The volume, in mL, of 0.02 M K₂Cr₂O₇ solution required to react with 0.288 g of ferrous oxalate in acidic medium is _______.
(Molar mass of Fe = 56 g mol^–1)

The number of chiral carbons present in sucrose is _____.

For a dimerization reaction,
2A(g) $$ \to $$ A₂(g)
at 298 K, $$\Delta $$U^o = –20 kJ mol^–1, $$\Delta $$S^o = –30 JK^–1 mol^–1,
then the $$\Delta $$G^o will be _____ J.

Considering that $$\Delta $$₀ > P, the magnetic moment
(in BM) of [Ru(H₂O)₆]²⁺ would be _________.

For a reaction X + Y ⇌ 2Z , 1.0 mol of X, 1.5 mol
of Y and 0.5 mol of Z were taken in a 1 L vessel and
allowed to react. At equilibrium, the concentration
of Z was 1.0 mol L^–1. The equilibrium constant of reaction
is $${x \over {15}}$$. The value of x is _________.

The increasing order of boiling points of the following compounds is :

The correct order of the ionic radii of
O^2–, N^3–, F^– , Mg²⁺, Na⁺ and Al³⁺ is :

Consider the complex ions,
trans-[Co(en)₂Cl₂]⁺ (A) and
cis-[Co(en)₂Cl₂]⁺ (B).
The correct statement regarding them is :

Lattice enthalpy and enthalpy of solution of NaCl are 788 kJ mol^–1, and 4 kJ mol^–1, respectively.
The hydration enthalpy of NaCl is :

Among the following compounds, geometrical isomerism is exhibited by :

The major product of the following reaction is :

The final major product of the following reaction is :

The variation of molar conductivity with concentration of an electrolyte (X) in aqueous solution is shown in the given figure.
The electrolyte X is :

The rate constant (k) of a reaction is measured at differenct temperatures (T), and the data are plotted in the given figure. The activation energy of the reaction in kJ mol^–1 is :
(R is gas constant)

The compound that has the largest H–M–H bond angle (M = N, O, S, C) is :

The correct statement about probability density (except at infinite distance from nucleus) is :

Boron and silicon of very high purity can be obtained through :

The major product formed in the following reaction is :
CH₃CH = CHCH(CH₃)₂ $$\buildrel {HBr} \over \longrightarrow $$

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :

Let y = y(x) be the solution of the differential equation

cosx$${{dy} \over {dx}}$$ + 2ysinx = sin2x, x $$ \in $$ $$\left( {0,{\pi \over 2}} \right)$$.

If y$$\left( {{\pi \over 3}} \right)$$ = 0, then y$$\left( {{\pi \over 4}} \right)$$ is equal to :

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :

The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :

If a + x = b + y = c + z + 1, where a, b, c, x, y, z
are non-zero distinct real numbers, then
$$\left| {\matrix{ x & {a + y} & {x + a} \cr y & {b + y} & {y + b} \cr z & {c + y} & {z + c} \cr } } \right|$$ is equal to :

$$\mathop {\lim }\limits_{x \to 0} {{x\left( {{e^{\left( {\sqrt {1 + {x^2} + {x^4}} - 1} \right)/x}} - 1} \right)} \over {\sqrt {1 + {x^2} + {x^4}} - 1}}$$

Let the vectors $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be such that
$$\left| {\overrightarrow a } \right| = 2$$, $$\left| {\overrightarrow b } \right| = 4$$ and $$\left| {\overrightarrow c } \right| = 4$$. If the projection of
$$\overrightarrow b $$ on $$\overrightarrow a $$ is equal to the projection of $$\overrightarrow c $$ on $$\overrightarrow a $$
and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, then the value of
$$\left| {\overrightarrow a + \vec b - \overrightarrow c } \right|$$ is ___________.

The area (in sq. units) of the region

A = {(x, y) : (x – 1)[x] $$ \le $$ y $$ \le $$ 2$$\sqrt x $$, 0 $$ \le $$ x $$ \le $$ 2}, where [t]

denotes the greatest integer function, is :

Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set
C = {f : A $$ \to $$ B | 2 $$ \in $$ f(A) and f is not one-one} is ______.

If $$\alpha $$ and $$\beta $$ are the roots of the equation,
7x² – 3x – 2 = 0, then the value of
$${\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}$$ is equal to :

If L = sin²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$ and
M = cos²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$, then :

The derivative of
$${\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)$$ with
respect to $${\tan ^{ - 1}}\left( {{{2x\sqrt {1 - {x^2}} } \over {1 - 2{x^2}}}} \right)$$ at x = $${1 \over 2}$$ is :

If the system of linear equations
x + y + 3z = 0
x + 3y + k²z = 0
3x + y + 3z = 0
has a non-zero solution (x, y, z) for some k $$ \in $$ R, then x + $$\left( {{y \over z}} \right)$$ is equal to :

If the length of the chord of the circle,
x² + y² = r² (r > 0) along the line, y – 2x = 3 is r,
then r² is equal to :

If
$$\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta $$ = A$${\log _e}\left| {B\left( \theta \right)} \right| + C$$,

where C is a constant of integration, then $${{{B\left( \theta \right)} \over A}}$$
can be :

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

If x = 1 is a critical point of the function
f(x) = (3x² + ax – 2 – a)e^x , then :

An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length $$l$$ and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :

In an experiment to verify Stokes law, a small spherical ball of radius r and density $$\rho $$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to :
(ignore viscosity of air)

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :

Two coherent sources of sound, S₁ and S₂, produce sound waves of the same wavelength, $$\lambda $$ = 1 m, in phase. S₁ and S₂ are placed 1.5 m apart (see fig). A listener, located at L, directly in front of S₂ finds that the intensity is at a minimum
when he is 2 m away from S₂. The listener moves away from S₁, keeping his distance from S₂ fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from S₁. Then, d is :

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2^o, its figure of merit is close to :

A parallel plate capacitor has plate of length 'l', width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth about the axis passing through the pole is $$\omega $$. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is (h << R, where R is the radius of the earth)

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

An iron rod of volume 10^–3 m³ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be :

In the circuit shown, charge on the 5 $$\mu $$F capacitor is :

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is :

Two different wires having lengths L₁ and L₂, and respective temperature coefficient of linear expansion $$\alpha $$₁ and $$\alpha $$₂, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respectively, are connected as shown in the circuit below. The output voltage V₀ variation with input voltage linearly increasing with time, is given by :
(V_input = 0 V at t = 0)
(figures are qualitative)

The correct match between the entries in column I and column II are :

I	II
Radiation	Wavelength
(a) Microwave	(i) 100 m
(b) Gamma rays	(ii) 10–15 m
(c) A.M. radio waves	(iii) 10–10 m
(d) X-rays	(iv) 10–3 m

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively.
(Take V = 0 at infinity)

The quantities x = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$, y = $${E \over B}$$ and z = $${l \over {CR}}$$ are
defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $${{\varepsilon _0}}$$, $${{\mu _0}}$$, - free space permittivity and permeability respectively. Then :

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv²(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T₁ and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T₂. The ratio $${{{T_1}} \over {{T_2}}}$$ will be :

A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.

The surface of a metal is illuminated alternately with photons of energies E₁ = 4 eV and E₂ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.

A prism of angle A = 1^o has a refractive index $$\mu $$ = 1.5. A good estimate for the minimum angle of deviation (in degrees) is close to $${N \over {10}}$$.
Value of N is ____.

Nitrogen gas is at 300^oC temperature. The temperature (in K) at which the rms speed of a H₂ molecule would be equal to the rms speed of a nitrogen molecule, is _______.
(Molar mass of N₂ gas 28 g).

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be _________.