IIT JEE 2010 Solved Paper - II

The species having pyramidal shape is

In the reaction the structure of the product T is

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

The packing efficiency of the two-dimensional square unit cell shown below is

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

The compounds P,Q and S

were separately subjected to nitration using mixture. The major product formed in each case respectively, is

Silver (atomic weight = ) has a density of . The number of silver atoms on a surface of area can be expressed in scientific notation as . The value of x is

One mole of an ideal gas is taken from a to 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 and that along the dotted line path is , then the integer closest to the ratio is

Total number of geometrical isomers for the complex is

Among the following, the number of elements showing only one nonzero oxidation state is

The total number of diprotic acids among the following is

Two aliphatic aldehydes P and Q react in the presence of queous to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below :

The compounds P and Q respectively are

Two aliphatic aldehydes P and Q react in the presence of aqueous to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below :

The compound R is

Two aliphatic aldehydes P and Q react in the presence of aqueous to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below :

The compound S is

The hydrogenlike species is in a spherically symmetric state with one radial node. Upon absorbing light the ion undergoes transition to a state . The state has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
The state is

The hydrogenlike species is in a spherically symmetric state with one radial node. Upon absorbing light the ion undergoes transition to a state . The state has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Energy of the state in units of the hydrogen atom ground state energy is

The hydrogenlike species is in a spherically symmetric state with one radial node. Upon absorbing light the ion undergoes transition to a state . The state has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
The orbital angular momentum quantum number of the state is

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

(A) – (RS) Diazonium ion goes for coupling via substitution
(B) – (T) Pinacole pinacolone goes through +ve ion intermediate
(C) – (PQ)It goes nucleophilic addition reaction through a complex formation
(D) –® SH is acidic with base. It is 1st converted into a nucleophile and then gives intra substitution.

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.

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

Let f be a real valued function defined on the interval (– 1, 1) such that for all , and let be the inverse function of f. Then is equal to

For , let denote respectively, the coefficient of in the expansions of Then is equal to

Two adjacent sides of a parallelogram ABCD are given by and .
The side AD is rotated by an acute angle in the plane of the parallelogram that AD becomes . If makes a right angle with the side AB, then cosine of the angle is given by

A signal which can be green or red with probability 4 / 5 or 1 / 5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3 / 4. If the signal received at station B is green, then the probability that the original signal was green is

If the distance of the point from the plane , where , is 5, then the foot of perpendicular from P to the plane is

Let be real numbers satisfying for k = 3, 4, ...., 11. If , then the value of is equal to

Let k be a positive real number and let

If , then [k] is equal to

[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k]

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is . If is obtuse and if r denotes the radius of the incircle of the triangle, then is equal to

Let f be a function defined on R (the set of all real numbers) such that , for all
If g is a function defined on R with values in the interval such that f(x) = ln (g(x)), for all , then the number of points in R at which g has a local maximum is

Two parallel chords of a circle of radius 2 are at a distance apart. If the chords subtend at the center, angles of , where k>0, then the value of [k] is
[Note: [k] denotes the largest integer less than or equal to k]

Consider the polynomial

Let s be the sum of all distinct real roots of f(x) and let t = | s |
The real number s lies in the interval

The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval

The function is

Tangents are drawn from the point P (3, 4 ) to the ellipse 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 touching the ellipse at points A and B.
The orthocenter of the triangle PAB is

Tangents are drawn from the point P (3, 4 ) to the ellipse touching the ellipse at points A and B.
The equation of the locus of the point whose distances from the point P and the line AB are equal, is

Match the statements in ColumnI with those in ColumnII.

[ Note : Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.]

Match the statements in Column I with the values in Column II.

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is , the mass of the string is

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 Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is:

A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength . When the field is switch off, the drop is observed to fall with terminal velocity . Given , viscosity of the air and the density of oil , the magnitude of q is

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

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent froce F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

A large glass slab 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 ?

To determine the half life of a radioactive element, a student plots a graph of versus t. Here is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is.

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 become 4 V? [Take : ln 5 = 1.6, ln 3 = 1.1]

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

A diatomic ideal gas is compressed adiabatically to (1 / 32) of its initial volume. In the initial temperature of the gas is (in Kelvin) and the final temperature is a , the value of a is

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When liquid medicine of density r is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r << R) is

If , the radius of the drop when it detaches from the dropper is approximately

After the drop detaches, its surface energy is

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The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.

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 closes to . Then the moment of inertia of CO molecule about its center of mass is close to (Take

In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.), where

Two transparent media of refractive indices have a solid lens shaped transparent material of refractive index between them as show in figures in Column I I. A ray traversing these media is also shown in the figures. In Column I different relationships between are given. Match them to the ray diagrams shown in Column I I.