This practice test consists of IIT JEE 2007 questions to help you practice for actual IIT JEE main examination.

IIT JEE Question Paper 2007

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Question

Q. No. – 1. A circuit is connected as shown in the figure with the switch S open. When the switch is closed the total amount of charge that flows from Y to X is

Possible Answers

Selected	Possible Answer
	$81 \mu C$

	$27 \mu C$
	$54 \mu C$

Question

Q. No. – 2. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

Possible Answers

Selected	Possible Answer
	A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
	No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
	A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
	No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.

Question

Q. No. – 3. In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

Possible Answers

Selected	Possible Answer
	$E\big(_{92}^{236}U\big) < E\big(_{56}^{140}Ba\big) + E\big(_{36}^{94}Kr\big) + 2E(n)$
	$E\big(_{92}^{236}U\big) = E\big(_{56}^{140}Ba\big) + E\big(_{36}^{94}Kr\big) + 2E(n)$
	$E\big(_{92}^{236}U\big) < E\big(_{53}^{137}I\big) + E\big(_{39}^{97}Y\big) + 2E(n)$
	$E\big(_{92}^{236}U\big) > E\big(_{53}^{137}I\big) + E\big(_{39}^{97}Y\big) + 2E(n)$

Question

Q. No. – 4. In an experiment to determine the focal length (f) of a concave mirror by the u–v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

Possible Answers

Selected	Possible Answer

Question

Q. No. – 5. The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Possible Answers

Selected	Possible Answer
	1648 nm
	823 nm
	1882 nm
	802 nm

Question

Q. No. – 6. A resistance of $2 \Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than $2 \Omega$ , is connected across the other gap. When these resistance are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

Possible Answers

Selected	Possible Answer
	$6 \Omega$
	$4 \Omega$
	$3 \Omega$
	$5 \Omega$

Question

Q. No. – 7. A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

Possible Answers

Selected	Possible Answer
	a reflected ray and a refracted ray and the angle between them would be greater than $180^o - 2\theta$
	only a reflected ray and no refracted ray
	a reflected ray and a refracted ray and the angle between them would be less than $180^o - 2\theta$
	only a refracted ray and no reflected ray

Question

Q. No. – 8. Two particle of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x is

Possible Answers

Selected	Possible Answer
	$\cfrac{F}{2m}\cfrac{x}{\sqrt{a^2-x^2}}$
	$\cfrac{F}{2m}\cfrac{a}{\sqrt{a^2-x^2}}$
	$\cfrac{F}{2m} \; \cfrac{x}{a}$
	$\cfrac{F}{2m}\cfrac{\sqrt{a^2-x^2}}{x}$

Question

Q. No. – 9. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

Possible Answers

Selected	Possible Answer
	negative and distributed uniformly over the surface of the sphere
	negative and appears only at the point on the sphere closest to the point charge
	negative and distributed non-uniformly over the entire surface of the sphere
	zero

Question

SECTION – II

Instruction for Question No. 10 to 13 Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Q. No. – 10.

STATEMENT-1
The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.

because

STATEMENT-2
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
	Statement -1 is False, Statement-2 is True.
	Statement -1 is True, Statement-2 is False.
	Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.

Question

Q. No. – 11.

STATEMENT-1
If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.

because

STATEMENT -2
When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
	Statement -1 is False, Statement-2 is True.
	Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
	Statement -1 is True, Statement-2 is False.

Question

Q. No. – 12.

STATEMENT-1
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 300 with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because

STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

Possible Answers

Selected	Possible Answer
	Statement -1 is True, Statement-2 is False.
	Statement -1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for statement-1.
	Statement -1 is True, Statement-2 is True; Statement-2 is a correct explanation for statement-1.
	Statement -1 is False, Statement-2 is True.

Question

Q. No. – 13.

STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

because

STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.

Possible Answers

Selected	Possible Answer
	Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
	Statement -1 is False, Statement-2 is True.
	Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
	Statement -1 is True, Statement-2 is False.

Question

SECTION – II

Paragraph for Question Nos. 14 to 16

A fixed thermally conducting cylinder has a radius R and height L_0 . The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P_0 .

Q. No. – 14. The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

Possible Answers

Selected	Possible Answer
	$\cfrac{P_0}{2}-\cfrac{Mg}{\pi R^2}$
	$\cfrac{P_0}{2}$

	$\cfrac{P_0}{2}+\cfrac{Mg}{\pi R^2}$

Question

Q. No. – 15. While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

Possible Answers

Selected	Possible Answer
	$\bigg(\cfrac{P_0\pi R^2-Mg}{\pi R^2 P_0}\bigg)\bigg(2L\bigg)$
	$\bigg(\cfrac{P_0\pi R^2+Mg}{\pi R^2 P_0}\bigg)\bigg(2L\bigg)$
	$\bigg(\cfrac{P_0\pi R^2}{\pi R^2 P_0-Mg}\bigg)\bigg(2L\bigg)$
	$\bigg(\cfrac{2P_0\pi R^2}{\pi R^2 P_0+Mg}\bigg)\bigg(2L\bigg)$

Question

Q. No. – 16. The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies

Possible Answers

Selected	Possible Answer
	$\rho g(L_0-H)^2-P_0(L_0-H) + L_0P_0=0$
	$\rho g(L_0-H)^2-P_0(L_0-H) - L_0P_0=0$
	$\rho g(L_0-H)^2+P_0(L_0-H) + L_0P_0=0$
	$\rho g(L_0-H)^2+P_0(L_0-H) - L_0P_0=0$

Question

Paragraph for Question Nos. 17 to 19

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia and respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance x_1 . Disc B is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance x_2 . Both the discs rotate in the clockwise direction.

Q. No. – 17. The ratio of x_1/x_2 is

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{\sqrt 2}$
	$\sqrt 2$

	$\cfrac{1}{2}$

Question

Q. No. – 18. When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

Possible Answers

Selected	Possible Answer
	$\cfrac{2I\omega}{3t}$
	$\cfrac{9I\omega}{4t}$
	$\cfrac{3I\omega}{2t}$
	$\cfrac{9I\omega}{2t}$

Question

Q. No. – 19. The loss of kinetic energy during the above process is

Possible Answers

Selected	Possible Answer
	$\cfrac{I\omega^2}{6}$
	$\cfrac{I\omega^2}{2}$
	$\cfrac{I\omega^2}{3}$
	$\cfrac{I\omega^2}{4}$

Question

Section – IV

Instruction for Q. No. -20 to 22

p<>. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct match are A-p, A-s, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

Q. No. – 20. Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Choose the answer from the given option : –
1. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (r) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (r) & (s).

2. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (r) & (s).

3. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (q) & (s), (D) $\rightarrow$ (r) & (s).

4. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (p) & (r).

Possible Answers

Selected	Possible Answer
	4
	3
	1
	2

Question

Q. No. – 21. Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) Transition between two atomic energy levels	(p) Characteristic X-rays
(B) Electron emission from a material	(q) Photoelectric effect
(C) Mosley’s law	(r) Hydrogen spectrum
(D) Change of photon energy into kinetic energy of electrons	(s) $\beta$ -decay

Choose the answer from the given option : –
1. (A) $\rightarrow$ (p) & (r), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (s), (D) $\rightarrow$ (r)

2. (A) $\rightarrow$ (p) & (r), (B) $\rightarrow$ (q) & (s), (C) $\rightarrow$ (p), (D) $\rightarrow$ (q)

3. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (q) & (s), (D) $\rightarrow$ (r) & (s).

4. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (p) & (r).

Possible Answers

Selected	Possible Answer
	4
	1
	2
	3

Question

Q. No. – 22. Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) A charged capacitor is connected to the ends of the wire	(p) A constant current flows through the wire
(B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion	(q) Thermal energy is generated in the wire
(C) The wire is placed in a constant electric field that has a direction along the length of the wire.	(r) A constant potential difference develops between the ends of the wire
(D) A battery of constant emf is connected to the ends of the wire	(s) Charges of constant magnitude appear at the ends of the wire

Choose the answer from the given option : -
1. (A) $\rightarrow$ (q), (B) $\rightarrow$ (r) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (p),(q) & (r)

2. (A) $\rightarrow$ (p) & (r), (B) $\rightarrow$ (q) & (s), (C) $\rightarrow$ (p), (D) $\rightarrow$ (s)

3. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (q) & (s), (D) $\rightarrow$ (r) & (s).

4. (A) $\rightarrow$ (p) & (q), (B) $\rightarrow$ (p) & (s), (C) $\rightarrow$ (r) & (s), (D) $\rightarrow$ (p) & (s).

Possible Answers

Selected	Possible Answer
	4
	2
	1
	3

Question

Section – 1

This section contains 9 questions From 23 to 31.

Q. No. – 23. The number of structural isomers for $C_6H_{14}$ is

Possible Answers

Selected	Possible Answer
	3
	4
	6
	5

Question

Q. No. – 24. In the following reaction,

the structure of the major product ‘X’ is

Possible Answers

Selected	Possible Answer
	!{width:200px}
	!{width:200px}
	!{width:200px}
	!{width:200px}

Question

Q. No. – 25. When 20 g of naphthoic acid $(C_{11}H_8O_2)$ is dissolved in 50 g of benzene $(K_f = 1.72\; K\; kg\; mol^{-1})$ , a freezing point depression of 2 K is observed. The van’t Hoff factor (i) is

Possible Answers

Selected	Possible Answer
	3
	1
	2
	0.5

Question

Q. No. – 26. Among the following, the paramagnetic compound is

Possible Answers

Selected	Possible Answer

Question

Q. No. – 27. The value of $log_{10}K$ for a reaction $A \leftrightharpoons B$ is

(Given : $\Delta_rH^0_{298K}=-54.07kJ\; mol^{-1}$ , $\Delta_rS^0_{298K}=10JK^{-1}\; and$ $R=8.314 JK^{-1}\; mol^{-1}; 2.303*8.314*298=5705)$

Possible Answers

Selected	Possible Answer
	5
	10
	95
	100

Question

Q. No. – 28. The species having bond order different from that in CO is

Possible Answers

Selected	Possible Answer

Question

Q. No. – 29. The percentage of p-character in the orbitals forming P−P bonds in P_4 is

Possible Answers

Selected	Possible Answer
	25
	50
	33
	75

Question

Q. No. – 30. Extraction of zinc from zinc blende is achieved by

Possible Answers

Selected	Possible Answer
	electrolytic reduction
	roasting followed by reduction with carbon
	roasting followed by self-reduction
	roasting followed by reduction with another metal

Question

Q. No. – 31. The reagent(s) for the following conversion,

Is/are

Possible Answers

Selected	Possible Answer
	aqueous followed by
	alcoholic

	alcoholic followed by

Question

Section – II

This section contains 4 questions numbered 32 to 35. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason).

Q. No. – 32.
STATEMENT-1: p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.

because

STATEMENT-2: o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement -2 is False.
	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
	Statement-1 is False, Statement-2 is True.

Question

Q. No. – 33.
STATEMENT-1: Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).

because

STATEMENT-2: The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
	Statement-1 is False, Statement-2 is True.
	Statement-1 is True, Statement-2 is False.
	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question

Q. No. – 34.
STATEMENT-1: Boron always forms covalent bond.

because

STATEMENT-2: The small size of B3+ favours formation of covalent bond.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
	Statement-1 is True, Statement-2 is True.
	Statement-1 is False, Statement-2 is True.

Question

Q. No. – 35.
STATEMENT-1: In water, orthoboric acid behaves as a weak monobasic acid.

because

STATEMENT-2: In water, orthoboric acid acts as a proton donor.

Possible Answers

Selected	Possible Answer
	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
	Statement-1is True, Statement-2 is False.
	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
	Statement-1 is False, Statement-2 is True.

Question

Section – II

This section contains 2 paragraphs 36-38 and 39-41. Based upon each paragraph, 3 multiple choice questions have to be answered.

Paragraph for question Nos 36 to 38

Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 * 10^23

) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.

$A\; 4.0$ molar aqueous solution of NaCl

is prepared and $500\quad mL$ of this solution is electrolysed. This leads to the evolution of chlorine gas at one of the electrodes (atomic mass: Na = 23, Hg = 200; 1 Faraday=96500 coulombs)

Q. No. – 36. The total number of moles of chlorine gas evolved is

Possible Answers

Selected	Possible Answer
	2.0
	1.0
	0.5
	3.0

Question

Q. No. – 37. If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is

Possible Answers

Selected	Possible Answer
	446
	200
	400
	225

Question

Q. No. – 38. The total charge (coulombs) required for complete electrolysis is

Possible Answers

Selected	Possible Answer
	48250
	193000
	24125
	96500

Question

Paragraph for Question Nos. 39 to 41

The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers +2, +4 and +6. XeF_4 reacts violently with water to give XeO_3 . The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.

Q. No. – 39. Argon is used in arc welding because of its

Possible Answers

Selected	Possible Answer
	flammability
	high calorific value
	ability to lower the melting point of metal
	low reactivity with metal

Question

Q. No. – 40. The structure of XeO_3 is

Possible Answers

Selected	Possible Answer
	planar
	linear
	pyramidal
	T-shaped

Question

Q. No. – 41. XeF_4 and XeF_6 are expected to be

Possible Answers

Selected	Possible Answer
	reducing
	unreactive
	strongly basic
	oxidizing

Question

Section – IV

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column-I have to be matched with statements (p, q, r, s) in Column-II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

Q. No. – 42. Match the complexes in Column-I with their properties listed in Column-II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column-I	Column-II
(A)	(p) geometrical isomers
(B)	(q) paramagnetic
(C)	(r) diamagnetic
(D)	(s) metal ion with +2 oxidation state

Choose correct answer from the given option

1 $A\rightarrow p,q,s,\; B\rightarrow p,r,s,$ $C\rightarrow q,s,\; D\rightarrow q,s$
2 $A\rightarrow p,q,r,\; B\rightarrow p,q,s,$ $C\rightarrow p,r,\; D\rightarrow p,r$
3 $A\rightarrow q,r,s\; B\rightarrow q,r,s,$ $C\rightarrow r,\; D\rightarrow p$
4 $A\rightarrow p,r,s,\; B\rightarrow q$ $C\rightarrow p,\; D\rightarrow q,s$

Possible Answers

Selected	Possible Answer
	2
	4
	1
	3

Question

Q. No. – 43. Match gases under specified conditions listed in Column-I with their properties/laws in Column-II. Indicate your answer by darkening the appropriate bubsbles of the 4 × 4 matrix given in the ORS.

Column-I	Column-II
(A) hydrogen gas $(P = 200\;atm,\; T = 273K)$	(p) compressibility factor $\not = 1$
(B) hydrogen gas $(P \sim 0, T = 273K)$	(q) attractive forces are dominant
(C) $CO_2 (P = 1\;atm, T = 273K)$	(r)
(D) real gas with very large molar volume	(s)

Choose the correct Answer from the given option

1. $A\rightarrow p,s,\; B \rightarrow r, C \rightarrow p, q,\; D\rightarrow p, s$
2. $A\rightarrow q,r,\; B \rightarrow p, C \rightarrow r, s,\; D\rightarrow q, r$
3. $A\rightarrow q,s,\; B \rightarrow r, C \rightarrow q, s,\; D\rightarrow q, r$
4. $A\rightarrow p,s,\; B \rightarrow q, C \rightarrow r, s,\; D\rightarrow q, r$

Possible Answers

Selected	Possible Answer
	4
	1
	2
	3

Question

Q. No. – 44. Match the chemical substances in Column-I with type of polymers/type of bonds in Column-II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column-I	Column-II
(A) cellulose	(p) natural polymer
(B) nylon-6, 6	(q) synthetic polymer
(C) protein	(r) amide linkage
(D) sucrose	(s) glycoside linkage

Choose the correct answer from the given option

1 $A \rightarrow q, s, B \rightarrow r,s; C \rightarrow p, r D \rightarrow s$
2 $A \rightarrow r, s, B \rightarrow q, s; C \rightarrow p, r D \rightarrow s$
3 $A \rightarrow p, s, B \rightarrow q, r; C \rightarrow p, r D \rightarrow s$
4 $A \rightarrow p,r, B \rightarrow q, r; C \rightarrow p, q D \rightarrow s$

Possible Answers

Selected	Possible Answer
	3
	4
	1
	2

Question

Section – I

This section contains 9 multiple choice questions numbered 45 to 53. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Q. No. – 45. A hyperbola, having the transverse axis of length $2 sin\theta$ , is confocal with the ellipse 3x^2 + 4y^2 = 12 . Then its equation is

Possible Answers

Selected	Possible Answer
	$x^2 sin^2\theta - y2 cos^2\theta = 1$
	$x^2 sec2\theta - y2 cosec^2\theta = 1$
	$x^2 cos^2\theta - y^2 sin^2\theta = 1$
	$x^2 cosec^2\theta - y^2 sec^2\theta = 1$

Question

Q. No. – 46. The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points $(c-1, e^{c-1})$ and $(c + 1, e^{c+1})$

Possible Answers

Selected	Possible Answer
	on the right of
	at all points
	on the left of
	at no point

Question

Q. No. – 47. A man walks a distance of 3 units from the origin towards the north-east (N 45^o E) direction. From there, he walks a distance of 4 units towards the north-west (N 45^o W) direction to reach a point P. Then the position of P in the Argand plane is

Possible Answers

Selected	Possible Answer
	$(3+4i)\;e^{i\pi/4}$
	$(4+3i)\;e^{i\pi/4}$
	$(3-4i)\;e^{i\pi/4}$
	$3e^{i\pi/4}+4i$

Question

Q. No. – 48. Let f(x) be differentiable on the interval $(0, \infty)$ such that f(1) = 1 , and

$\underset{t \rightarrow x} {lim}$ $\cfrac{t^2f(x)-x^2f(t)}{t-x}=1$
for each x > 0

. Then

Possible Answers

Selected	Possible Answer
	$- \cfrac{1}{x}+\cfrac{2}{x^2}$
	$- \cfrac{1}{3x}+\cfrac{4x^2}{3}$
	$\cfrac{1}{3x}+\cfrac{2x^2}{3}$
	$\cfrac{1}{x}$

Question

Q. No. – 49. The number of solutions of the pair of equations

$2 sin^2\theta - cos^2\theta = 0$
$2 cos^2\theta - 3 sin\theta = 0$

in the interval $[0, 2\pi]$ is

Possible Answers

Selected	Possible Answer
	two
	one
	zero
	four

Question

Q. No. – 50. Let $\alpha, \beta$ be the roots of the equation x^2 - px + r = 0 and , $\frac{\alpha}{2},\;2\beta$ be the roots of the equation x^2 - qx + r = 0. Then the value of r is

Possible Answers

Selected	Possible Answer
	$\cfrac{2}{9}(p-q)(2q-p)$
	$\cfrac{2}{9}(q-p)(2q-p)$
	$\cfrac{2}{9}(2p-q)(2q-p)$
	$\cfrac{2}{9}(q-2p)(2q-p)$

Question

Q. No. – 51. The number of distinct real values of $\lambda$ , for which the vectors $- \lambda^2 \hat i+\hat j+\hat k,$ $\hat i-\lambda^2\hat j+\hat k$ and $\hat i +\hat j -\lambda^2\hat k$ are coplanar, is

Possible Answers

Selected	Possible Answer
	one
	three
	zero
	two

Question

Q. No. – 52. One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

Possible Answers

Selected	Possible Answer
	1/2
	1/3
	1/5
	2/5

Question

Q. No. – 53.

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Possible Answers

Selected	Possible Answer

	$\frac{2}{\pi}f(\frac{1}{2})$
	$\frac{8}{\pi}f(2)$
	$\frac{2}{\pi}f(2)$

Question

Section – II

This section contains 4 questions numbered 54 to 57. Each question contains STATEMENT − 1 (Assertion) and STATEMENT -2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Each question contains STATEMENT − 1 (Assertion) and STATEMENT -2 (Reason). Each question has 4 choices Choose the correct answer from given option.

Q. No. – 54. Let the vectors $\overrightarrow {PQ}, \overrightarrow {QR}, \overrightarrow {RS}, \overrightarrow {ST}, \overrightarrow {TU}$ and $\overrightarrow {UP}$ represent the sides of a regular hexagon.
STATEMENT -1 : $\overrightarrow {PQ}*(\overrightarrow {RS}+\overrightarrow {ST})\not=\overrightarrow0$

because

STATEMENT -2 : $\overrightarrow {PQ}*\overrightarrow {RS}=0$ and $\overrightarrow {PQ}*\overrightarrow {ST}\not=\overrightarrow 0$

Possible Answers

Selected	Possible Answer
	Statement -1 is True, Statement -2 is False
	Statement -1 is True, Statement -2 is True; Statement-2 is a correct explanation for Statement-1
	Statement -1 is False, Statement -2 is True
	Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1

Question

Q. No. – 55. Let F(x) be an indefinite integral of sin^2x .

STATEMENT -1 : The function F(x) satisfies $F(x + \pi) = F(x)$ for all real .

because

STATEMENT -2 : $sin^2(x + \pi) = sin^2x$ for all real .

Possible Answers

Selected	Possible Answer
	Statement -1 is False, Statement -2 is True
	Statement -1 is True, Statement -2 is True; Statement-2 is a correct explanation for Statement-1
	Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1
	Statement -1 is True, Statement -2 is False

Question

Q. No. – 56. Let H_1, H_2, ..., H_n be mutually exclusive and exhaustive events with P(H_i) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1 .

STATEMENT -1 : P(H_i|E)>P(E|H_i).P(H_i) for i = 1, 2,..., n

because

STATEMENT -2 : $\overset{n}{\underset{i=1}{\sum}} P(H_i)=1$

Possible Answers

Selected	Possible Answer
	Statement -1 is False, Statement -2 is True
	Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1
	Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1
	Statement -1 is True, Statement -2 is False

Question

Q. No. – 57. Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169.

STATEMENT -1 : The tangents are mutually perpendicular.

because

STATEMENT -2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given

circle is x^2 + y^2 = 338

Possible Answers

Selected	Possible Answer
	Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1
	Statement -1 is True, Statement -2 is False
	Statement -1 is False, Statement -2 is True
	Statement -1 is True, Statement -2 is true; Statement-2 is NOT a correct explanation for Statement-1

Question

Section – III

Linked Comprehension Type

This section contains 2 paragraphs 58−60 and 61−63. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choice (A), (B), (C) and (D), out of which ONLY ONE is correct.

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S.

Q. No. – 58. The ratio of the areas of the triangles PQS and PQR is

Possible Answers

Selected	Possible Answer
	$1 : \sqrt 2$

Question

Q. No. – 59. The radius of the circumcircle of the triangle PRS is

Possible Answers

Selected	Possible Answer
	$3\sqrt 3$
	$2\sqrt 3$

	$3\sqrt 2$

Question

Q. No. – 60. The radius of the incircle of the triangle PQR is

Possible Answers

Selected	Possible Answer
	8/3
	2
	3
	4

Question

Paragraph for Question Nos. 61 to 63

Let V_r denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r - 1) . Let

$T_r = V_{r+1} - V_r -2$ and $Q_r = T_{r+1} - T_r$ for r = 1, 2, ...

Q. No. – 61. The sum V_1 + V_2 + ... + V_n

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{12}n(n+1)(3n^2+ n+2)$
	$\cfrac{1}{12}n(n+1)(3n^2- n+1)$
	$\cfrac{1}{2}n(2n^2- n+1)$
	$\cfrac{1}{3}(2n^3-2n+3)$

Question

Q. No. – 62. T_r is always

Possible Answers

Selected	Possible Answer
	a prime number
	an odd number
	a composite number
	an even number

Question

Q. No. – 63. Which one of the following is a correct statement?

Possible Answers

Selected	Possible Answer

	are in A.P. with common difference 5
	are in A.P. with common difference 11
	are in A.P. with common difference 6

Question

Section – IV

Matrix-Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A−p, A−s, B−q, B−r, C−p, C−q and D−s, then the correctly bubbled 4 × 4 matrix should be as follows:

Q. No. – 64. Consider the following linear equations

Match the conditions / expressions in Column I with statements in Column II and indicate your answers by darkening the appropriate bubbles in 4 × 4 matrix given in the ORS.

Column I	Column I
(A) $a + b + c \not = 0$ and	(p) the equations represent planes meeting only at a single point.
(B) and $a^2 + b^2 + c^2 \not = ab + bc + ca$	(q) the equations represent the line x = y = z.
(C) $a + b + c \not = 0$ and $a^2 + b^2 + c^2 \not = ab + bc + ca$	(r) the equations represent identical planes.
(D) and	(s) the equations represent the whole of the three dimensional space.

Possible Answers

Selected	Possible Answer
	A – s, B – q, C – p, D – r
	A – r, B – q, C – p, D – s
	A – q, B – r, C – p, D – s
	A – r, B – p, C – q, D – s

Question

Q. No. – 65. Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
$(A) \overset{1}{\underset{-1}{\int}} \cfrac{dx}{1+x^2}$	$(p)\;\cfrac{1}{2}log\bigg(\cfrac{2}{3}\bigg)$
$(B) \overset{0}{\underset{1}{\int}} \cfrac{dx}{1-x^2}$	$(q)\;2log\bigg(\cfrac{2}{3}\bigg)$
$(C) \overset{3}{\underset{-2}{\int}} \cfrac{dx}{1-x^2}$	$(r)\;\cfrac{\pi}{3}$
$(D) \overset{2}{\underset{1}{\int}} \cfrac{dx}{x\sqrt{x^2-1}}$	$(s)\;\cfrac{\pi}{2}$

Possible Answers

Selected	Possible Answer
	A-s, B-s, C-p, D-r
	A-s, B-s, C-r, D-q
	A-s, B-q, C-p, D-r
	A-p, B-s, C-p, D-r

Question

Q. No. – 66. In the following [x] denotes the greatest integer less than or equal to x.
Match the functions in Column I with the properties Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Possible Answers

Selected	Possible Answer
	A-p,s : B-p,r : C-r,s, : D – p,q
	A-p,q,r : B-p,s : C-p,q, : D – r,s
	A-q,r : B-p,s : C-r,s, : D – r,q
	A-p,q,r : B-p,s : C-r,s, : D – p,q

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