For same mass of two different ideal gases of molecular weights M1 and M2, Plots of log V vs log p at a given constant t

Which of the following has the dimension if [$$M{L^0}{T^{ - 2}}$$] ?

If the given four electronic configurations.(i) n = 4, l = 1(ii) n = 4, l = 0(iii) n = 3, l = 2(iv) n = 3, l = 1are arra

Which of the following sets of quantum numbers represents the 19th electron of Cr(Z = 24) ?

0.126 g of an acid is needed to completely neutralise 20 mL 0.1 (N) NaOH solution. The equivalent weight of the acid is

In a flask, the weight ratio of CH4(g) and SO2(g) at 298 K and 1 bar is 1 : 2. The ratio of the number of molecules of S

C6H5F18 is a F18 radio-isotope labelled organic compound. F18 decays by positron emission. The product resulting on deca

Dissolving NaCN in de-ionised water will result in a solution having

Among Me3N, C5H5N and MeCN (Me = methyl group) the electronegativity of N is in the order

The shape of $$XeF_5^ - $$ will be

The ground state magnetic property of B2 and C2 molecules will be

The number of unpaired electrons in $${[NiC{l_4}]^{2 - }}$$, $$Ni{(CO)_4}$$ and $${[Cu{(N{H_3})_4}]^{2 + }}$$ respective

Which of the following atoms should have the highest 1st electron affinity?

PbCl2 is insoluble in cold water. Addition of HCl increases its solubility due to

Of the following compounds, which one of the strongest Bronsted acid in a aqueous solution?

The correct basicity order of the following lanthanide ions is

When BaCl2 is added to an aqueous salt solution, a white precipitate is obtained. The anion among CO$$_3^{2 - }$$, SO$$_

In the IUPAC system, PhCH2CH2CO2H is named as

The isomerisation of 1-butyne to 2-butyne can be achieved by treatment with

The correct order of acid strengths of benzoic acid (X), peroxybenzoic acid (Y) and p-nitrobenzoic acid (Z) is

The yield of acetanilide in the reaction (100% conversion) of 2 moles of aniline with 1 mole of acetic anhydride is

The structure of the product P of the following reaction is

ADP and ATP differ in the number of

The compound that would produce a nauseating smell/odour with a hot mixture of chloroform and ethanolic potassium hydrox

For the reaction belowthe structure of the product Q is

You are supplied with 500 mL each of 2N HCl and 5N HCl. What is the maximum volume of 3M HCl that you can prepare using

Which one of the following corresponds to a photon of highest energy?

Assuming the compounds to be completely dissociated in aqueous solution, identify the pair of the solutions that can be

How many faradays are required to reduce 1 mol of $$C{r_2}O_7^{2 - }$$ to Cr3+ in acid medium?

Equilibrium constants for the following reactions at 1200 K are given2H2O(g) $$\rightleftharpoons$$ 2H2(g) + O2(g), K1 =

In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius (r) of potassi

Which of the following solutions will turn violet when a drop of lime juice is added to it?

The reaction sequence given below given product R.The structure of the product R is

Reduction of the lactol S with sodium borohydride gives

What will be the normality of the salt solution obtained by neutralising x mL y (N) HCl with y mL x(N) NaOH, and finally

During electrolysis of molten NaCl, some water was added. What will happen?

The role of fluorspar, which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cr

The reduction of benzene diazonium chloride to phenyl hydrazine can be accomplished by

The major product(s) obtained form the following reaction of 1 mole of hexadeuteriobenzene is/are

The conversion of CH3 $$-$$ CH2 $$-$$ COOH to can be accomplished by

The number of all numbers having 5 digits, with distinct digits is

The greatest integer which divides $$(p + 1)(p + 2)(p + 3)...(p + q)$$ for all $$p \in N$$ and fixed $$q \in N$$ is

Let $${(1 + x + {x^2})^9} = {a_0} + {a_1}x + {a_2}{x^2} + ... + {a_{18}}{x^{18}}$$. Then,

The linear system of equations$$\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y

Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 o

Let $$A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{

The value of det A, where $$A\, = \left( {\matrix{ 1 & {\cos \theta } & 0 \cr { - \cos \theta } & 1

Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z)

On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is

On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,

Mean of n observations x1, x2, ...., xn is $$\overline x $$. If an observation xq is replaced by xq' then the new mean i

The probability that a non-leap year selected at random will have 53 Sunday is

The equation $$\sin x(\sin x + \cos x) = k$$ has real solutions, where k is a real number. Then,

The possible values of x, which satisfy the trigonometric equation $${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \rig

Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes

Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the

The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-

Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines

The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an

The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$

Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

B is an extremity of the minor axis of an ellipse whose foci are S and S'. If $$\angle SBS'$$ is a right angle, then the

The axis of the parabola $${x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0$$ is

The line segment joining the foci of the hyperbola $${x^2} - {y^2} + 1 = 0$$ is one of the diameters of a circle. The eq

The equation of the plane through (1, 2, $$-$$3) and (2, $$-$$2, 1) and parallel to X-axis is

Three lines are drawn from the origin O with direction cosines proportional to (1, $$-$$1, 1), (2, $$-$$3, 0) and (1, 0,

Consider the non-constant differentiable function f one one variable which obeys the relation $${{f(x)} \over {f(y)}} =

If $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to

Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$

If f'' (0) = k, k $$ \ne $$ 0, then the value of $$\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^

If $$y = {e^{m{{\sin }^{ - 1}}x}}$$ then $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} - $$ky = 0, where k

The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel t

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has

Let $$f(x) = \left\{ {\matrix{ {{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr {

$$\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}$$ is equal to

$$\int {\cos (\log x)dx} $$ = F(x) + C, where C is an arbitrary constant. Here, F(x) is equal to

$$\int {{{{x^2} - 1} \over {{x^4} + 3{x^2} + 1}}dx} $$ (x > 0) is

Let I = $$\left| {\int {_{10}^{19}{{\sin x} \over {1 + {x^8}}}dx} } \right|$$. Then,

Let $${I_1} = \int_0^n {[x]} \,dx$$ and $${I_2} = \int_0^n {\{ x\} } \,dx$$, where [x] and {x} are integral and fraction

The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ..

The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$

$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to

Solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2}$$ ('a' belong a constant) is

The integrating factor of the first order differential equation $${x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x

In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of

If $$({\log _5}x)({\log _x}3x)({\log _{3x}}y) = {\log _x}{x^3}$$, then y equals

The expression $${{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}$$ equals

Let z = x + iy, where x and y are real. The points (x, y) in the X-Y plane for which $${{{z + i} \over {z - i}}}$$ is pu

If p, q are odd integers, then the roots of the equation $$2p{x^2} + (2p + q)x + q = 0$$ are

Out of 7 consonants and 4 vowels, words are formed each having 3 consonants and 2 vowels. The number of such words that

Let $$A = \left( {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right

Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} &a

On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3

If one of the diameters of the curve x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the ra

Let A($$-$$ 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $$\angle MBA$$ = 2$$\angle

If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to

Let for all x > 0, $$f(x) = \mathop {\lim }\limits_{n \to \infty } n({x^{1/n}} - 1)$$, then

Let $$I = \int_0^{100\pi } {\sqrt {(1 - \cos 2x)} } \,dx$$, then

The area of the figure bounded by the parabolas x = $$-$$ 2y2 and x = 1 $$-$$ 3y2 is

Tangents are drawn to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ at the ends of both latusrectum. The ar

The value of K in order that f(x) = sin x $$-$$ cos x $$-$$ kx + 5 decreases for all positive real values of x is given

For any vector x, where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings the value of $${(x \tim

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

Let $$\alpha$$ and $$\beta$$ be the roots of $${x^2} + x + 1 = 0$$. If n be a positive integer, then $$\alpha$$n + $$\be

For real x, the greatest value of $${{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}$$ is

If a, b$$ \in $$ {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then

If the tangent to $${y^2} = 4ax$$ at the point $$(a{t^2},2at)$$ where | t | > 1 is a normal to $${x^2} - {y^2} = {a^2

The focus of the conic x2 $$-$$ 6x + 4y + 1 = 0 is

Let f : R $$ \to $$ R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,

If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) +

Let f be a non-constant continuous function for all x $$ \ge $$ 0. Let f satisfy the relation f(x) f(a $$-$$ x) = 1 for

If the line ax + by + c = 0, ab $$ \ne $$ 0, is a tangent to the curve xy = 1 $$-$$ 2x, then

Two particles move in the same straight line starting at the same moment from the same point in the same direction. The

The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is

On R, the set of real numbers, a relation $$\rho $$ is defined as 'a$$\rho $$b if and only if 1 + ab > 0'. Then,

The velocity of a particle executing a simple harmonic motion is 13 ms$$-$$1, when its distance from the equilibrium pos

A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at freq

A uniform capillary tube of length l and inner radius r with its upper end sealed is submerged vertically into water. Th

A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01%. The

Temperature of an ideal gas, initially at 27$$^\circ$$C, is raised by 6$$^\circ$$C. The rms velocity of the gas molecule

2 moles of an ideal monoatomic gas is carried from a state (p0, V0) to state (2p0, 2V0) along a straight line path in a

A solid rectangular sheet has two different coefficients of linear expansion $$\alpha$$1 and $$\alpha$$2 along its lengt

A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)

Three capacitors of capacitance 1.0, 2.0 and 5.0 $$\mu$$F are connected in series to a 10 V source. The potential differ

A charge of 0.8 coulomb is divided into two charges Q1 and Q2. These are kept at a separation of 30 cm. The force on Q1

The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at

The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic

A proton is moving with a uniform velocity of $${{{10}^6}}$$ ms$$-$$1 along the Y-axis, under the joint action of a magn

When the frequency of the AC voltage applied to a series LCR circuit is gradually increased from a low value, the impeda

Six wires, each of resistance r, are connected so as to form a tetrahedron. The equivalent resistance of the combination

Consider the circuit shown in the figure.The value of the resistance X for which the thermal power generated in it is pr

Consider the circuit shown in the figure where all the resistances are of magnitude 1 k$$\Omega$$. If the current in the

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately 0.009. The approxima

Two monochromatic coherent light beams A and B have intensities L and $${{L \over 4}}$$, respectively. If these beams ar

A point object is held above a thin equiconvex lens at its focus. The focal length is 0.1 m and the lens rests on a hori

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius R = 0.05 m and refrac

The de-Broglie wavelength of an electron is $$0.4 \times {10^{ - 10}}$$ m when its kinetic energy is 1.0 keV. Its wavele

When light of frequency v1 is incident on a metal with work function W (where hv1 > W), then photocurrent falls to ze

Radon-222 has a half-life of 3.8 days. If one starts with 0.064 kg of radon-222 left after 19 days will be

In the given circuit, the binary inputs at A and B are both 1 in one case and both 0 in the next case. The respective ou

When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the c

The dimension of the universal constant of gravitation, G is

Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At th

Three vectors $$\overrightarrow A $$ = a$$\widehat i$$ + $$\widehat j$$ + $$\widehat k$$; $$\overrightarrow B $$ = $$\wi

A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is

A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical pl

A bullet of mass 4.2 $$ \times $$ 10$$-$$2 kg, moving at a speed of 300 ms$$-$$1, gets stuck into a block with a mass 9

A particle with charge e and mass m, moving along the X-axis with a uniform speed u, enters a region where a uniform ele

A unit negative charge with mass M resides at the mid-point of the straight line of length 2a adjoining two fixed charge

Consider the circuit given here. The potential difference VBC between the points B and C is

If the pressure, temperature and density of an ideal gas are denoted by p, T and $$\rho $$, respectively, the velocity o

Two long parallel wires separated by 0.1 m carry currents of 1A and 2A, respectively in opposite directions. A third cur

If $$\chi $$ stands for the magnetic susceptibility of a substance, $$\mu$$ for its magnetic permeability and $$\mu$$0 f

Let vn and En be the respective speed and energy of an electron in the nth orbit of radius rn, in a hydrogen atom, as pr

A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plat