One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alken

The correct order of increasing basicity of the given conjugate bases (R = CH3) is

Out of the following, the alkene that exhibits optical isomerism is

Solubility product of silver bromide is 5.0 $$\times$$ 10–13. The quantity of potassium bromide (molar mass taken as 120

In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11 Select the corre

At 25°C, the solubility product of Mg(OH)2 is 1.0 $$\times$$ 10–11. At which pH, will Mg2+ ions start precipitating in t

Three reactions involving $$H_2PO_4^−$$ are given below : (i) H3PO4 + H2O $$\to$$ H3O+ + $$H_2PO_4^−$$ (ii) $$H_2PO_4^−$

For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is the temperature at

The standard enthalpy of formation of NH3 is –46.0 kJ mol–1. If the enthalpy of formation of H2 from its atoms is –436 k

Biuret test is not given by

In the chemical reactions, the compounds $$'A'$$ and $$'B'$$ respectively are

The main product of the following reaction is $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $${C_6}{H_5}C{H_2}CH\lef

Consider the following bromides : The correct order of $${S_N}1$$ reactive is

From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous ZnCl2, is

A solution containing 2.675g of CoCl3. 6NH3 (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chlor

Which one of the following has an optical isomer ? (en = ethylenediamine)

29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia w

The time for half life period of a certain reaction A $$\to$$ products is 1 hour. When the initial concentration of the

Consider the reaction : Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq) The rate equation for this reaction is rate = k

The Gibbs energy for the decomposition of Al2O3 at 500oC is as follows : $${2 \over 3}A{l_2}{O_3}$$ $$\to$$ $${4 \over 3

The correct order of $$E_{{M^{2 + }}/M}^o$$ values with negative sign for the four successive elements Cr, Mn, Fe and Co

On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (hepta

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in

The correct sequence which shows decreasing order of the ionic radii of the elements is

Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is

The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest wavelength of light capable of

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 a

Let $$f:R \to R$$ be a positive increasing function with $$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}}

The number of complex numbers z such that $$\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|$$ e

Let $$f:R \to R$$ be defined by $$$f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random with

Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$ Statement - 1

Solution of the differential equation $$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x

Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x)=p'(1-x),$$ for all $$x \in \left[ {0,1} \right],p\left( 0

The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x=0$$ and $$x = {{3\pi } \over

The number of $$3 \times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is :

Consider the system of linear equations; $$$\matrix{ {{x_1} + 2{x_2} + {x_3} = 3} \cr {2{x_1} + 3{x_2} + {x_3}

Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$ where $$I$$ is $$2 \times 2$$ ident

Let $$f:R \to R$$ be a continuous function defined by $$$f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}$$$ Stateme

Let $$f:\left( { - 1,1} \right) \to R$$ be a differentiable function with $$f\left( 0 \right) = - 1$$ and $$f'\left( 0

If two tangents drawn from a point $$P$$ to the parabola $${y^2} = 4x$$ are at right angles, then the locus of $$P$$ is

The circle $${x^2} + {y^2} = 4x + 8y + 5$$ intersects the line $$3x - 4y = m$$ at two distinct points if :

The line $$L$$ given by $${x \over 5} + {y \over b} = 1$$ passes through the point $$\left( {13,32} \right)$$. The line

A person is to count 4500 currency notes. Let $${a_n}$$ denote the number of notes he counts in the $${n^{th}}$$ minute.

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are take

If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2

Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \ov

A line $$AB$$ in three-dimensional space makes angles $${45^ \circ }$$ and $${120^ \circ }$$ with the positive $$x$$-axi

If the vectors $$\overrightarrow a = \widehat i - \widehat j + 2\widehat k,\,\,\,\,\,\overrightarrow b = 2\widehat i +

Consider the following relations $R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$; $

The combination of gates shown below yields

If a source of power $$4kW$$ produces $${10^{20}}$$ photons/second, the radiation belongs to a part of the spectrum call

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each.

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each.

Statement - $$1$$ : When ultraviolet light is incident on a photocell, its stopping potential is $${V_0}$$ and the max

In the circuit shown below, the key $$K$$ is closed at $$t=0.$$ The current through the battery is

A rectangular loop has a sliding connector $$PQ$$ of length $$l$$ and resistance $$R$$ $$\Omega $$ and it is moving with

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

A point $$P$$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $$P$$ is s

A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}

The figure shows the position$$-$$time $$(x-t)$$ graph of one-dimensional motion of body of mass $$0.4$$ $$kg.$$ The mag

Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the

In a series $$LCR$$ circuit $$R = 200\Omega $$ and the voltage and the frequency of the main supply is $$220V$$ and $$50

Two conductors have the same resistance at $${0^ \circ }C$$ but their temperature coefficients of resistance are $${\alp

Let $$C$$ be the capacitance of a capacitor discharging through a resistor $$R.$$ Suppose $${t_1}$$ is the time taken fo

A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\o

Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho

The equation of a wave on a string of linear mass density $$0.04\,\,kg\,{m^{ - 1}}$$ is given by $$$y = 0.02\left( m \r

A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho

Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $${30^ \circ }$$ w

Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic colli

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $$U\left(

For a particle in uniform circular motion the acceleration $$\overrightarrow a $$ at a point P(R, θ) on the circle of ra

A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a co

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$ \times $$ 10–3 are