IIT-JEE 2010 Paper 2 Offline

The compounds $\mathbf{P}, \mathbf{Q}$ and $\mathbf{S}$ were separately subjected to nitration using $\mathrm{HNO}_3 / \mathrm{H}_2 \mathrm{SO}_4$ mixture. The major product formed in each case respectively, is :

The compounds P and Q respectively are :

The compound R is :

The compound S is :

The species having pyramidal shape is

Assuming that Hund’s rule is violated, the bond order and magnetic nature of the diatomic molecule B2 is

In the reaction,

The structure of the product T is :

Match the reactions in Column I with
appropriate options in Column II.



Column I
Column II


(A)


(P) Racemic mixture


(B)


(Q) Addition reaction


(C)


(...

The complex showing a spin-only magnetic moment of 2.82 B.M. is :

Total number of geometrical isomers for the complex $\left[\mathrm{RhCl}(\mathrm{CO})\left(\mathrm{PPh}_3\right)\left(\mathrm{NH}_3\right)\right]$ is ___________.

The total number of diprotic acids among the following is:
H3PO4, H2SO4, H3PO3, H2CO3, H2S2O7, H3BO3, H3PO2, H2CrO4 and H2SO3

All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.



Column I
Column II


(A) (CH3)2SiCl2
(P) Hydrogen halide formatio...

Among the following, the number of elements showing only one non-zero oxidation state is :
O, Cl, F, N, P, Sn, Tl, Na, Ti

The packing efficiency of the twodimensional square unit cell shown below is

Silver (atomic weight = 108 g mol-1) has a density of 10.5 g.cm-3. The number of silver atoms on a surface of area 10-12 m2 can be expressed in scientific notation as y \(\times\) 10x. The value of x is?

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state energy...

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state energy...

The hydrogen like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state energy...

One mole of an ideal gas is taken from $\mathbf{a}$ to $\mathbf{b}$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $W_{\text {s }}$ and that dotted line p...

If the distance of the point \(P(1, -2, 1)\) from the plane \(x+2y-2z\)\(\, = \alpha ,\) where \(\alpha > 0,\) is \(5,\) then the foot of the perpendicular from \(P\) to the planes is

Match the statement in Column-\(I\) with the values in Column-\(II\)
\(\,\,\,\,\) \(\,\,\,\,\) \(\,\,\,\,\) Column-\(I\)
(A)\(\,\,\,\,\) A line from the origin meets the lines $$\,{{x - 2} \over 1} = {{y - 1} \over { - 2}} = {{z + 1} \ov...

Let \(f\) be a function defined on \(R\) (the set of all real numbers)
such that \(f'\left( x \right) = 2010\left( {x - 2009} \right){\left( {x - 2010} \right)^2}{\left( {x - 2011} \right)^3}{\left( {x - 2012} \right)^4}\) for all $$x \in...

Consider the polynomial
\(f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.\)
Let \(s\) be the sum of all distinct real roots of \(f(x)\) and let \(t = \left| s \right|.\)
The area bounded by the curve \(y=f(x)\) and the lines \(x=0,\) \(y=0\) ...

Match the statements in Column I with those in Column II.
[Note : Here z takes value in the complex plane and Im z and Re z denotes, respectively, the imaginary part and the real part of z.]
Column I
(A) The set of points z sat...

Let \(f\) be a real-valued function defined on the interval \((-1, 1)\) such that
\({e^{ - x}}f\left( x \right) = 2 + \int\limits_0^x {\sqrt {{t^4} + 1} \,\,dt,}\) for all \(x \in \left( { - 1,1} \right)\),
and let \({f^{ - 1}}\) be the ...

Tangents are drawn from the point \(P(3, 4)\) to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) touching the ellipse at points \(A\) and \(B\).
The coordinates of \(A\) and \(B\) are

Tangents are drawn from the point \(P(3, 4)\) to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) touching the ellipse at points \(A\) and \(B\).
The orthocentre of the triangle \(PAB\) is

Tangents are drawn from the point \(P(3, 4)\) to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) touching the ellipse at points \(A\) and \(B\).
The equation of the locus of the point whose distances from the point \(P\) and the l...

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to :

Consider the polynomial
\(f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.\)
Let \(s\) be the sum of all distinct real roots of \(f(x)\) and let \(t = \left| s \right|.\)
The function\(f'(x)\) is

Consider the polynomial
\(f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.\)
Let \(s\) be the sum of all distinct real roots of \(f(x)\) and let \(t = \left| s \right|.\)
The real numbers lies in the interval

For \(r = 0,\,1,....,\) let \({A_r},\,{B_r}\) and \({C_r}\) denote, respectively, the coefficient of \({X^r}\) in the expansions of \({\left( {1 + x} \right)^{10}},\) \({\left( {1 + x} \right)^{20}}\) and \({\left( {1 + x} \right)^{30}}.\)...

Let $k$ be a positive real number and let
$$ \begin{aligned} A & =\left[\begin{array}{ccc} 2 k-1 & 2 \sqrt{k} & 2 \sqrt{k} \\ 2 \sqrt{k} & 1 & -2 k \\ -2 \sqrt{k} & 2 k & -1 \end{array}\right] \text { and } \\\\ \mathbf{B} & =\left[\begin{a...

A signal which can be green or red with probability \({4 \over 5}\) and \({1 \over 5}\) respectively, is received by station A and then transmitted to station \(B\). The probability of each station receving the signal correctly is $${3 \ove...

Consider a triangle \(ABC\) and let \(a, b\) and \(c\) denote the lengths of the sides opposit to vertices \(A, B\) and \(C\) respectively. Suppose \(a = 6,b = 10\) and the area of the triangle is \(15\sqrt 3\), if \(\angle ACB\) is obtuse...

Let \({a_1},\,{a_{2\,}},\,{a_3}\)......,\({a_{11}}\) be real numbers satisfying \({a_1} = 15,27 - 2{a_2} > 0\,\,and\,\,{a_k} = 2{a_{k - 1}} - {a_{k - 2}}\,\,for\,k = 3,4,........11\). if $$\,\,\,{{a_1^2 + a_2^2 + .... + a_{11}^2} \over {11}...

Two parallel chords of a circle of radius 2 are at a distance \(\sqrt 3 + 1\) apart. If the chords subtend at the center , angles of \({\pi \over k}\) and \({{2\pi } \over k},\) where\(k > 0,\) then the value of \(\left[ k \right]\) is
[N...

Two adjacent sides of a parallelogram \(ABCD\) are given by
\(\overrightarrow {AB} = 2\widehat i + 10\widehat j + 11\widehat k\) and \(\,\overrightarrow {AD} = -\widehat i + 2\widehat j + 2\widehat k\)
The side \(AD\) is rotated by an a...

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column...

To determine the half-life of a radioactive element, a student plots a graph of \(\ln \left| {{{dN(t)} \over {dt}}} \right|\) versus t. Here, \({{dN(t)} \over {dt}}\) is the rate of radioactive decay at time t. If the number of radioactive ...

A diatomic molecule has moment of inertia I. By Bohr's quantization condition, its rotational energy in the nth level (n = 0 is not allowed) is

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to \({4 \over \pi } \times {10^{11}}\) Hz. Then, the moment of inertia of CO molecule about its centre of mass is clos...

In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu \(= {5 \over 3} \times {10^{ - 27}}\) kg, is close to :

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)

A uniformly charged thin spherical shell of radius \(R\) carries uniform surface charge density of \(\sigma\) per unit area. It is made of two hemispherical shells, held together by pressing them with force \(F\) (see figure). \(F\) is pro...

A tiny spherical oil drop carrying a net charge \(q\) is balanced in still air with a vertical uniform electric field of strength \({{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.\) When the field is switched off, the drop is observed to f...

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A large glass slab (\(\mu\) = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from \({{25} \over 3}\) m to \({{50} \over 7}\) m in 30 s. What is the speed of the object in km per hour?

Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens shaped transparent material of refractive index $\mu_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figur...