The number of gram molecules of chlorine in $$6.02\times10^{25}$$ hydrogen chloride molecules is

Which one of the following has maximum number of atoms of oxygen?

Which one of the following shows functional isomerism?

In the ionic equation,

$$\mathrm{BiO_3^-+6H^++xe^-\rightarrow Bi^{3+}+3H_2O}$$,

the value of x is

Molarity of a given orthophosphoric acid solution is 3M. It’s normality is

Acidified sodium fusion extract on addition of ferric chloride solution gives blood red colouration which confirms the presence of

A body of mass 10 mg is moving with a velocity of 100 ms$$^{-1}$$. The wavelength of de-Broglie wave associated with it would be

($$h=6.63\times10^{-34}$$ Js)

Mg$$^{2+}$$ is isoelectronic with

Presence of halogen in organic compounds can be detected using

The electronic configuration of Cr$$^{3+}$$ is

The mass of a metal, with equivalent mass 31.75, which would combine with 8 g of oxygen is

Benzene reacts with chlorine in sunlight to give a final product

In the periodic table metals usually used as catalysts belong to

The general formula of a cycloalkene is

In acetylene molecule, between the carbon atoms there are

Denatured alcohol is

During the formation of a chemical bond

+I-effect is shown by

Formation of coloured solution is possible, when metal ion in the compound contains

Which of the following is an intensive property?

Hofmann’s bromamide reaction is to convert

IUPAC name of Na$$_3$$[Co(NO$$_2$$)$$_6$$] is

Thermodynamic standard conditions of temperature and pressure are

How many chiral carbon atoms are present in 2, 3, 4-trichloropentane ?

The number of unidentate ligands in the complex ion is called

$$2S{O_2}(g) + {O_2}(g)\buildrel {{V_2}{O_5}} \over \rightleftharpoons $$ is an example for

The amino acid which is not optically active is

For a stable molecule the value of bond order must be

Which one of the following is a second order reaction?

According to Baeyer's strain theory which is highly stable?

The number of antibonding electron pairs in O$$_2^{2-}$$ molecular ion on the basis of molecular orbital theory is

[Atomic number of O is 18]

Hydroxyl ion concentration of 1M HCl is

Geometrical isomerism is shown by

The oxidation state of iron in K$$_4$$[Fe(CN)$$_6$$] is,

In which of the following process, a maximum increase in entropy is observed?

Decomposition of benzene diazonium chloride by using Cu$$_2$$Cl$$_2$$/HCl to form chlorobenzene is

Which complex cannot ionise in solution?

Consider the reaction,

C(s) + O$$_2$$(g) $$\rightarrow$$ CO$$_2$$(g) + 393.5 kJ

The signs of $$\Delta H,\Delta S$$ and $$\Delta G$$ respectively are

The product formed when hydroxylamine condenses with a carbonyl compound is called

Which of the following forms a colourless solution in aqueous medium?

An alkyl halide reacts with alcoholic ammonia in a sealed tube, the product formed will be

Entropy of the universe is

Which of the following salts on being dissolved in water gives pH > 7 at 25$$^\circ$$C ?

The reagent used in Clemmenson's reduction is

When KBr is dissolved in water, K$$^+$$ ions are

The volume of 10N and 4N HCl required to make 1 litre of 7N HCl are

Carbon forms two oxides which have different compositions. The equivalent mass of which remains constant?

Maximum number of molecules of CH$$_3$$I that can react with a molecule of CH$$_3$$NH$$_2$$ are

In the group $$(G\,{ \otimes _{15}})$$, where $$G = \{ 3,6,9,12\} $$, $${ \otimes _{15}}$$ is multiplication modulo 15, the identity element is

A group (G *) has 10 elements. The minimum number of elements of G, which are their own inverses is

If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is

$${{3{x^2} + 1} \over {{x^2} - 6x + 8}}$$ is equal to

If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k$$, then a vector perpendicular to a and in the plane containing b and c is

OA and BO are two vectors of magnitudes 5 and 6 respectively. If $$\angle BOA=60^\circ$$, then OA . OB is equal to

A vector perpendicular to the plane containing the points $$A(1, - 1,2),B(2,0, - 1),C(0,2,1)$$ is

$${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} = $$

The ninth term of the expansion $${\left( {3x - {1 \over {2x}}} \right)^8}$$ is

If $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right],10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]$$ and B is the inverse of A, then the value of $$\alpha$$ is

If $$A = \left[ {\matrix{ 0 & x & {16} \cr x & 5 & 7 \cr 0 & 9 & x \cr } } \right]$$ is singular, then the possible values of x are

If $$A = \left[ {\matrix{ 1 & { - 2} & 2 \cr 0 & 2 & { - 3} \cr 3 & { - 2} & 4 \cr } } \right]$$, then A . adj (A) is equal to

If $$f:R \to R$$ is defined by $$f(x) = |x|$$, then

The value of $$\left| {\matrix{ x & p & q \cr p & x & q \cr p & q & x \cr } } \right|$$ is

The number of common tangents to the circles $$x^2+y^2=4$$ and $$x^2+y^2-6x-8y-24=0$$ is,

If $$3x+y+k=0$$ is a tangent to the circle $$x^2+y^2=10$$, the values of k are

The equation to two circles which touch the Y-axis at (0, 3) and make an intercept of 8 units on X-axis are

The orthocentre of the triangle with vertices A(0, 0), B(0, 3/2), C($$-$$5, 0) is

$${x^2} + {y^2} - 6x - 6y + 4 = 0$$, $${x^2} + {y^2} - 2x - 4y + 3 = 0$$, $${x^2} + {y^2} + 2kx + 2y + 1 = 0$$. If the radical centre of the above three circles exists, then which of the following cannot be the value of k?

If the circles $${x^2} + {y^2} - 2x - 2y - 7 = 0$$ and $${x^2} + {y^2} + 4x + 2y + k = 0$$ cut orthogonally, then the length of the common chord of the circles is

The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line $$2x+y-7=0$$ is

The area enclosed by the pair of lines $$xy=0$$, the line $$x-4=0$$ and $$y+5=0$$ is

If the area of the auxillary circle of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)$$ is twice the area of the ellipse, then the eccentricity of the ellipse is

A graph G has m vertices of odd degree and ‘n’ vertices of even degree. Then which of the following statements is necessarily true?

If p is any point on the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$, and S and S' are the foci, then $$PS + PS' = $$

The value of $$\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]$$ is

If $${{{x^2}} \over {36}} - {{{y^2}} \over {{k^2}}} = 1$$ is a hyperbola, then which of the following statements can be true?

The focus of the parabola is

The solution of $${\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = {{2\pi } \over 3}$$ is

$${\sin ^2}17.5^\circ + \sin 72.5^\circ $$ is equal to

The conjugate of the complex number $${{{{(1 + i)}^2}} \over {1 - i}}$$ is

ABC is a triangle with $$\angle A=30^\circ$$ and BC = 10 cm. The area of the circumcircle of the triangle is

If $$\sin 3\theta = \sin \theta $$, how many solutions exist such that $$ - 2\pi < \theta < 2\pi $$?

The imaginary part of $$i^i$$ is

The amplitude of $${(1 + i)^5}$$ is

ABC is a triangle, G is the centroid, D is the mid-point of BC. If A = (2, 3) and G = (7, 5), then the point D is

$$\mathop {\lim }\limits_{x \to 1} {{\tan ({x^2} - 1)} \over {x - 1}}$$ is equal to

If $$y = {2^{\log x}}$$, then $${{dy} \over {dx}}$$ is

If $${\sec ^{ - 1}}\left( {{{1 + x} \over {1 - y}}} \right) = a$$, then $${{dy} \over {dx}}$$ is

If $$y = {\cos ^2}{{3x} \over 2} - {\sin ^2}{{3x} \over 2}$$, then $${{{d^2}y} \over {d{x^2}}}$$ is

If the function $$f(x) = \left\{ {\matrix{ {{{1 - \cos x} \over {{x^2}}},} & {\mathrm{for}\,x \ne 0} \cr {k,} & {\mathrm{for}\,x = 0} \cr } } \right.$$ is continuous at x = 0, then the value of k is

If $$1,\omega ,{\omega ^2}$$ are the cube roots of unity, then $$(1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\omega ^8})$$ is equal to

If $${x^x} = {y^y}$$, then $${{dy} \over {dx}}$$ is

The point on the curve $$y^2=x$$, the tangent at which makes an angle 45$$^\circ$$ with X-axis is

The length of the subtangent to the curve $${x^2}{y^2} = {a^4}$$ at $$( - a,a)$$ is

The number of positive divisors of 252 is

The remainder obtained when 5¹²⁴ is divided by 124 is

Which of the following is not a group with respect to the given operation?

The range in which $$y = - {x^2} + 6x - 3$$ is increasing, is

The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx} $$ is

OA and OB are two roads enclosing an angle of 120$$^\circ$$. X and Y start from O at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h. The rate at which the shortest distance between X and Y is increasing after 1 hour is

If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} } $$, then the value of $$k$$ is

The value of $$\int {{1 \over {1 + \cos 8x}}dx} $$ is

The value of $$\int {{e^x}({x^5} + 5{x^4} + 1)\,.\,dx} $$ is

The value of $$\int {{{{x^2} + 1} \over {{x^2} - 1}}dx} $$ is

The area bounded by the curve $$x=4-y^2$$ and the Y-axis is

The differential equation of the family of straight lines whose slope is equal to y-intercept is

The order and degree of the differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \over 3}}} = {{{d^2}y} \over {d{x^2}}}$$ are respectively

Light of frequency 10¹⁵ Hz falls on a metal surface of work function 2.5 eV. The stopping potential of photoelectrons (in V) is

A proton accelerated through a potential V has de-Broglie wavelength $$\lambda$$. Then, the de-Broglie wavelength of an $$\alpha$$-particle, when accelerated through the same potential V is

Consider a thin spherical shell of radius R consisting of uniform surface charge density s. The electric field at a point of distance x from its centre and outside the shell is

An electron of an atom transits from $$n_1$$ to $$n_2$$. In which of the following maximum frequency of photon will be emitted?

Two protons are kept at a separation of 40 $$\mathop A\limits^o $$. F$$_n$$ is the nuclear force and F$$_e$$ is the electrostatic force between them. Then,

Two radioactive materials X$$_1$$ and X$$_2$$ have decay constant 5$$\lambda$$ and $$\lambda$$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X$$_1$$ to X$$_2$$ will be $$1/e$$ after a time

The Poisson's ratio of a material is 0.1. If the longitudinal strain of a rod of this material is $$10^{-3}$$, then the percentage change in the volume of the rod will be

A satellite can be in a geostationary orbit around a planet if it is at a distance R from the centre of the planet. If the planet starts rotating about its axis with double the angular velocity, then to make the satellite geostationary, its orbital radius should be

When a $$p$$-$$n$$ junction diode is connected in forward bias, its barrier potential

A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by 50%, then the energy of the soap film will be changed by

A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductivities in the ratio 4 : 1. The free face of copper is at 0$$^\circ$$C. The temperature of the interface is 20$$^\circ$$C. What is the temperature of the free face of brass?

In mm$$^3$$ of a gas is compressed at 1 atmospheric pressure and temperature 27$$^\circ$$C to 627$$^\circ$$C. What is the final pressure under adiabatic condition?

($$\gamma$$ for the gas = 1.5)

If sink is at a temperature of $$-39\Upsilon$$C and source at 0$$^\circ$$C, then efficiency will be

Which of the following laws of Physics is valid across all domains of nature?

A particle of mass m is moving in a horizontal circle of radius R under a centripetal force equal to $$-\frac{A}{R^2}$$ (A = constant). The total energy of the particle is

A force of 20 N is applied on a body of mass 5 kg resting on a horizontal plane. The body gains a kinetic energy of 10 J after it moves a distance 2 m. The frictional force is

A body under the action of a force $$F = 6\widehat i - 8\widehat j + 10\widehat k$$, acquires an acceleration of 1 m/s². The mass of this body must be

A body of mass 1000 kg is moving horizontally with a velocity 50 m/s. A mass of 250 kg is added. Find the final velocity.

Equal volumes of two gases, having their densities in the ratio of 1 : 16 exert equal pressures on the walls of two containers. The ratio of their rms velocities $$\left(\frac{c_1}{c_2}\right)$$

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $$C_p/C_V$$ of the mixture is

A particle executes a linear SHM with an amplitude of 4 cm. At the mean position the velocity of the particle is 10 cm/s. What is the displacement of the particle when its speed becomes 5 cm/s?

The equation of a progressive wave can be given by $$y=15\sin(660\pi t-0.02\pi x)$$ cm. The frequency of the wave is

A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$$^{-1}$$. The second harmonic of the source, together with a source of frequency 205 s$$^{-1}$$ gives 5 beats per second. What is frequency of the source?

A charge of 0.8 C is divided into two charges Q$$_1$$ and Q$$_2$$. These are kept at a separation of 30 cm. The force on Q$$_1$$ is maximum when

An electric dipole has a pair of equal and opposite point charges $$q$$ and $$-q$$ separated by a distance $$2x$$. The axis of the dipole is defined as

An electric dipole is placed in a uniform electric field with the dipole axis making an angle $$\theta$$ with the direction of the electric field. The orientation of the dipole for stable equilibrium is

Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is

The potential energies associated with four orientations of an electric dipole in an electric field are

(i) $$-5U_0$$ (ii) $$-7U_0$$ (iii) $$3U_0$$ (iv) $$5U_0$$

where $$U_0$$ is positive. Rank the orientations according to the angle between the electric dipole moment p and electric field E, greatest first

Suppose refractive index $$\alpha$$ is given as $$ \alpha = A + {B \over {{\lambda ^2}}}$$, where A and B are constants and $$\lambda$$ is wavelength, then dimensions of B are same as that of

If voltage $$V=(200\pm 8)V$$ and current $$I=(20\pm0.5)A$$, then the percentage error in resistance R is

A body is projected vertically upwards. The times corresponding to height $$h$$, while ascending and while descending are $$t_1$$ and $$t _2$$ , respectively. Then, the velocity of projection is ($$g$$ is acceleration due to gravity)

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

A fluid is in streamline flow across a horizontal pipe of variable area of cross-section. For this which of the following statements is correct?

Two capacitors $$C_1$$ and $$C_2$$ are charged to 120 V and 200 V, respectively. When they are connected in parallel, it is found that potential on each one of them is zero. Therefore,

Point out the right statements about the validity of Kirchhoff’s junction rule,

Four particles each of the mass m are placed at the corners of a square of side length $$l$$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

A steel wire of length 4.7 m and cross-sectional area $$3.0\times10^{-5}$$ m$$^2$$ stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of $$4.0\times10^{-5}~\mathrm{m^2}$$ under a given load. What is the ratio of Young's modulus of steel to that of copper?

The masses of 200 g and 300 g are attached to the 20 cm and 70 cm marks of a light meter rod, respectively. The moment of inertia of the system about an axis passing through 50 cm mark is

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

If $$P=Q=R=10\Omega$$ and $$S=20\Omega$$, then what resistance should be joined with S to balance the Wheatstone's network?

To the potentiometer wire of length L and 10$$\Omega$$ resistance, a battery of emf 2.5 V and a resistance R are connected in series. If a potential difference of 1 V is balanced across L/2 length, the value of R in $$\Omega$$ will be

An electron moves with speed of 2 $$\times$$ 10$$^5$$ m/s along the positive x-direction in a magnetic field $$B = (\widehat i - 4\widehat j - 3\widehat k)\,T$$. The magnitude of the force (in N) experienced by the electron is

A horizontal overhead power line carries a current of 90 A in East to West direction. What is the magnitude and direction of the magnetic field due to the current, 1.5 m below the line?

A moving coil galvanometer has 28 turns and area of coil is $$4\times 10^{-2}$$ m$$^2$$. If the magnetic field is 0.2 T, then to increase the sensitivity by 25% without changing area and field, the number of turns should be changed to

The intensity of magnetic field due to an isolated pole of strength $$m_p$$ at a point distant $$r$$ from it will be

The particle that cannot be accelerated by a cyclotron is

The angle which the total magnetic field of earth makes with the surface of the earth is called

The angle of dip of at a place where horizontal and vertical components of earth’s magnetic field are equal is

A coil of wire of a certain radius has 100 turns and a self inductance of 15 mH. The self inductance of a second similar coil of 500 turns will be

A coil of 100 turns carries a current of 5 mA and creates a magnetic flux of 10$$^{-5}$$ Wb. The inductance is

In step-up transformer, relation between number of turns in primary (N$$_P$$) and number of turns in secondary (N$$_S$$) coils is

For a series L-C-R circuit at resonance, which statement is not true?

Which of the following has/have zero average value in a plane electromagnetic wave?

A convex lens is made of 3 layers of glass of 3 different materials as in the figure.

A point object is placed on its axis. The number of images of the object are

A ray of light suffers minimum deviation in equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in figure. The ray will now suffer

Two identical light waves, propagating in the same direction, have a phase difference $$\delta$$. After they superpose the intensity of the resulting wave will be proportional to

A plastic sheet (refractive index = 1 6. ) covers one slit of a double slit arrangement for the Young’s experiment. When the double slit is illuminated by monochromatic light (wavelength = 5867 $$\mathop A\limits^o $$), the centre of the screen appears dark rather than bright. The minimum thickness of the plastic sheet to be used for this to happen is

A particle starts moving from point (2, 10, 1). Displacement for the particle is $$8\widehat i - 2\widehat j + \widehat k$$. The final coordinates of the particle is