The species having pyramidal shape is

Silver (atomic weight = 108 g mol-1) has a density of 10.5 g.cm-3. The number of silver atoms on a surface of area 10-12

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion

Among the following, the number of elements showing only one non-zero oxidation state is : O, Cl, F, N, P, Sn, Tl, Na, T

Assuming that Hund’s rule is violated, the bond order and magnetic nature of the diatomic molecule B2 is

The total number of diprotic acids among the following is: H3PO4, H2SO4, H3PO3, H2CO3, H2S2O7, H3BO3, H3PO2, H2CrO4 and

Match the statement in Column-$$I$$ with the values in Column-$$II$$ $$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column-$$I

Match the statements in Column I with those in Column II. [Note : Here z takes value in the complex plane and Im z

Two adjacent sides of a parallelogram $$ABCD$$ are given by $$\overrightarrow {AB} = 2\widehat i + 10\widehat j + 11\w

Two parallel chords of a circle of radius 2 are at a distance $$\sqrt 3 + 1$$ apart. If the chords subtend at the cente

For $$r = 0,\,1,....,$$ let $${A_r},\,{B_r}$$ and $${C_r}$$ denote, respectively, the coefficient of $${X^r}$$ in the e

Let $${a_1},\,{a_{2\,}},\,{a_3}$$......,$${a_{11}}$$ be real numbers satisfying $${a_1} = 15,27 - 2{a_2} > 0\,\,and\,

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the

Consider a triangle $$ABC$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposit to vertices $$A, B$$ and

Let $$f$$ be a function defined on $$R$$ (the set of all real numbers) such that $$f'\left( x \right) = 2010\left( {x -

Let $k$ be a positive real number and let $$ \begin{aligned} A & =\left[\begin{array}{ccc} 2 k-1 & 2 \sqrt{k} & 2 \sqrt{

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to :

Consider the polynomial $$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$ Let $$s$$ be the sum of all distinct real root

Consider the polynomial $$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$ Let $$s$$ be the sum of all distinct real root

Consider the polynomial $$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$ Let $$s$$ be the sum of all distinct real root

A signal which can be green or red with probability $${4 \over 5}$$ and $${1 \over 5}$$ respectively, is received by sta

If the distance of the point $$P(1, -2, 1)$$ from the plane $$x+2y-2z$$$$\, = \alpha ,$$ where $$\alpha > 0,$$ is $

Let $$f$$ be a real-valued function defined on the interval $$(-1, 1)$$ such that $${e^{ - x}}f\left( x \right) = 2 + \

A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on

A diatomic ideal gas is compressed adiabatically $${1 \over {32}}$$ of its initial volume. If the initial temperature of

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its seco

A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air with a vertical uniform electric field of

A uniformly charged thin spherical shell of radius $$R$$ carries uniform surface charge density of $$\sigma $$ per unit

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-d

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10

A large glass slab ($$\mu$$ = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is se

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move fr

To determine the half-life of a radioactive element, a student plots a graph of $$\ln \left| {{{dN(t)} \over {dt}}} \rig

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no char

A diatomic molecule has moment of inertia I. By Bohr's quantization condition, its rotational energy in the nth level (n

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is clos

In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu $$ = {5 \over 3} \times {10^