This practice test consists of IIT JEE 2009 questions to help you practice for actual IIT JEE main examination.

IIT JEE 2009

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Question

Section I

Let z=x+iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $z\bar z^3+\bar zz^3=350$ is

Possible Answers

Selected	Possible Answer
	32
	80
	48
	40

Question

Section I

If $\vec a, \vec b, \vec c$ and $\vec d$ are unit vectors such that $(\vec a * \vec b).(\vec c*\vec d)=1$ and $\vec a.\vec c=\frac {1}{2}$ , then

Possible Answers

Selected	Possible Answer
	$\vec a, \vec b, \vec c$ are non coplanar
	$\vec b, \vec c, \vec d$ are non coplanar
	$\vec a, \vec d$ parallel and $\vec b, \vec c$ are parallel
	$\vec b, \vec d$ are non parallel

Question

Section I

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2+9y^2=9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin.

Possible Answers

Selected	Possible Answer
	$\cfrac {21}{10}$
	$\cfrac {31}{10}$
	$\cfrac {27}{10}$
	$\cfrac {29}{10}$

Question

Section I

Let $z=\cos \theta +i\sin \theta$ . Then the value of $\overset {15}{\underset {m=1}{\sum}}Im (z^{2m-1})at\, \theta=2^\circ$ is

Possible Answers

Selected	Possible Answer
	$\cfrac {1}{3 \sin 2^\circ}$
	$\cfrac {1}{\sin 2^\circ}$
	$\cfrac {1}{4 \sin 2^\circ}$
	$\cfrac {1}{2 \sin 2^\circ}$

Question

Section I

Let P(3, 2, 6) be a point in space and Q be a point on the line $\vec r=(\hat i-\hat j+2\hat k)+\mu (3\hat i+\hat j+5\hat k)$ . Then the value of $\mu$ for which the vector $\overrightarrow {PQ}$ is parallel to the plane x-4y+3z=1 is

Possible Answers

Selected	Possible Answer
	$-\cfrac {1}{8}$
	$-\cfrac {1}{4}$
	$\cfrac {1}{4}$
	$\cfrac {1}{8}$

Question

Section I

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

Possible Answers

Selected	Possible Answer
	77
	55
	88
	66

Question

Section I

Tangents drawn from the point P(1, 8) to the circle x^2+y^2-6x-4y-11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is

Possible Answers

Selected	Possible Answer

Question

Section II

If $\cfrac {\sin^4x}{2}+\cfrac {\cos^4x}{3}=\cfrac {1}{5}$ , then

$(A) \quad \tan^2x=\cfrac {2}{3}$
$(B) \quad \cfrac {\sin^8x}{8}+\cfrac {\cos^8x}{27}=\cfrac {1}{125}$
$(C) \quad \tan^2x=\frac {1}{3}$
$(D) \quad \cfrac {\sin^8x}{8}+\cfrac {\cos^8x}{27}=\cfrac {2}{125}$

Possible Answers

Selected	Possible Answer
	AD
	AB
	CD
	BC

Question

Section II

Let $L=\overset {Lim}{x\rightarrow 0}\cfrac {a-\sqrt {a^2-x^2}-\frac {x^2}{4}}{x^4}$ , a>0 . If L is finite, then

$(A) \quad a=2$
$(B) \quad a=1$
$(C) \quad L=\frac {1}{64}$
$(D) \quad L=\frac {1}{32}$

Possible Answers

Selected	Possible Answer
	AC
	CD
	BC
	AD

Question

Section II

Area of the region bounded by the curve y=e^x and lines x = 0 and y = e is

$(A) \quad e-1$
$(B) \quad \int_1^e In (e+1-y)dy$
$(C) \quad e-\int_0^1e^xdx$
$(D) \quad \int_1^e ln\, y\,dy$

Possible Answers

Selected	Possible Answer
	BCD
	All correct
	ACD
	ABC

Question

Section III

Paragraph for Next 3 Questions

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The probability that X = 3 equals

Possible Answers

Selected	Possible Answer
	$\cfrac {5}{36}$
	$\cfrac {125}{216}$
	$\cfrac {25}{216}$
	$\cfrac {25}{36}$

Question

Section III

The probability that $X\geq 3$ equals

Possible Answers

Selected	Possible Answer
	$\cfrac {25}{216}$
	$\cfrac {125}{216}$
	$\cfrac {25}{36}$
	$\cfrac {5}{36}$

Question

Section III

The conditional probability that $X\geq 6$ given X>3 equals

Possible Answers

Selected	Possible Answer
	$\cfrac {5}{36}$
	$\cfrac {125}{216}$
	$\cfrac {25}{36}$
	$\cfrac {25}{216}$

Question

Section III

Paragraph for Next 3 Questions

Let A be the set of all 3 × 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices in A is

Possible Answers

Selected	Possible Answer
	6
	12
	3
	9

Question

Section III

The number of matrices A in for which the system of linear equation

has a unique solution, is

Possible Answers

Selected	Possible Answer
	at least 4 but less than 7
	at least 10
	at least 7 but less than 10
	less than 4

Question

Section III

The number of matrices A in A for which the system of linear equations

is inconsistent, is

Possible Answers

Selected	Possible Answer
	0
	1
	more than 2
	2

Question

Section IV

Match the statements/ expressions in Column I with the open intervals in Column II

(A) Interval contained in the domain of definition on non-zero solutions of the differential equation	$(P) \quad (-\frac {\pi}{2},\frac{\pi}{2})$
(B) Interval containing the value of the intergal $\int_1^5(x-1)(x-2)(x-3)(x-4)(x-5)dx$	$(Q) \quad \Big (0,\frac {\pi}{2}\Big )$
(C) Interval in which at least one of the points of local maximum of $\cos^2x+\sin x$ lies	$(R) \quad (\frac {\pi}{8},\frac{5\pi}{4})$
(D) Interval in which $\tan^{-1}(\sin x\cos x)$ is increasing	$(S) \quad (0,\frac{\pi}{8})$ $(T) \quad (-\pi, \pi)$

Possible Answers

Selected	Possible Answer
	$(A)\rightarrow (PQ); (B)\rightarrow (ST); (C)\rightarrow (RT); (D)\rightarrow (ST)$
	$(A)\rightarrow (PQS); (B)\rightarrow (PT); (C)\rightarrow (PQRT); (D)\rightarrow (S)$
	$(A)\rightarrow (S); (B)\rightarrow (Q); (C)\rightarrow (PRT); (D)\rightarrow (ST)$
	$(A)\rightarrow (P); (B)\rightarrow (PQT); (C)\rightarrow (PQRT); (D)\rightarrow (ST)$

Question

Section I

Let f be a non negative function defined on the interval [0,1]. if $\overset{x}{\underset {o}{\int}}$ $\sqrt {1-f'(t))^2 dt}$

$= \overset {x}{\underset {0}{\int}} f(t)dt,$ $0 \leq x \leq 1$ and f(0)=0

Possible Answers

Selected	Possible Answer
	$f \Big( \frac {1}{2} \Big) < \frac {1}{2}$ and $f \Big( \frac {1}{3}\Big ) < \frac {1}{3}$
	$f \Big( \frac {1}{2} \Big) < \frac {1}{2}$ and $f \Big( \frac {1}{3}\Big ) > \frac {1}{3}$
	$f \Big( \frac {1}{2} \Big) > \frac {1}{2}$ and $f \Big( \frac {1}{3}\Big ) < \frac {1}{3}$
	$f \Big( \frac {1}{2} \Big) > \frac {1}{2}$ and $f \Big( \frac {1}{3}\Big ) > \frac {1}{3}$

Question

Section II

In a triangle ABC with fixed base BC, the vertex A moves such that $\cos B+\cos C=4 \sin^2 \frac {A}{2}$ . If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then
(A) b + c =4a
(B) b + c = 2a
(C) locus of point A is an ellipse
(D) locus of point A is a pair of straight lines

Possible Answers

Selected	Possible Answer
	A
	AD
	AB
	BC

Question

Section VI

Match the conics in Column I with the statements/expression in Column II

Column I	column II
(A) Circle	(p) The locus of the point (h, k) for which the line touch the circle
(B) Parabola	(q) Points z in the complex plane satisfying $\pm 3$
(C) Ellipse	(r) Points of the conic have parametric representation $x= \sqrt{3}$ $\Big (\cfrac {1-t^2}{1+t^2}\Big ),y$ $=\cfrac {2t}{1+t^2}$
(D) Hyperbola	(s) The eccentricity of the conic lies in the interval $1 \leq x < \infty$ (t) Points z in the complex plane satisfying

Possible Answers

Selected	Possible Answer
	$(A) \rightarrow (s)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (r)$ ; $(D)\rightarrow (qs)$
	$(A) \rightarrow (t)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (r)$ ; $(D)\rightarrow (qs)$
	$(A) \rightarrow (q)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (r)$ ; $(D)\rightarrow (qs)$
	$(A) \rightarrow (p)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (r)$ ; $(D)\rightarrow (qs)$

Question

Section I

Look at the drawing given in the figure which has been drawn with ink of uniform line thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0) left inner circle (–a, a), right inner circle (a, a), vertical line (0,0) and horizontal line (0, – a). The y-coordinate of the centre of mass of the ink in this drawing is

Possible Answers

Selected	Possible Answer
	a / 8
	a / 10
	a / 12
	a / 3

Question

Section I

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I_1

and

are the currents in the segments ab and cd. Then,

Possible Answers

Selected	Possible Answer
	is in the direction ab and is in the direction dc

	is in the direction ba and is in the direction cd

Question

Section I

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are u and 2u, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?

Possible Answers

Selected	Possible Answer
	4
	1
	3
	2

Question

Section I

A disk of radius a / 4 having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at (-a / 2, 0, 0). A rod of length a carrying a uniformly distributed charge 8 C is place on the x-axis from x = a / 4 to x = 5a / 4. Two point charges -7 C and 3 C are placed at (a / 4, – a / 4, 0) and (–3a / 4, 3a / 4, 0), respectively. Consider a cubical surface formed by six surfaces $x = \pm a / 2, y = \pm a / 2, z = \pm a / 2$ . The electric flux through this cubical surface is

Possible Answers

Selected	Possible Answer
	$2C/ \epsilon _0$
	$-2C/ \epsilon _0$
	$10C/ \epsilon _0$
	$12C/ \epsilon _0$

Question

Section I

Three concentric metallic spherical shells of radii R, 2R, 3R, are given charge Q_1 , Q_2 , Q_3 , respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells Q_1 : Q_2 : Q_3 , is

Possible Answers

Selected	Possible Answer
	1 : 4 : 9
	1 : 2 : 3
	1 : 3 : 5
	1 : 8 : 18

Question

Section I

The x–t graph of particle undergoing simple harmonic motion is shown in the pic. The acceleration of the particle at t = 4 / 3 s is

Possible Answers

Selected	Possible Answer
	$(\pi^2/32 )cm /s^2$
	$(- \pi ^2 /32 ) cm / s^2$
	$(\sqrt {3}/ 32 ) \pi^2 \, cm \, /s^2$
	$-(\pi^3 /32 ) \pi^2 \, cm \, /s ^2$

Question

Section I

A ball is dropped from height of 20 m above the surface of water in a lake. The refractive index of water is 4 / 3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as

Possible Answers

Selected	Possible Answer
	12 m / s
	9 m / s
	21.33 m / s
	16 m / s

Question

Section I

A block of base 10 cm * 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $\sqrt {3}$ . The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from $0^{\circ}$ . Then

Possible Answers

Selected	Possible Answer
	The block will remain at rest on the plane up to certain $\theta$ and then it will topple
	at $\theta = 60^{\circ}$ , the block will start sliding down the plane and continue to do so at higher angles
	at $\theta = 60^{\circ}$ , the block will start sliding down the plane and on further increasing q, it will topple at certain $\theta$
	At $\theta = 30^{\circ}$ , the block will start sliding down the plane

Question

Section II

For circuit shown in the figure

(A) The current I through the battery is 7.5 mA
(B) The potential difference across R_L

is 18 V
(C) Ratio of powers dissipated in R_1

and

is 3
(D) If R_1

and

are interchanged, magnitude of the power dissipated in R_L

will decrease by a factor of 9

Possible Answers

Selected	Possible Answer
	AD
	AB
	BD
	AC

Question

Section II

and

denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

(A) C_p-C_v

is larger for a diatomic ideal gas than for a monoatomic ideal gas
(B) C_p+C_v

is larger for a diatomic ideal gas than for a monoatomic ideal gas
(C) C_p / C_v

is larger for a diatomic ideal gas than for a monoatomic ideal gas
(D) $C_p \cdot C_v$ is larger for a diatomic ideal gas than for a monoatomic ideal gas

Possible Answers

Selected	Possible Answer
	BC
	AD
	BD
	CD

Question

Section II

A student performed the experiment of determination of focal length of a concave mirror by u–v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are (42,56) (48,48), (60,40), (66, 33) (78,39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

(A) (42,56)
(B) (48,48)
(C) (66,38)
(D) (78,39)

Possible Answers

Selected	Possible Answer
	AB
	BD
	AD
	CD

Question

Section II

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

Possible Answers

Selected	Possible Answer
	linear momentum of the system does not change in time
	kinetic energy of the system does not change in time
	angular momentum of the system does not change in time
	potential energy of the system does not change in time

Question

Section III

Paragraph for Next 3 Questions

When a particle is restricted to move along xaxis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as $E=\cfrac {p^2}{2m}$ Thus, the energy of the particle can be denoted by a quantum number ‘n’ taking values 1, 2, 3 … (n = 1, called the ground state) corresponding to the number of loops in the standing wave.
Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a. Take $h=6.6 * 10^{-34} Js$ and $e=1.6*10^{-19}C$ .

The allowed energy for the particle for a particular value of n is proportional to

Possible Answers

Selected	Possible Answer
	$a^{-3/2}$
	$a^{-2}$
	$a^{-1}$
	$a^{2}$

Question

Section III

If the mass of the particle is $m = 1.0*10^{-30} kg$ and a = 6.6 nm, the energy of the particle in its ground state is closest to

Possible Answers

Selected	Possible Answer
	80 meV
	0.8 meV
	8 meV
	800 meV

Question

Section III

The speed of the particle, that can take discrete values, is proportional to

Possible Answers

Selected	Possible Answer
	$n^{-1}$
	$n^{1/2}$
	$n^{-3/2}$

Question

Section III

Paragraph for Next 3 Questions

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $\overset {2}{1} H$ known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D – D reaction is $\overset {2}{1} H + \overset {2}{1} H \rightarrow \overset {3}{2} He +n + energy$ In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of $\overset {2}{1} H$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than $5 * 10^{14} \, s cm^{-3}$ It may be helpful to use the following: Boltzmann constant $k=8.6 *10^{-5}eV/K$ ;
$\cfrac {e^2}{4 \pi \epsilon _0}$ $=1.44 *10^{-9} eVm$

In the core of nuclear fusion reactor, the gas becomes plasma because of

Possible Answers

Selected	Possible Answer
	The high temperature maintained inside the reactor core
	Coulomb force acting between the deuterons
	Strong nuclear force acting between the deuterons
	Coulomb force acting between deuteronelectron pairs

Question

Section III

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 kT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of $4 *10^{-15}m$ is in the range

Possible Answers

Selected	Possible Answer

Question

Section III

Results of calculations for four different designs of a fusion reactor using D – D reaction are given below. Which of these is most promising based on Lawson criterion?

Possible Answers

Selected	Possible Answer
	$Deuteron \, density = 2.0 * 10^{12} cm^{-3}$ , $confinement \, \, time = 5.0 * 10^{-3} s$
	$Deuteron \, density = 4.0 * 10^{23} cm^{-3}$ , $confinement \, \, time = 1.0 * 10^{-11} s$
	$Deuteron \, density = 1.0 * 10^{24} cm^{-3}$ , $confinement \, \, time = 4.0 * 10^{-12} s$
	$Deuteron \, density = 8.0 * 10^{14} cm^{-3}$ , $confinement \, \,time = 9.0 * 10^{-1} s$

Question

Section IV

This section contains 2 questions. Each questions contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with one or more statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example :
If the correct matches are A – p, s and t; B – q and r ; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following.

Column II shows five systems in which two objects are labbled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and / or Y Match these statements to the appropriate system(s) from Column II

Column I	Column II
(A) the force exerted by X on Y has a magnitude Mg.	Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity
(B) The gravitational potential energy of X is continuously increasing	Two ring magnets Y and Z, each of mass M, are kept in frictionless vertical plastic stand so that they repel each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity.
(C) Mechanical energy of the system X + Y is continuously decreasing.	A pulley Y of mass is fixed to a table X through a clam X. A block of mass M hangs from a string that goes over the pulley and is fixed at point P of the table. The whole system is kept in a lift that is going down with a constant velocity.
(D) The torque of the weight of Y about point P is zero	A sphere Y of mass M is put in a nonviscous liquid X kept in a container at rest. The sphere is releases and it moves down in the liquid.
	A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container,

Possible Answers

Selected	Possible Answer
	$\therefore (B) \rightarrow(p,t), \, \,$ $(A) \rightarrow (q,s,t),$ $\, \, (D) \rightarrow (p,r,t),$ $\,\, (C) \rightarrow (q)$
	$\therefore (A) \rightarrow(p,t), \, \,$ $(B) \rightarrow (q,s,t),$ $\, \, (C) \rightarrow (p,r,t),$ $\,\, (D) \rightarrow (q)$
	$\therefore (B) \rightarrow(p,t), \, \,$ $(A) \rightarrow (q,s,t),$ $\, \, (C) \rightarrow (p,r,t),$ $\,\, (D) \rightarrow (q)$
	$\therefore (C) \rightarrow(p,t), \, \,$ $(A) \rightarrow (q,s,t),$ $\, \, (D) \rightarrow (p,r,t),$ $\,\, (B) \rightarrow (q)$

Question

Section VI

Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

Column I	Column II
(A) E = 0	Charges are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon.
(B) $v \not = 0$	Charges are on a line perpendicular to PQ at equal intervals. M is the midpoint between the two innermost charges.
(C) B = 0	Charges are placed on two coplanar insulting rings at equal intervals M is the common centre of the rings. PQ is perpendicular to the plane of the rings.
(D) $\mu \not = 0$	Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides
	Charges are placed on two coplanar, identical insulting rings at equal intervals. M is the midpoint between the centres of the rings. PQ is perpendicular to the line joining the centres and coplanar to the ring

Selected	Possible Answer
	$\therefore$ (B) $\rightarrow$ (p,r,s), (A) $\rightarrow$ (r,s), (C) $\rightarrow$ (p,q,t), (D) $\rightarrow$ (r,s)
	$\therefore$ (A) $\rightarrow$ (p,r,s), (B) $\rightarrow$ (r,s), (C) $\rightarrow$ (p,q,t), (D) $\rightarrow$ (r,s)
	$\therefore$ (A) $\rightarrow$ (p,r,s), (B) $\rightarrow$ (r,s), (D) $\rightarrow$ (p,q,t), (C) $\rightarrow$ (r,s)
	$\therefore$ (D) $\rightarrow$ (p,r,s), (B) $\rightarrow$ (r,s), (C) $\rightarrow$ (p,q,t), (A) $\rightarrow$ (r,s)

Question

Section I

The Henry’s law constant for the solubility of N_2 gas in water at 298 K is 1.0*10^5 atm. The mole fraction of N_2 in air is 0.8. The number of moles of N_2 from air dissolved in 10 moles of water at 298 K and 5 atm pressure is

Possible Answers

Selected	Possible Answer
	$4.0 *10^{-6}$
	$4.0*10^{-4}$
	$4.0 *10^{-5}$
	$5.0*10^{-4}$

Question

Section I

The correct acidity order of the following is

Possible Answers

Selected	Possible Answer
	(III) > (IV) > (II) > (I)
	(II) > (III) > (IV) > (I)
	(IV) > (III) > (I) > (II)
	(III) > (II) > (I) > (IV)

Question

Section I

The reaction of P_4

with X leads selectively to P_4 O_6

. The X

Possible Answers

Selected	Possible Answer
	A mixture of and
	Dry
	Moist
	in the presence of aqueous

Question

Section I

Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is

Possible Answers

Selected	Possible Answer
	Natural Rubber
	Poly(vinyl chloride)
	Nylon
	Cellulose

Question

Section I

Given that the abundances of isotopes $^{54}Fe$ , $^{56}Fe$ and $^{57}Fe$ are $5 \% , 90 \% \, and \, 5 \%$ respectively, the astomic mass of Fe is

Possible Answers

Selected	Possible Answer
	55.85
	55.95
	56.05
	55.75

Question

Section I

The IUPAC name of the following compound is

Possible Answers

Selected	Possible Answer
	2-Cyano-4-hydroxybromobenzene
	2-Bromo-5-hydroxybenzonitrile
	6-Bromo-3-hydroxybenzonitrile
	4-Bromo-3-cyanophenol

Question

Section I
Among the electrolytes Na_2 SO_4, CaCl_2, Al_2 (SO_4)_3

and

the most effective coagulating agent for Sb_2 S_3

Sol is

Possible Answers

Selected	Possible Answer

Question

Section I

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

Possible Answers

Selected	Possible Answer
	$- \cfrac {an^2}{V^2}$
	$\cfrac {an^2}{V^2}$

Question

Section II

The compound(s) formed upon combustion of sodium metal in excess air is (are)
(A) Na_2 O_2

(B)

(C)

(D)

Possible Answers

Selected	Possible Answer
	(ABC)
	(ABD)
	(ADC)
	(AB)

Question

Section II

The correct statement(s) about the compound H_3 C(HO)HC - CH = CH -CH (OH)CH_3 (X) is (are)
(A) The total number of stereoisomers possible for X is 6
(B) The total number of diastereomers possible for X is 3
(C) If the sterechemistry about the double bond in X is trans, the number of enantiomers possible for X is 4
(D) If the sterechemistry about the double bond in X is cis, the number of enantiomers possible for X is 2

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Selected	Possible Answer
	(AB)
	(AC)
	(BC)
	(AD)

Question

Section II

The compound(s) that exhibit(s) geometrical isomerism is (are)
(A) [Pt(en)Cl_2]

(B)

(C)

(D)

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Selected	Possible Answer
	CD
	AD
	BD
	AC

Question

Section II

The correct statement(s) regarding defects in solids is(are)
(A) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion
(B) Frenkel defect is a dislocation defect
(C) Trapping of an electron in the lasttice leads to the formation of F-center
(D) Schottky defects have no effect on the physical properties of solids

Possible Answers

Selected	Possible Answer
	DC
	AB
	AC
	BC

Question

Section III

Paragraph for Questions Below three

A carbonyl compound P, which gives iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.

The structure of the carbonyl compound P is :

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Question

Section III

The structure of the products Q and R, respectively, are

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Section III

The structure of the product S is

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Section III

Paragraph for Questions below three

p-AminoN, N-dimethylaniline is added to a strongly acidic solution of X. The resulting solution is treated with a few drops of aqueous solution of Y to field blue coloration due to the formation of methylene blue. Treatment of the aqueous solution of Y with the reagent potassium hexacyanoferrate (II) leads to the formation of an intense blue precipitate. The precipitate dissolves on excess addition of the reagent. Similarly, treatment of the solution Y with the solution of potassium hexacyanoferrate (III) leads to a brown coloration due to the formation of Z.

The compound X is

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Section III

The compound Y is

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Section III

The compound Z is

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Section IV

Match each of the Compounds in Column I with its characteristic reaction (s) in Column II.

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Selected	Possible Answer
	$(D) \rightarrow (pqst)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (p)$ ; $(A) \rightarrow (r)$
	$(A) \rightarrow (pqst)$ ; $(B) \rightarrow (st)$ ; $(B) \rightarrow (p)$ ; $(C) \rightarrow (r)$
	$(B) \rightarrow (pqst)$ ; $(A) \rightarrow (st)$ ; $(C) \rightarrow (p)$ ; $(D) \rightarrow (r)$
	$(A) \rightarrow (pqst)$ ; $(B) \rightarrow (st)$ ; $(C) \rightarrow (p)$ ; $(D) \rightarrow (r)$

Question

Section VI

Match each of the diatomic molecules in Column I with its property / properties in Column II.

Possible Answers

Selected	Possible Answer
	$(A) \rightarrow (pqrt)$ ; $(C) \rightarrow (qrst)$ ; $(B) \rightarrow (pqr)$ ; $(D) \rightarrow (pqrs)$
	$(A) \rightarrow (pqrt)$ ; $(B) \rightarrow (qrst)$ ; $(C) \rightarrow (pqr)$ ; $(D) \rightarrow (pqrs)$
	$(A) \rightarrow (pqrt)$ ; $(B) \rightarrow (qrst)$ ; $(D) \rightarrow (pqr)$ ; $(C) \rightarrow (pqrs)$
	$(D) \rightarrow (pqrt)$ ; $(B) \rightarrow (qrst)$ ; $(C) \rightarrow (pqr)$ ; $(A) \rightarrow (pqrs)$