The vapour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 moles o

The rate of a first order reaction is 0.04 mol litre-1 s-1 at 10 minutes and 0.03 mol litre-1 s-1 at 20 minutes after in

The standard potential of the following cell is 0.23V at 15oC and 0.21 V at 35oC. Pt | H2 (g) | HCl (aq) | AgCl (s) | Ag

Hydrogen peroxide solution (20 ml) reacts quantitatively with a solution of KMnO4 solution is just decolourised by 10 ml

Let $${a_1}$$, $${a_2}$$,.....,$${a_n}$$ be positive real numbers in geometric progression. For each n, let $${A_n}$$, $

Let $$\overrightarrow A \left( t \right) = {f_1}\left( t \right)\widehat i + {f_2}\left( t \right)\widehat j$$ and $$$\

Find $$3-$$dimensional vectors $${\overrightarrow v _1},{\overrightarrow v _2},{\overrightarrow v _3}$$ satisfying $$\

Show, by vector methods, that the angular bisectors of a triangle are concurrent and find an expression for the position

An unbiased die, with faces numbered $$1,2,3,4,5,6,$$ is thrown $$n$$ times and the list of $$n$$ numbers showing up is

An urn contains $$m$$ white and $$n$$ black balls. A ball is drawn at random and is put back into the urn along with $$k

A hemispherical tank of radius $$2$$ metres is initially full of water and has an outlet of $$12$$ cm2 cross-sectional a

Let $$b \ne 0$$ and for $$j=0, 1, 2, ..., n,$$ let $${S_j}$$ be the area of the region bounded by the $$y$$-axis and t

Evaluate $$\int {{{\sin }^{ - 1}}\left( {{{2x + 2} \over {\sqrt {4{x^2} + 8x + 13} }}} \right)} \,dx.$$

Let $$ - 1 \le p \le 1$$. Show that the equation $$4{x^3} - 3x - p = 0$$ has a unique root in the interval $$\left[ {1/

If $$\Delta $$ is the area of a triangle with side lengths $$a, b, c, $$ then show that $$\Delta \le {1 \over 4}\sqrt {

Let $$P$$ be a point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,0 < b < a$$. Let the l

Let $$\,2{x^2}\, + \,{y^2} - \,3xy = 0$$ be the equation of a pair of tangents drawn from the origin O to a circle of ra

Let $$C_1$$ and $$C_2$$ be two circles with $$C_2$$ lying inside $$C_1$$. A circle C lying inside $$C_1$$ touches $$C_1$

Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that the equation $$\left| {\matrix{ {ax -

Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta $$ be the roots of the equation $$a{x^2} +

One quarter section is cut from a uniform circular disc of radius $R$. This section has a mass $M$. It is made to rotate