Many elements have non-integral atomic masses because:

2.68 $$\times$$ 10-3 moles of a solution containing an ion An+ require 1.61 $$\times$$ 10-3 moles of $$MnO_4^-$$ for the

Correct set of four quantum numbers for the valence (outermost) electron of rubidium (Z = 37) is

The increasing order (lowest first) for the values of e/m (charges/mass) for electron (e), proton (p), neutron (n) and

Which electronic level would allow the hydrogen atom to absorb a photon but not to emit a photon?

An isotone of $${}_{32}^{76}Ge$$ is

When alpha particles are sent through a thin metal foil, most of them go straight through the foil because

The electron energy in hydrogen atom is given by E = (-21.7 $$\times$$ 10-12)/n2 ergs. Calculate the energy required to

On hybridization of one s and one p orbitals we get:

The total energy of one mole of an ideal monatomic gas at 27o is _______ calories.

Cp - Cv for an ideal gas is _______

Equal weights of methane and hydrogen are mixed in an empty container at 25oC. The fraction of the total pressure exerte

The hydration energy of Mg++ is larger than that of:

The IUPAC name of the compound having the formula is :

When 16.8 g of white solid X were heated, 4.4 g of acid gas A, that turned lime water milky was driven off together with

Given a function $$f(x)$$ such that (i) it is integrable over every interval on the real line and (ii) $$f(t+x)=f(x),$

Find the area of the region bounded by the $$x$$-axis and the curves defined by $$$y = \tan x, - {\pi \over 3} \le x \

Three identical dice are rolled. The probability that the same number will appear on each of them is

A box contains $$24$$ identical balls of which $$12$$ are white and $$12$$ are black. The balls are drawn at random from

If $$M$$ and $$N$$ are any two events, the probability that exactly one of them occurs is

In a certain city only two newspapers $$A$$ and $$B$$ are published, it is known that $$25$$% of the city population rea

$$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, c$$ and $$d$$ respectively such that $$$

The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear for all real values of $$k.$$

If the complex numbers, $${Z_1},{Z_2}$$ and $${Z_3}$$ represent the vertics of an equilateral triangle such that $$\lef

Evaluate the following $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$

There exists a value of $$\theta $$ between 0 and $$2\pi $$ that satisfies the equation $$\,\,{\sin ^4}\theta - 2{\sin

$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}}

If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, then show that (1- $${{a_1}}$$) (1- $${{a

Find the values of $$x \in \left( { - \pi , + \pi } \right)$$ which satisfy the equation $${g^{(1 + \left| {\cos x} \rig

For real $$x$$, the function $$\,{{\left( {x - a} \right)\left( {x - b} \right)} \over {x - c}}$$ will assume all real v

If the product of the roots of the equation $$\,{x^2} - 3\,k\,x + 2\,{e^{2lnk}} - 1 = 0\,\,\,\,is\,7$$, then the roots a

If a < b < c < d, then the roots of the equation (x - a) (x - c) + 2 ( x - b) (x - d) = 0 are real and distinct

The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has

If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval

The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles t

If $$p$$ be a natural number then prove that $${p^{n + 1}} + {\left( {p + 1} \right)^{2n - 1}}$$ is divisible by $${p^2}

Given $${s_n} = 1 + q + {q^2} + ...... + {q^2};$$ $${S_n} = 1 + {{q + 1} \over 2} + {\left( {{{q + 1} \over 2}} \right)

The sum of integers from 1 to 100 that are divisible by 2 or 5 is ............

If $$a > 0,\,b > 0$$ and $$\,c > 0,$$ prove that $$\,c > 0,$$ prove that $$\left( {a + b + c} \right)\left(

If $$n$$ is a natural number such that $$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p

If $$a,\,b$$ and $$c$$ are in A.P., then the straight line $$ax + by + c = 0$$ will always pass through a fixed point wh

Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thi

The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ............

The locus of the mid-point of a chord of the circle $${x^2} + {y^2} = 4$$ which subtends a right angle at the origin is

The abscissa of the two points A and B are the roots of the equation $${x^2}\, + \,2ax\, - {b^2} = 0$$ and their ordinat

If $$\alpha $$ be a repeated root of a quadratic equation $$f(x)=0$$ and $$A(x), B(x)$$ and $$C(x)$$ be polynomials of d

For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilater

With usual notation, if in a triangle $$ABC$$; $${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$

The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \right) - {\pi \over 4}} \right\}$$ is eq

For $$0 < a < x,$$ the minimum value of the function $$lo{g_a}x + {\log _x}a$$ is $$2$$.

Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$

Four person K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform spe

A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its pa

A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and t

A simple pendulum with a bob of mass m swings with an angular amplitude of $$40^\circ $$. When its angular displacement

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in the time