A 5.2 molal aqueous solution of methyl alcohol, CH3OH, is supplied. What is the mole fraction of methyl alcohol in the s

The degree of dissociation ($$\alpha$$ ) of a weak electrolyte, AxBy is related to van’t Hoff factor (i) by the expressi

Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :

Identify the compound that exhibits tautomerism.

A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of the CO2 is converted into CO on the addition of grap

The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm3 to

Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of wat

Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium

The outer electron configuration of $$Gd$$ (Atomic No. $$64$$) is :

Outer electronic configuration of Gd (Atomic no : 64) is -

The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

Silver Mirror test is given by which one of the following compounds ?

Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is

The strongest acid amongst the following compounds is :

Which of the following reagents may be used to distinguish between phenol and benzoic acid ?

Phenol is heated with a solution of mixture of KBr and KBrO3. The major product obtained in the above reaction is

The magnetic moment (spin only) of [NiCl4]2− is

Which of the following facts about the complex [Cr (NH3)6 ]Cl3 is wrong?

In context of the lanthanoids, which of the following statements is not correct?

Which of the following statement is wrong?

Which of the following statements regarding sulphur is incorrect?

The rate of a chemical reaction doubles for every 10oC rise of temperature. If the temperature is raised by 50oC , the r

The reduction potential of hydrogen half cell will be negative if :

The structure of IF7 is :

The hybridization of orbitals of N atom in $$NO_3^-$$, $$NO_2^+$$ and $$NH_4^+$$ are respectively :

Among the following the maximum covalent character is shown by the compound :

Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?

A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

The value of $$p$$ and $$q$$ for which the function $$f\left( x \right) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x

$$\mathop {\lim }\limits_{x \to 2} \left( {{{\sqrt {1 - \cos \left\{ {2(x - 2)} \right\}} } \over {x - 2}}} \right)$$

The domain of the function f(x) = $${1 \over {\sqrt {\left| x \right| - x} }}$$ is

Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots

For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $

The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\ov

If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement

If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :

Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The va

The area of the region enclosed by the curves $$y = x,x = e,y = {1 \over x}$$ and the positive $$x$$-axis is :

The value of $$\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$$ is

The number of values of $$k$$ for which the linear equations $$4x + ky + 2z = 0,kx + 4y + z = 0$$ and $$2x+2y+z=0$$ pos

Let $$A$$ and $$B$$ be two symmetric matrices of order $$3$$. Statement - 1 : $$A(BA)$$ and $$(AB)$$$$A$$ are symmetri

$${{{d^2}x} \over {d{y^2}}}$$ equals:

Equation of the ellipse whose axes of coordinates and which passes through the point $$(-3,1)$$ and has eccentricity $$\

A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increase

Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these po

If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals :

If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:

Statement - 1 : The point $$A(1,0,7)$$ is the mirror image of the point $$B(1,6,3)$$ in the line : $${x \over 1} = {{y

Let $R$ be the set of real numbers. Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence

Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three non-zero vectors which are pairwise

This question has Statement - $$1$$ and Statement - $$2$$. Of the four choices given after the statements, choose the on

Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :

This question has a paragraph followed by two statements, Statement $$-1$$ and Statement $$-2$$. Of the given four alte

A car is fitted with a convex side-view mirror of focal length $$20$$ $$cm$$. A second car $$2.8m$$ behind the first car

Let $$x$$-$$z$$ plane be the boundary between two transparent media. Medium $$1$$ in $$z \ge 0$$ has a refractive index

A resistor $$'R'$$ and $$2\mu F$$ capacitor in series is connected through a switch to $$200$$ $$V$$ direct supply. Acro

A boat is moving due east in a region where the earth's magnetic fields is $$5.0 \times {10^{ - 5}}$$ $$N{A^{ - 1}}\,{m^

A fully charged capacitor $$C$$ with initial charge $${q_0}$$ is connected to a coil of self inductance $$L$$ at $$t=0.$

A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$

If a wire is stretched to make it $$0.1\% $$ longer, its resistance will:

The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distan

Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a dist

Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$

The transverse displacement $$y(x, t)$$ of a wave on a string is given by $$y\left( {x,t} \right) = {e^{ - \left( {a{x^2

A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes

$$100g$$ of water is heated from $${30^ \circ }C$$ to $${50^ \circ }C$$. Ignoring the slight expansion of the water, the

A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It i

Three perfect gases at absolute temperatures $${T_1},\,{T_2}$$ and $${T_3}$$ are mixed. The masses of molecules are $${m

Water is flowing continuously from a tap having an internal diameter $$8 \times {10^{ - 3}}\,\,m.$$ The water velocity a

Work done in increasing the size of a soap bubble from a radius of $$3$$ $$cm$$ to $$5$$ $$cm$$ is nearly (Surface tensi

Two bodies of masses $$m$$ and $$4$$ $$m$$ are placed at a distance $$r.$$ The gravitational potential at a point on the

A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where

A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : $${{dv} \over {dt}} = - 2.5\sqrt v $$ w

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circula