The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$$\alpha_0$$ is Bohr radius]

An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its ini

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction

29.2 % (w/w) HCl stock solution has density of 1.25 g mL-1 . The molecular weight of HCl is 36.5 g mol-1 . The volume (m

Choose the correct reason for the stability of the Iyophobic colloidal particles

In allene (C3H4), the type(s) of hybridisation of the carbon atoms is (are):

A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical fo

The carboxyl functional group ($$-$$COOH) is present in

As per IUPAC nomenclature, the name of the complex $$[Co{({H_2}O)_4}{(N{H_3})_2}]C{l_3}$$ is

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van d

The number of aldol reactions that occur in the given transformation are

The colour of light absorbed by an aqueous solution of CuSO4 is

The number of optically active products obtained from the complete ozonolysis of the given compound is ______.

Which of the following hydrogen halides reacts with AgNO3(aq.) to give a precipitate that dissolves in Na2S2O3 (aq.) ?

Identify the binary mixtures that can be separated into individual compounds, by differential extraction, as shown in th

For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be

Which of the following molecules, in pure form, is(are) unstable at room temperature?

The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positiv

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is _

Let z be a complex number such that the imaginary part of z is non-zero and $$a\, = \,{z^2} + \,z\, + 1$$ is real. Then

If $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying $${\left| {\overrig

Tangents are drawn to the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,$$ parallel to the straight line $$2x -

Let $$\theta ,\,\varphi \, \in \,\left[ {0,2\pi } \right]$$ be such that $$2\cos \theta \left( {1 - \sin \,\varphi } \r

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person ge

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20

The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parall

The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the

Let $$S$$ be the focus of the parabola $${y^2} = 8x$$ and let $$PQ$$ be the common chord of the circle $${x^2} + {y^2} -

Let $$p(x)$$ be a real polynomial of least degree which has a local maximum at $$x=1$$ and a local minimum at $$x=3$$. I

Let $$f:IR \to IR$$ be defined as $$f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.$$ The total numbe

The integral $\int \frac{\sec ^2 x}{(\sec x+\tan x)^{9 / 2}} d x$ equals (for some arbitrary constant $$K$$)

Let $$S$$ be the area of the region enclosed by $$y = {e^{ - {x^2}}}$$, $$y=0$$, $$x=0$$, and $$x=1$$; then

If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then

A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with

If $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + x + 1} \over {x + 1}} - ax - b} \right) = 4$$, then

Let $$P = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix and let $$Q = [{b_{ij}}]$$, where $${b_{ij}} = {2^{i + j}}{a_{ij}}$$ f

Let $$f(x) = \left\{ {\matrix{ {{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr {0,} & {x = 0} \cr

The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is

The value of $$6 + {\log _{3/2}}\left( {{1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt 2 }}\sqrt {4 - {1 \over {3\sqrt

A cubical region of side $$a$$ has its center at the origin. It encloses three fixed point charges, $$-q$$ at $$\left( {

Consider a thin spherical shell of radius $$R$$ with center at the origin, carrying uniform positive surface charge dens

Two large vertical and parallel metal plates having a separation of $$1$$ $$cm$$ are connected to a $$DC$$ voltage sourc

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K

In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$ by using Searle's method, a

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is underg

A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $$\omega$$, as shown i

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfa

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (se

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe width

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When t

A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A ho

For the resistance network shown in the figure, choose the correct option(s).

A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R

An infinitely long solid cylinder of radius R has a uniform volume charge density $$\rho$$. It has a spherical cavity of

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as sh

A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and th