In the following sequence of reactions, the alkene affords the compound ‘B’ CH3 - CH = CH - CH3 $$\buildrel {{O_3}} \ov

Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diaz

The hydrocarbon which can react with sodium in liquid ammonia is

The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclat

For the following three reactions a, b and c, equilibrium constants are given: a. CO (g) + H2O (g) $$\leftrightharpoons

The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the correspo

Four species are listed below i. $$HCO_3^−$$ ii. $$H_3O^+$$ iii. $$HSO_4^−$$ iv. $$HSO_3F$$ Which one of the following

The equilibrium constants KP1 and KP2 for the reactions X $$\leftrightharpoons$$ 2Y and Z $$\leftrightharpoons$$ P + Q,

Standard entropy of X2, Y2 and XY3 are 60, 40 and 50 JK−1 mol−1 , respectively. For the reaction, $${1 \over 2} X_2$$

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $${1 \over 2}C{l_2

Amount of oxalic acid present in a solution can be determined by its titration with $$KMn{O_4}$$ solution in the presen

The treatment of $$C{H_3}MgX\,\,$$ with $$C{H_3}C \equiv C - H$$ produces

The absolute configuration of

The electrophile, $${E^ \oplus }$$ attacks the benzene ring to generate the intermediate $$\sigma - $$complex. Of the f

$$\alpha$$-D-(+)-glucose and $$\beta$$-D-(+)-glucose are

Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction, is

The coordination number and the oxidation state of the element ‘E’ in the complex [E(en)2(C2O4)]NO2 (where (en) is ethyl

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $$\Delta _o$$ be the highest?

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :

Which one of the following is the correct statement?

For a reaction $${1 \over 2}A \to 2B$$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the

Given $$E_{C{r^{3 + }}/Cr}^o$$ = -0.72 V; $$E_{Fe^{2+}/Fe}^o$$ = -0.42V, The potential for the cell Cr | Cr3+ (0.1M) ||

The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose (C6H12O6) is added to 178.2 g of water at 20oC, t

At 80oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture sol

Which of the following pair of species have the same bond order?

The bond dissociation energy of B - F in BF3 is 646 kJ mol-1 whereas that of C - F in CF4 is 515 kj mol-1. The correct r

The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the electron in the atom

Which one of the following constitutes a group of the isoelectronic species?

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible val

Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr

Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where Y = { y $$ \in $$ N, y = 4x + 3 for some x $$ \in $$ N }

A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the

It is given that the events $$A$$ and $$B$$ are such that $$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1

The solution of the differential equation $${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$

The area of the plane region bounded by the curves $$x + 2{y^2} = 0$$ and $$\,x + 3{y^2} = 1$$ is equal to :

The value of $$\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}} $$ is

Let $$a, b, c$$ be any real numbers. Suppose that there are real numbers $$x, y, z$$ not all zero such that $$x=cy+bz,$$

Let $$A$$ be $$a\,2 \times 2$$ matrix with real entries. Let $$I$$ be the $$2 \times 2$$ identity matrix. Denote by tr$$

Suppose the cubic $${x^3} - px + q$$ has three distinct real roots where $$p>0$$ and $$q>0$$. Then which one of t

How many real solutions does the equation $${x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0$$ have?

The value of $$cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$ is :

The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\ove

A parabola has the origin as its focus and the line $$x=2$$ as the directrix. Then the vertex of the parabola is at :

A focus of an ellipse is at the origin. The directrix is the line $$x=4$$ and the eccentricity is $${{1 \over 2}}$$. The

The point diametrically opposite to the point $$P(1, 0)$$ on the circle $${x^2} + {y^2} + 2x + 4y - 3 = 0$$ is :

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of

The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the ter

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of diffe

The quadratic equations $${x^2} - 6x + a = 0$$ and $${x^2} - cx + 6 = 0$$ have one root in common. The other roots of th

STATEMENT - 1 : For every natural number $$n \ge 2,$$ $$${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \o

Let R be the real line. Consider the following subsets of the plane $$R \times R$$ : $$S = \left\{ {(x,y):y = x + 1\,\,

The conjugate of a complex number is $${1 \over {i - 1}}$$ then that complex number is :

If the straight lines $$\,\,\,\,\,$$ $$\,\,\,\,\,$$ $${{x - 1} \over k} = {{y - 2} \over 2} = {{z - 3} \over 3}$$ $$\,\,

The line passing through the points $$(5,1,a)$$ and $$(3, b, 1)$$ crosses the $$yz$$-plane at the point $$\left( {0,{{1

In the circuit below, $$A$$ and $$B$$ represent two inputs and $$C$$ represents the output. The circuit represents

Suppose an electron is attracted towards the origin by a force $${k \over r}$$ where $$'k'$$ is a constant and $$'r'$$ i

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one t

A student measures the focal length of a convex lens by putting an object pin at a distance $$'u'$$ from the lens and me

In an experiment, electrons are made to pass through a narrow slit of width $$'d'$$ comparable to their de Broglie wavel

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment dista

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $$A=$$ $$10\,\,c{m^2}$

A horizontal overhead powerline is at height of $$4m$$ from the ground and carries a current of $$100A$$ from east to we

Relative permittivity and permeability of a material $${\varepsilon _r}$$ and $${\mu _r},$$ respectively. Which of the f

A $$5V$$ battery with internal resistance $$2\Omega $$ and a $$2V$$ battery with internal resistance $$1\Omega $$ are co

Consider a block of conducting material of resistivity $$'\rho '$$ shown in the figure. Current $$'I'$$ enters at $$'A'$

A body is at rest at $$x=0.$$ At $$t=0,$$ it starts moving in the positive $$x$$-direction with a constant acceleration.

Consider a block of conducting material of resistivity $$'\rho '$$ shown in the figure. Current $$'I'$$ enters at $$'A'$

A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. G

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown

A thin spherical shell of radius $$R$$ has charge $$Q$$ spread uniformly over its surface. Which of the following graphs

A parallel plate capacitor with air between the plates has capacitance of $$9$$ $$pF.$$ The separation between its plate

A wave travelling along the $$x$$-axis is described by the equation $$y(x, t)=0.005$$ $$\cos \,\left( {\alpha \,x - \bet

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condi

A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respective

A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the fol

A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mas

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${

The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of

A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of

This question contains Statement - $$1$$ and Statement - $$2$$. of the four choices given after the statements, choose t

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis pe

An athlete in the olympic games covers a distance of $$100$$ $$m$$ in $$10$$ $$s.$$ His kinetic energy can be estimated

A block of mass $$0.50$$ $$kg$$ is moving with a speed of $$2.00$$ $$m{s^{ - 1}}$$ on a smooth surface. It strike anothe

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of di

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recor

The dimension of magnetic field in M, L, T and C (coulomb) is given as