Cl2O7 is the anhydride of

The main reason that SiCl4 is easily hydrolysed as compared to CCl4 is that

Silver chloride dissolves in excess of ammonium hydroxide solution. The cation present in the resulting solution is

The ease of hydrolysis in the compounds CH3COCl(I), CH3 $$-$$ CO $$-$$ O $$-$$ COCH3 (II), CH3COOC2H5 (III) and CH3CONH2

CH3 $$-$$ C $$ \equiv $$ C MgBr can be prepared by the reaction of

The number of alkene (s) which can produce 2-butanol by the successive treatment of (i) B2H6 in tetrahydrofuran solvent

Identify 'M' in the following sequence of reactions

Methoxybenzene on treatment with HI produces

$$\mathop {{C_4}{H_{10}}O}\limits_{(N)} \mathop {\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{{H_2}S{O_4}}^{{K_2}C

The correct order of reactivity for the addition reaction of the following carbonyl compounds with ethylmagnesium iodide

If aniline is treated with conc. H2SO4 and heated at 200$$^\circ$$C, the product is

Which of the following electronic configuration is not possible?

The number of unpaired electrons in Ni (atomic number = 28) are

Which of the following has the strongest H-bond?

The half-life of C14 is 5760 years. For a 200 mg sample of C14, the time taken to change to 25 mg is

Ferric ion forms a Prussian blue precipitate due to the formation of

The nucleus $$_{29}^{64}$$Cu accepts an orbital electron to yield,

How many moles of electrons will weigh one kilogram?

Equal weights of ethane and hydrogen are mixed in an empty container at 25$$^\circ$$C. The fraction of total pressure ex

The heat of neutralisation of a strong base and a strong acid is 13.7 kcal. The heat released when 0.6 mole HCl solution

A compound formed by elements X and Y crystallises in the cubic structure, where X atoms are at the corners of a cube an

What amount of electricity can deposit 1 mole of Al metal at cathode when passed through molten AlCl3 ?

Given the standard half-cell potentials (E$$^\circ$$) of the following as$$\matrix{ {Zn \to Z{n^{2 + }} + 2{e^ - };}

The following equilibrium constants are given$${N_2} + 3{H_2}$$ $$\rightleftharpoons$$ $$2N{H_3}$$; $${K_1}$$$${N_2} + {

Which one of the following is a condensation polymer?

Which of the following is present in maximum amount in 'acid rain'?

Which of the set of oxides are arranged in the proper order of basic, amphoteric, acidic?

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

At room temperature, the reaction between water and fluorine produces

Which of the following is least thermally stable?

$$[P]\buildrel {B{r_2}} \over \longrightarrow {C_2}{H_4}B{r_2}\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{N{H_3}

The number of possible organobromine compounds which can be obtained in the allylic bromination of 1-butene with N-bromo

A metal M (specific heat 0.16) forms a metal chloride with 65% chlorine present in it. The formula of the metal chloride

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute tem

$$[X] + Dil.\,{H_2}S{O_4} \to [Y]:$$ Colourless, suffocating gas$$[Y] + {K_2}C{r_2}{O_7} + {H_2}S{O_4} \to $$ Green colo

The possible product(s) to be obtained from the reaction of cyclobutyl amine with HNO2 is/are

The major products obtained in the following reaction is/are

Which statements are correct for the peroxide ion?

Among the following, the extensive variables are

White phosphorus P4 has the following characteristics

The approximate value of sin31$$^\circ$$ is

Let $${f_1}(x) = {e^x}$$, $${f_2}(x) = {e^{{f_1}(x)}}$$, ......, $${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$ for all n $$ \ge $$

The domain of definition of $$f(x) = \sqrt {{{1 - |x|} \over {2 - |x|}}} $$ is

Let f : [a, b] $$ \to $$ R be differentiable on [a, b] and k $$ \in $$ R. Let f(a) = 0 = f(b). Also let J(x) = f'(x) + k

Let $$f(x) = 3{x^{10}} - 7{x^8} + 5{x^6} - 21{x^3} + 3{x^2} - 7$$. Then $$\mathop {\lim }\limits_{h \to 0} {{f(1 - h) -

Let f : [a, b] $$ \to $$ R be such that f is differentiable in (a, b), f is continuous at x = a and x = b and moreover f

Let f : R $$ \to $$ R be a twice continuously differentiable function such that f(0) = f(1) = f'(0) = 0. Then

If $$\int {{e^{\sin x}}} .\left[ {{{x{{\cos }^3}x - \sin x} \over {{{\cos }^2}x}}} \right]dx = {e^{\sin x}}f(x) + c$$, w

If $$\int {f(x)} \sin x\cos xdx = {1 \over {2({b^2} - {a^2})}}\log (f(x)) + c$$, where c is the constant of integration,

If $$M = \int\limits_0^{\pi /2} {{{\cos x} \over {x + 2}}dx} $$, $$N = \int\limits_0^{\pi /4} {{{\sin x\cos x} \over {{{

The value of the integral $$I = \int_{1/2014}^{2014} {{{{{\tan }^{ - 1}}x} \over x}} dx$$ is

Let $$I = \int\limits_{\pi /4}^{\pi /3} {{{\sin x} \over x}} dx$$. Then

The value of $$I = \int_{\pi /2}^{5\pi /2} {{{{e^{{{\tan }^{ - 1}}(\sin x)}}} \over {{e^{{{\tan }^{ - 1}}(\sin x)}} + {e

The value of $$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left\{ {{{\sec }^2}{\pi \over {4n}} + {{\sec }^2}{{2\

The differential equation representing the family of curves $${y^2} = 2d(x + \sqrt d )$$, where d is a parameter, is of

Let y(x) be a solution of $$(1 + {x^2}){{dy} \over {dx}} + 2xy - 4{x^2} = 0$$. Then y(1) is equal to

The law of motion of a body moving along a straight line is x = $${1 \over 2}$$ vt. x being its distance from a fixed po

Number of common tangents of y = x2 and y = $$-$$x2 + 4x $$-$$ 4 is

Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R

If $$x + {\log _{10}}(1 + {2^x}) = x{\log _{10}}5 + {\log _{10}}6$$, then the value of x is

If $${Z_r} = \sin {{2\pi r} \over {11}} - i\cos {{2\pi r} \over {11}}$$, then $$\sum\limits_{r = 0}^{10} {{Z_r}} $$ is e

If z1 and z2 be two non-zero complex numbers such that $${{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1$$, then t

If $${b_1}{b_2} = 2({c_1} + {c_2})$$ and b1, b2, c1, c2 are all real numbers, then at least one of the equations $${x^2}

The number of selection of n objects from 2n objects of which n are identical and the rest are different, is

If (2 $$ \le $$ r $$ \le $$ n), then $${}^n{C_r}$$ + 2 . $${}^n{C_{r + 1}}$$ + $${}^n{C_{r + 2}}$$ is equal to

The number (101)100 $$-$$ 1 is divisible by

If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)n may also have the

If $$\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \

If $${a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}$$, then the value of $$\left| {\matrix{ {{a_1}} & {{a_2}} &

If $${S_r} = \left| {\matrix{ {2r} & x & {n(n + 1)} \cr {6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr

If the following three linear equations have a non-trivial solution, thenx + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz =

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

On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.

If f : R $$ \to $$ R be defined by f (x) = ex and g : R $$ \to $$ R be defined by g(x) = x2. The mapping gof : R $$ \to

In order to get a head at least once with probability $$ \ge $$ 0.9, the minimum number of times a unbiased coin needs t

A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabil

If sin6$$\theta$$ + sin4$$\theta$$ + sin2$$\theta$$ = 0, then general value of $$\theta$$ is

If $$0 \le A \le {\pi \over 4}$$, then $${\tan ^{ - 1}}\left( {{1 \over 2}\tan 2A} \right) + {\tan ^{ - 1}}(\cot A) + {

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 $$-

The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x $$-$$ 6y + 9sin2$$\alpha$$ + 13cos2

The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y =

The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle

If one of the diameter of the circle, given by the equation x2 + y2 + 4x + 6y $$-$$ 12 = 0, is a chord of a circle S, wh

A chord AB is drawn from the point A(0, 3) on the circle x2 + 4x + (y $$-$$ 3)2 = 0, and is extended to M such that AM =

Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of

Let A, B the two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r havin

Let P(at2, 2at), Q, R(ar2, 2ar) be three points on a parabola y2 = 4ax. If PQ is the focal chord and PK, QR are parallel

Let P be a point on the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and the line through P parallel to the Y-a

A point P lies on a line through Q(1, $$-$$2, 3) and is parallel to the line $${x \over 1} = {y \over 4} = {z \over 5}$$

The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, $$-$$11, 4) and (2, $$-$$

A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate

For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then

Let $$\overrightarrow \alpha $$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta $$ = $$\widehat i

Let $$\overrightarrow \alpha $$, $${\overrightarrow \beta }$$, $${\overrightarrow \gamma }$$ be the three unit vector

Let z1 and z2 be complex numbers such that z1 $$ \ne $$ z2 and |z1| = |z2|. If Re(z1) > 0 and Im(z2) < 0, then $${

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of

The least positive integer n such that $${\left( {\matrix{ {\cos \pi /4} & {\sin \pi /4} \cr { - \sin {\pi

Let $$\rho $$ be a relation defined on N, the set of natural numbers, as$$\rho $$ = {(x, y) $$ \in $$ N $$ \times $$ N :

If the polynomial $$f(x) = \left| {\matrix{ {{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr 1 & {{{(1 + x)

A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cuttin

Let A be the centre of the circle $${x^2} + {y^2} - 2x - 4y - 20 = 0$$. Let B(1, 7) and D(4, $$-$$2) be two points on th

Let $$f(x) = \left\{ {\matrix{ { - 2\sin x,} & {if\,x \le - {\pi \over 2}} \cr {A\sin x + B,} & {if\,

The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and

The equation x log x = 3 $$-$$ x

Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, $$-$$ 4) and Q(9, 6). Let R be a point o

Let $$I = \int\limits_0^I {{{{x^3}\cos 3x} \over {2 + {x^2}}}dx} $$, then

A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in

The area of the region lying above X-axis, and included between the circle x2 + y2 = 2ax and the parabola y2 = ax, a &gt

If the equation $${x^2} - cx + d = 0$$ has roots equal to the fourth powers of the roots of $${x^2} + ax + b = 0$$, wher

On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are 20 students in

In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j= 1 for i > j=

The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the l

A hyperbola, having the transverse axis of length 2sin$$\theta$$ is confocal wit6h the ellipse 3x2 + 4y2 = 12. Its equat

Let $$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer,

Consider the function $$y = {\log _a}(x + \sqrt {{x^2} + 1} ),a > 0,a \ne 1$$. The inverse of the function

Four resistors, 100$$\Omega $$, 200$$\Omega $$, 300$$\Omega $$ and 400$$\Omega $$ are connected to form four sides of a

What will be current through the 200$$\Omega $$ resistor in the given circuit, a long time after the switch K is made on

A point source is placed at coordinates (0, 1) in xy-plane. A ray of light from the source is reflected on a plane mirro

Two identical equiconvex lenses, each of focal length f are placed side by side in contact with each other with a layer

There is a small air bubble at the centre of a solid glass sphere of radius r and refractive index $$\mu$$. What will be

If Young's double slit experiment is done with white light, which of the following statements will be true?

How the linear velocity v of an electron in the Bohr orbit is related to its quantum number n?

If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on

An electron accelerated through a potential of 10000 V from rest has a de-Broglie wave length $$\lambda$$. What should b

In the circuit shown, inputs A and B are in states 1 and 0 respectively. What is the only possible stable state of the o

What will be the current flowing through the 6k$$\Omega $$ resistor in the circuit shown, where the breakdown voltage of

In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibr

A block of mass m2 is placed on a horizontal table and another block of mass m1 is placed on top of it. An increasing ho

In a triangle ABC, the sides AB and AC are represented by the vectors $$3\widehat i + \widehat j + \widehat k$$ and $$\w

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) $$v \propto

The ratio of accelerations due to gravity g1 : g2 on the surfaces of two planets is 5 : 2 and the ratio of their respect

A spherical liquid drop is placed on a horizontal plane. A small distance causes the volume of the drop to oscillate. Th

The stress along the length of a rod (with rectangular cross-section) is 1% of the Young's modulus of its material. What

What will be the approximate terminal velocity of a rain drop of diameter $${1.8 \times {{10}^{ - 3}}}$$ m, when density

The water equivalent of a calorimeter is 10 g and it contains 50 g of water at 15$$^\circ$$C. Some amount of ice, initia

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points

For an ideal gas with initial pressure and volume pi and Vi respectively, a reversible isothermal expansion happens, whe

A point charge $$-$$ q is carried from a point A to another point B on the axis of a charged ring of radius r carrying a

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length a as shown in the fi

Four equal charges of value + Q are placed at any four vertices of a regular hexagon of side 'a'. By suitably choosing t

A proton of mass m moving with a speed v (< < c, velocity of light in vacuum) completes a circular orbit in time T

A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius R. The magnetic

A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a ma

An alternating current is flowing through a series L-C-R circuit. It is found that the current reaches a value of 1 mA a

An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light va

A light charged particle is revolving in a circle of radius r in electrostatic attraction of a static heavy particle wit

As shown in the figure, a rectangular loop of conducting wire is moving away with a constant velocity v in a perpendicul

A solid spherical ball and a hollow spherical ball of two different materials of densities $$\rho $$1 and $$\rho $$2 res

The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching ea

The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small

A non-zero current passes through the galvanometer G shown in the circuit when the key K is closed and its value does no

A ray of light is incident on a right angled isosceles prism parallel to its base as shown in the figure. Refractive ind

The intensity of a sound appears to an observer to be periodic. Which of the following can be the cause of it?

Which of the following statement(s) is/are true?"Internal energy of an ideal gas .............."

Two positive charges Q and 4Q are placed at points A and B respectively, where B is at a distance d units to the right o