The energy of the electron in the second and the third Bohr's orbits of the hydrogen atom is -5.42 $$\times$$ 10-12 erg

If 0.50 mol of BaCl2 is mixed with 0.20 mol of Na3PO4, the maximum amount of Ba3(PO4)2 that can be formed is

1 mole of N2H4 loses 10 moles of electrons to form a new compound Y. assuming that all nitrogen appears in the new compo

A 1.00 gm sample of H2O2 solution containing X percent H2O2 by weight requires X ml of a KMnO4 solution for complete ox

Balance the following Equations: (i) Cu2O + H+ + $$NO_3^ - \to $$ Cu2+ + NO + H2O (ii) K4[Fe(CN)6] + H2SO4 + H2O $$\to$

Rutherford's experiment on scattering of $$\alpha-particles$$ showed for the first time that the atom has

The correct order of second ionisation potential of carbon, nitrogen, oxygen and fluorine is

The angle between two convalent bonds is maximum in ________. (CH4, H2O, CO2)

If a molecule MX3 has zero dipole moment, the sigma bonding orbitals used by M (atomic number < 21) are

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

The temperature at which a real gas obeys the ideal gas aws over a wide range of pressure is

The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is

A solution of sodium metal in liquid ammonia is strongly reducing due to the presence of

Give reasons of the following: Sodium carbonate is made by Solvay process but the same process is not extended to the ma

The vapour pressure of pure benzene is 639.7 mm of mercury and the vapour of a solution of a solute in benzene at the sa

Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n

For a biased die the probabilities for the different faces to turn up are given below : This die tossed and you are to

An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitti

Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ be vectors of length $$3, 4, 5$$ respectively. Let $$\o

Let $$\overrightarrow A ,\overrightarrow B $$ and $${\overrightarrow C }$$ be unit vectors suppose that $$\overrightarro

The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow

Find the area bounded by the curve $${x^2} = 4y$$ and the straight

Suppose that the normals drawn at three different points on the parabola $${y^2} = 4x$$ pass through the point $$(h, k)$

The general solution of the trigonometric equation sin x+cos x=1 is given by:

For complex number $${z_1} = {x_1} + i{y_1}$$ and $${z_2} = {x_2} + i{y_2},$$ we write $${z_1} \cap {z_2},\,\,if\,\,{x_1

The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie o

Let the complex number $${{z_1}}$$, $${{z_2}}$$ and $${{z_3}}$$ be the vertices of an equilateral triangle. Let $${{z_0}

For every integer n > 1, the inequality $${(n!)^{1/n}} < {{n + 1} \over 2}$$ holds.

Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how ma

The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................

Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the

Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.

The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents

Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have t

Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C0, C1 ,....Cn are

Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$

Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqrt 3 :\sqrt 2 $$. Find the angle $$A$$.

Let $$a, b, c$$ be positive real numbers Let $$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}

Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where $$0

For all $$x$$ in $$\left[ {0,1} \right]$$, let the second derivative $$f''(x)$$ of a function $$f(x)$$ exist and satisfy

Let $$x$$ and $$y$$ be two real variables such that $$x>0$$ and $$xy=1$$. Find the minimum value of $$x+y$$.

Use the function $$f\left( x \right) = {x^{1/x}},x > 0$$. to determine the bigger of the two numbers $${e^\pi }$$ and

Evaluate $$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$

The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx$$

Let $$a, b, c$$ be non-zero real numbers such that $$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} +

A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static

When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the di