The cyanide ion, CN^- and N₂ are isoelectronic, But in contrast to CN^-, N₂ is chemically inert, because of

For the redox reaction:
$$MnO_4^ - + {C_2}O_4^{ - 2} + {H^ + }$$ $$ \to M{n^{2 + }} + C{O_2} + {H_2}O$$
The correct coefficients of the reactants for the balanced reaction are

A 2.0 g sample of a mixture containing sodium carbonate, sodium bicarbonate and sodium suplphate is gently heated till the evolution of CO₂ ceases. The volume of CO₂ at 750 mm Hg pressure and at 298K is measured to be 123.9 ml. A 1.5g of the same sample requires 150 ml. of (M/10) HCl for complete neutralisation. Calculate the % composition of the components of the mixture.

One gram of commercial AgNO₃ is dissolved in 50 ml. of water. It is treated with 50 ml. of a KI solution. The silver iodide thus precipitated is filtered off. Excess of KI in the filterate is titrated with (M/10) KIO₃ solution in presence of 6M HCl till all I^- ions are converted into ICl. It requires 50 ml. of (M/10) KIO₃ solution. 20 ml. of the same stock solution of KI requires 30 ml. of (M/10) KIO₃ under similar conditions. Calculate the percentage of AgNO₃ in the sample.
(Reaction : KIO₃ + 2KI + 6HCl $$\to$$ 3ICl + 3KCl + 3H₂O)

Which of the following relates to photons both as wave motion and as a stream of particles?

Which of the following does not characterise X-rays?

The statement that is not correct for the periodic classification of element is

The maximum number of hydrogen bonds a water molecule can form is

The type of hybrid orbitals used by the chlorine atom in $$ClO_2^-$$ is

Which of the following have identical bond order?

The molecules that will have dipole moment are

At 27^oC, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another unknown gas at the same temperature and pressure as that of H₂ is leaked through the same hole for 20 minutes After the effusion of the gases the mixture exerts a pressure of 6 atmosphere. The hydrogen content of the mixture is 0.7 mole. If the volume of ther container is 3 litres, what is the molecular weight of the unknown gas?

At room temperature the following reacton is procedd nearly to completion:

2NO + O₂ $$\to$$ 2NO₂ $$\to$$ N₂O₄

The dimer, N₂O₄, solidifies at 262 K. A 250 ml flask and a 100 ml flask are separated by a stop-cock. At 300 K, the nitric oxide in the larger flask exerts a pressure of 1.053 atm. and the smaller one contains oxygen at 0.789 atm. The gases are mixed by the opening stopcock and after the end of raction the flasks are cooled at 220K. Neglecting the vapour pressure of the dimer, find out the pressure and composition of the gas remaining at 220 K. (Assume the gases to behave ideally)

The species that do not contain peroxide ions are

Give reasons of the following:
Hydrogen peroxide acts as an oxidising as well as a reducing agent.

For the galvanic cell
Ag | AgCl(s), KCl (0.2M) || KBr (0.001M), AgBr(s) | Ag
Calculate the EMF generated and assign correct polarity to each electrode for a spontaneous process after taking into account the cell reaction at 25^oC.
[K_sp(AgCl) = 2.8 $$times$$ 10^-10; K_sp(AgBr) = 3.3 $$times$$ 10^-13]

An aqueous solution of NaCl on electrolysis gives H₂(g), Cl₂(g) and NaOH according to the reaction:
2Cl^- (aq) + 2H₂O = 2OH^- (aq) + H₂ (g) + Cl₂ (g)
A direct current of 25 amperes with a current efficiency of 62 % is passed through 20 litres of NaCl solution (20% by weight). Write down the reactions taking place at the anode and cathode. How long will it take to produce 1kg of Cl₂? What will be the molarity of the solution with respect to hydroxide ion? (Assume no loss due to evaporation)

A lot contains $$50$$ defective and $$50$$ non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events $$A, B, C$$ are defined as
$$A=$$ (the first bulbs is defective)
$$B=$$ (the second bulbs is non-defective)
$$C=$$ (the two bulbs are both defective or both non defective)
Determine whether
(i) $$\,\,\,\,\,$$ $$A, B, C$$ are pairwise independent
(ii)$$\,\,\,\,\,$$ $$A, B, C$$ are independent

A unit vector coplanar with $$\overrightarrow i + \overrightarrow j + 2\overrightarrow k $$ and $$\overrightarrow i + 2\overrightarrow j + \overrightarrow k $$ and perpendicular to $$\overrightarrow i + \overrightarrow j + \overrightarrow k $$ is ...........

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points $$0,$$ $$1$$ and $$2$$ are $$0.45, 0.05$$ and $$0.50$$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $$7$$ points is

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle $${x^2} + {y^2} = 9$$is

$${\rm{z }} \ne {\rm{0}}$$ is a complex number

Column I

(A) Re z = 0
(B) Arg $$z = {\pi \over 4}$$

Column II

(p) Re$${z^2}$$ = 0
(q) Im$${z^2}$$ = 0
(r) Re$${z^2}$$ = Im$${z^2}$$

Show that the value of $${{\tan x} \over {\tan 3x}},$$ wherever defined never lies between $${1 \over 3}$$ and 3.

Let $$\alpha \,,\,\beta $$ be the roots of the equation (x - a) (x - b) = c, $$c \ne 0$$. Then the roots of the equation $$(x - \alpha \,)\,(x - \beta ) + c = 0$$ are

The expansion $${\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5}$$ is a polynomial of degree

If $$\sum\limits_{r = 0}^{2n} {{a_r}{{\left( {x - 2} \right)}^r}\,\, = \sum\limits_{r = 0}^{2n} {{b_r}{{\left( {x - 3} \right)}^r}} } $$ and $${a_k} = 1$$ for all $$k \ge n,$$ then show that $${b_n} = {}^{2n + 1}{C_{n + 1}}$$

Let $$p \ge 3$$ be an integer and $$\alpha $$, $$\beta $$ be the roots of $${x^2} - \left( {p + 1} \right)x + 1 = 0$$ using mathematical induction show that $${\alpha ^n} + {\beta ^n}.$$
(i) is an integer and (ii) is not divisible by $$p$$

Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines $$$\matrix{ {2x + 3y - 1 = 0} \cr {x + 2y - 3 = 0} \cr {5x - 6y - 1 = 0} \cr } $$$

In this questions there are entries in columns 1 and 2. Each entry in column 1 is related to exactly one entry in column 2. Write the correct letter from column 2 against the entry number in column 1 in your answer book.

$${{\sin \,3\alpha } \over {\cos 2\alpha }}$$ is

Column $${\rm I}$$

(A) positive

(B) negative

Column $${\rm I}$$$${\rm I}$$

(p) $$\left( {{{13\pi } \over {48}},{{14\pi } \over {48}}} \right)$$

(q) $$\left( {{{14\pi } \over {48}},\,{{18\pi } \over {48}}} \right)$$

(r) $$\left( {{{18\pi } \over {48}},\,{{23\pi } \over {48}}} \right)$$

(s) $$\left( {0,\,{\pi \over 2}} \right)$$

Options:-

Let a circle be given by 2x (x - a) + y (2y - b) = 0, $$(a\, \ne \,0,\,\,b\, \ne 0)$$. Find the condition on a abd b if two chords, each bisected by the x-axis, can be drawn to the circle from $$\left( {a,\,\,{b \over 2}} \right)$$.

Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance from a point of contact is $$4$$. Find the ratio of the product of the radii to the sum of the radii of the circles.

A cubic $$f(x)$$ vanishes at $$x=2$$ and has relative minimum / maximum at $$x=-1$$ and $$x = {1 \over 3}$$ if $$\int\limits_{ - 1}^1 {f\,\,dx = {{14} \over 3}} $$, find the cubic $$f(x)$$.

What normal to the curve $$y = {x^2}$$ forms the shortest chord?

In this questions there are entries in columns $$I$$ and $$II$$. Each entry in column $$I$$ is related to exactly one entry in column $$II$$. Write the correct letter from column $$II$$ against the entry number in column $$I$$ in your answer book.

Let the functions defined in column $$I$$ have domain $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$

$$\,\,\,\,$$Column $$I$$
(A) $$x + \sin x$$
(B) $$\sec x$$

$$\,\,\,\,$$Column $$II$$
(p) increasing
(q) decreasing
(r) neither increasing nor decreasing

Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx$$

Sketch the region bounded by the curves $$y = {x^2}$$ and
$$y = {2 \over {1 + {x^2}}}.$$ Find the area.

Determine a positive integer $$n \le 5,$$ such that $$$\int\limits_0^1 {{e^x}{{\left( {x - 1} \right)}^n}dx = 16 - 6e} $$$

Three faces of a fair die are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours, yellow, red and blue, appear in the first, second and the third tosses respectively is ...............