An aqueous solution containing 0.10 g KIO3 (formula weight = 214.0) was treated with an excess of KI solution. The solut

The orbital diagram in which the Aufbau principle is violated is

Interpret the non-linear shape of H2S molecule and non-planar shape of PCl3 using valence shell electron pair repulsion

The rate constant of a reaction is 1.5 $$\times$$ 107 s-1 at 50oC and 4.5 $$\times$$ 107 s-1 at 100oC. Evaluate the Arrh

Find the solubility product of a saturated solution of Ag2CrO4 in water at 298 K if the emf of the cell Ag|Ag+ (satd. Ag

Calculate the equilibrium constant for the reaction: 2Fe3+ + 3I- $$\leftrightharpoons$$ 2Fe2+ + $$I_3^-$$. The standard

A solution of a nonvolatile solute in water freezes at -0.30oC. The vapour pressure of pure water at 298 K s 23.51 mm Hg

Hydrogen peroxide acts both as an oxidising and as a reducing agent in alkaline solution towards certain first row trans

Work out the following using chemical equation : Chlorination of calcium hydroxide produces bleaching powder.

Highly pure dilute solution of sodium in liquid ammonia

Read the following Assertion and Reason and answer as per the options given below Assetion: LiCl is predominantly a cov

The geometry and the type of hybrid orbital present about the central atom in BF3 is

ASSERTION: Nuclide $${}_{13}^{30}Al$$ is less stable than $${}_{20}^{40}Ca$$ REASON: Nuclides having odd number of proto

Which of the following statement(s) is (are) correct?

Decrease in atomic number is observed during

The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The possible energy value(s) of the excited sta

A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing o

For any two vectors $$u$$ and $$v,$$ prove that (a) $${\left( {u\,.\,v} \right)^2} + {\left| {u \times v} \right|^2} =

Prove, by vector methods or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line p

Which of the following expressions are meaningful?

For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?

If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vector

Let $${C_1}$$ and $${C_2}$$ be the graphs of the functions $$y = {x^2}$$ and $$y = 2x,$$ $$0 \le x \le 1$$ respectively.

Three players, $$A,B$$ and $$C,$$ toss a coin cyclically in that order (that is $$A, B, C, A, B, C, A, B,...$$) till a h

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random or

If $$E$$ and $$F$$ are events with $$P\left( E \right) \le P\left( F \right)$$ and $$P\left( {E \cap F} \right) > 0,$

If $$\overline E $$ and $$\overline F $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0

If from each of the three boxes containing $$3$$ white and $$1$$ black, $$2$$ white and $$2$$ black, $$1$$ white and $$3

The order of the differential equation whose general solution is given by $$y = \left( {{C_1} + {C_2}} \right)\cos \left

Prove that $$\int_0^1 {{{\tan }^{ - 1}}} \,\left( {{1 \over {1 - x + {x^2}}}} \right)dx = 2\int_0^1 {{{\tan }^{ - 1}}} \

Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, where $$\left[ x \right]$$ is the integra

An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using

Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.

If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of the following points of the triangle $$P

If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right

The diagonals of a parralleogram $$PQRS$$ are along the lines $$x + 3y = 4$$ and $$6x - 2y = 7$$. Then $$PQRS$$ must be

If $$x > 1,y > 1,z > 1$$ are in G.P., then $${1 \over {1 + In\,x}},{1 \over {1 + In\,y}},{1 \over {1 + In\,z}}$

Let $${T_r}$$ be the $${r^{th}}$$ term of an A.P., for $$r=1, 2, 3, ....$$ If for some positive integers $$m$$, $$n$$ we

Let $$n$$ be an odd integer. If $$\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta ,} $$ for every value of

Let $$p$$ be a prime and $$m$$ a positive integer. By mathematical induction on $$m$$, or otherwise, prove that whenever

If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}

If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}}}

Number of divisor of the form 4$$n$$$$ + 2\left( {n \ge 0} \right)$$ of the integer 240 is

Prove that $$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha = \cot \alpha $$

Which of the following number(s) is /are rational?

The number of values of $$x\,\,$$ in the interval $$\left[ {0,\,5\pi } \right]$$ satisfying the equation $$3\,{\sin ^2}x

If $$\,\left| {\matrix{ {6i} & { - 3i} & 1 \cr 4 & {3i} & { - 1} \cr {20} & 3 & i

The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals

Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of th

If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is

Suppose $$f(x)$$ is a function satisfying the following conditions (a) $$f(0)=2,f(1)=1$$, (b) $$f$$has a minimum value

A curve $$C$$ has the property that if the tangent drawn at any point $$P$$ on $$C$$ meets the co-ordinate axes at $$A$$

Let $$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right)^2} + {\left( {f\left( x \right)} \righ

If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real number $$x$$, then the minimum value of $$f$$

The number of values of $$x$$ where the function $$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attai

Prove that a triangle $$ABC$$ is equilateral if and only if $$\tan A + \tan B + \tan C = 3\sqrt 3 $$.

A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose $${60^ \circ }$$ an

If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals

If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then

If$$\,\,\,$$ $$y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)\left( {x - c} \right)}} + {{bx} \over {

The angle between a pair of tangents drawn from a point $$P$$ to the parabola $${y^2} = 4ax$$ is $${45^ \circ }$$. Show

If $$P=(x, y)$$, $${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)$$ and $$16{x^2} + 25{y^2} = 400,$$ the

The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches the curve $$\left( {{x^2}/4} \right) + {

$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C

The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is

Let [$${\mathrm\varepsilon}_\mathrm o$$] denote the dimentional formula of the permittivity of the vacuum, and [$$\mu_o$

The SI unit of inductance, the henry can be written as