A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at t

The following electrochemical cell has been set up. Pt(1) | Fe3+, Fe2+ (a = 1) | Ce4+, Ce3+ (a=1) | Pt(2) Eo (Fe3+, Fe2+

Copper sulphate solution (250 mL) was electrolysed using platinum anode and a copper cathode. A constant current of 2mA

To 500 cm3 of water, 3.0 $$\times$$ 10-3 kg of acetic acid is added. If 23% of acetic acid is dissociated, what will be

Write down the M.O. electron distribution of O2. Specify its bond order and magnetic property.

Calculate the energy required to excite one litre of hydrogen gas at 1 atm and 298 K to the first excited state of atomi

If $$\alpha ,\,\beta $$ are the roots of $$a{x^2} + bx + c = 0$$, $$\,\left( {a \ne 0} \right)$$ and $$\alpha + \delta

A coin has probability $$p$$ of showing head when tossed. It is tossed $$n$$ times. Let $${p_n}$$ denote the probability

For $$x>0,$$ let $$f\left( x \right) = \int\limits_e^x {{{\ln t} \over {1 + t}}dt.} $$ Find the function $$f\left( x

Suppose $$p\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + .......... + {a_n}{x^n}.$$ If $$\left| {p\left( x \right)}

Let $$ABC$$ be a triangle with incentre $$I$$ and inradius $$r$$. Let $$D,E,F$$ be the feet of the perpendiculars from $

If $${x^2} + {y^2} = 1$$ then

Let $${C_1}$$ and $${C_2}$$ be respectively, the parabolas $${x^2} = y - 1$$ and $${y^2} = x - 1$$. Let $$P$$ be any poi

Let $$ABC$$ be an equilateral triangle inscribed in the circle $${x^2} + {y^2} = {a^2}$$. Suppose perpendiculars from $$

Let $$ABC$$ and $$PQR$$ be any two triangles in the same plane. Assume that the prependiculars from the points $$A, B, C

For points $$P\,\,\, = \left( {{x_1},\,{y_1}} \right)$$ and $$Q\,\,\, = \left( {{x_2},\,{y_2}} \right)$$ of the co-ordin

The fourth power of the common difference of an arithmatic progression with integer entries is added to the product of a

A coin probability $$p$$ of showing head when tossed. It is tossed $$n$$ times. Let $${p_n}$$ denote the probability tha

Let $$a,\,b,\,c$$ be possitive real numbers such that $${b^2} - 4ac > 0$$ and let $${\alpha _1} = c.$$ Prove by induc

For every possitive integer $$n$$, prove that $$\sqrt {\left( {4n + 1} \right)} < \sqrt n + \sqrt {n + 1} < \s

For any positive integer $$m$$, $$n$$ (with $$n \ge m$$), let $$\left( {\matrix{ n \cr m \cr } } \right) = {

In any triangle $$ABC,$$ prove that $$$\cot {A \over 2} + \cot {B \over 2} + \cot {C \over 2} = \cot {A \over 2}\cot {B

A thin wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular loop with centre at $O$ as show