$. It approaches $$'Q'$$ upto a closest distance $$r$$ and then returns. If $$q$$ were given a speed of $$'2v'$$ the closest distances of approaches would be

Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $$\left( {g = 9.8m/{s^2}} \right)$$

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in $${T \over 3}$$ seconds?

If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetween A and B is

A projectile can have the same range 'R' for two angles of projection. If T₁ and T₂ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A ball is thrown from a point with a speed ν₀ at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed $${{{v_0}} \over 2}$$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?

A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of static friction between the block and the plane is $$0.8.$$ If the frictionless force on the block is $$10$$ $$N,$$ the mass of the block (in $$kg$$) is $$\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)$$