35. STATEMENT-1 : Band gap in germanium is small. because STATEMENT-2 : The energy spread of each germanium atomic energy level is infinitesimally small.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Answer [Figure] [Figure] [Figure] [Figure]
(A)
(B)
(C)
(D)

36. Among the following, identify the correct statement.
(A) Chloride ion is oxidised by $\mathrm { O } _ { 2 }$
(B) $\mathrm { Fe } ^ { 2 + }$ is oxidised by iodine
(C) Iodide ion is oxidised by chlorine
(D) $\mathrm { Mn } ^ { 2 + }$ is oxidised by chlorine
Answer
[Figure]
(A)
[Figure]
(A)
[Figure]
(B)
(C)
(D)

37. While $\mathrm { Fe } ^ { 3 + }$ is stable, $\mathrm { Mn } ^ { 3 + }$ is not stable in acid solution because
(A) $\mathrm { O } _ { 2 }$ oxidises $\mathrm { Mn } ^ { 2 + }$ to $\mathrm { Mn } ^ { 3 + }$
(B) $\mathrm { O } _ { 2 }$ oxidises both $\mathrm { Mn } ^ { 2 + }$ to $\mathrm { Mn } ^ { 3 + }$ and $\mathrm { Fe } ^ { 2 + }$ to $\mathrm { Fe } ^ { 3 + }$
(C) $\mathrm { Fe } ^ { 3 + }$ oxidises $\mathrm { H } _ { 2 } \mathrm { O }$ to $\mathrm { O } _ { 2 }$
(D) $\mathrm { Mn } ^ { 3 + }$ oxidises $\mathrm { H } _ { 2 } \mathrm { O }$ to $\mathrm { O } _ { 2 }$

Answer

[Figure]
(A)
(B)
(C)
(D)

38. Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and $\mathrm { H } _ { 2 } \mathrm { SO } _ { 4 }$ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of
(A) $\mathrm { Fe } _ { 4 } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] _ { 3 }$
(B) $\mathrm { Fe } _ { 3 } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] _ { 2 }$
(C) $\mathrm { Fe } _ { 4 } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] _ { 2 }$
(D) $\mathrm { Fe } _ { 3 } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] _ { 3 }$
Answer
(A)
(B)
(C)
(D)

39. Which one of the following reagents is used in the above reaction?
(A) aq. $\mathrm { NaOH } + \mathrm { CH } _ { 3 } \mathrm { Cl }$
(B) aq. $\mathrm { NaOH } + \mathrm { CH } _ { 2 } \mathrm { Cl } _ { 2 }$
(C) aq. $\mathrm { NaOH } + \mathrm { CHCl } _ { 3 }$
(D) aq. $\mathrm { NaOH } + \mathrm { CCl } _ { 4 }$

Answer

[Figure]
(A)
(B)
(C)
(D)

40. The electrophile in this reaction is
(A) $: \mathrm { CHCl }$
(B) ${ } ^ { + } \mathrm { CHCl } _ { 2 }$
(C) $: \mathrm { CCl } _ { 2 }$
(D) $\quad \mathrm { CCl } _ { 3 }$
Answer ◯
(A) ◯
(B)
[Figure]
(C)
◯
(D)

41. The structure of the intermediate $\mathbf { I }$ is
(A) [Figure]
(B) [Figure]
(C) [Figure]
(D) [Figure] ◯
(A)
(B)
(C) ◯
(D)
Answer

42. Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.

Column I

(A) $\mathrm { O } _ { 2 } ^ { - } \rightarrow \mathrm { O } _ { 2 } + \mathrm { O } _ { 2 } ^ { 2 - }$
(B) $\mathrm { CrO } _ { 4 } ^ { 2 - } + \mathrm { H } ^ { + } \rightarrow$
(C) $\mathrm { MnO } _ { 4 } ^ { - } + \mathrm { NO } _ { 2 } ^ { - } + \mathrm { H } ^ { + } \rightarrow$
(D) $\mathrm { NO } _ { 3 } ^ { - } + \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 } + \mathrm { Fe } ^ { 2 + } \rightarrow$

Column II

(p) redox reaction
(q) one of the products has trigonal planar structure
(r) dimeric bridged tetrahedral metal ion
(s) disproportionation

Answer

[Figure]

43. Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.

Column I

(A) $\mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { CHO }$
(B) $\mathrm { CH } _ { 3 } \mathrm { C } \equiv \mathrm { CH }$
(C) $\mathrm { CN } ^ { - }$
(D) $\mathrm { I } ^ { - }$

Column II

(p) gives precipitate with 2,4-dinitrophenylhydrazine
(q) gives precipitate with $\mathrm { AgNO } _ { 3 }$
(r) is a nucleophile
(s) is involved in cyanohydrin formation
Answer [Figure]

44. Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.

Column I

(A) simple cubic and face-centred cubic
(B) cubic and rhombohedral
(C) cubic and tetragonal
(D) hexagonal and monoclinic

Column II

(p) have these cell parameters $a = b = c$ and $\alpha = \beta = \gamma$
(q) are two crystal systems
(r) have only two crystallographic angles of $90 ^ { \circ }$
(s) belong to same crystal system
Answer [Figure]

5. $\quad \mathrm { AgNO } _ { 3 }$ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance ( $\Lambda$ ) versus the volume of $\mathrm { AgNO } _ { 3 }$ is
[Figure]
volume
(P)
[Figure]
volume (Q)
[Figure]
volume
(R) [Figure] volume (S)
(A) (P)
(B) (Q)
(C) $( \mathrm { R } )$
(D) (S)
ANSWER: D

6. Among the following compounds, the most acidic is
(A) $p$-nitrophenol
(B) p-hydroxybenzoic acid
(C) o-hydroxybenzoic acid
(D) $p$-toluic acid
ANSWER: C

7. The major product of the following reaction is [Figure]
(A) [Figure]
(B) [Figure]
(C) [Figure]
(D) [Figure]
ANSWER:A

SECTION - II (Total Marks : 16)

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct.

8. Extraction of metal from the ore cassiterite involves
(A) carbon reduction of an oxide ore
(B) self-reduction of a sulphide ore
(C) removal of copper impurity
(D) removal of iron impurity

ANSWER: AD

1. The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)
   (A) Adsorption is always exothermic.
   (B) Physisorption may transform into chemisorption at high temperature.
   (C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature.
   (D) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

ANSWER: ABD

1. According to kinetic theory of gases
   (A) collisions are always elastic.
   (B) heavier molecules transfer more momentum to the wall of the container.
   (C) only a small number of molecules have very high velocity.
   (D) between collisions, the molecules move in straight lines with constant velocities.

ANSWER: ACD

1. Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)

(A) [Figure]
(B) [Figure]
(C) $\mathrm { H } _ { 2 } \mathrm { C } = \mathrm { C } = \mathrm { O }$
(D) $\mathrm { H } _ { 2 } \mathrm { C } = \mathrm { C } = \mathrm { CH } _ { 2 }$
ANSWER: BC

SECTION - III (Total Marks : 15)

(Paragraph Type)

This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions and based on the other paragraph 2 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Question Nos. 12 to 14

When a metal rod $\mathbf { M }$ is dipped into an aqueous colourless concentrated solution of compound $\mathbf { N }$, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate $\mathbf { O }$. Addition of aqueous $\mathrm { NH } _ { 3 }$ dissolves $\mathbf { O }$ and gives an intense blue solution.

12. The metal rod $\mathbf { M }$ is
(A) Fe
(B) Cu
(C) Ni
(D) Co

ANSWER:B

1. The compound $\mathbf { N }$ is
   (A) $\mathrm { AgNO } _ { 3 }$
   (B) $\mathrm { Zn } \left( \mathrm { NO } _ { 3 } \right) _ { 2 }$
   (C) $\mathrm { Al } \left( \mathrm { NO } _ { 3 } \right) _ { 3 }$
   (D) $\mathrm { Pb } \left( \mathrm { NO } _ { 3 } \right) _ { 2 }$

ANSWER:A

14. The final solution contains
(A) $\left[ \mathrm { Pb } \left( \mathrm { NH } _ { 3 } \right) _ { 4 } \right] ^ { 2 + }$ and $\left[ \mathrm { CoCl } _ { 4 } \right] ^ { 2 - }$
(B) $\left[ \mathrm { Al } \left( \mathrm { NH } _ { 3 } \right) _ { 4 } \right] ^ { 3 + }$ and $\left[ \mathrm { Cu } \left( \mathrm { NH } _ { 3 } \right) _ { 4 } \right] ^ { 2 + }$
(C) $\left[ \mathrm { Ag } \left( \mathrm { NH } _ { 3 } \right) _ { 2 } \right] ^ { + }$and $\left[ \mathrm { Cu } \left( \mathrm { NH } _ { 3 } \right) _ { 4 } \right] ^ { 2 + }$
(D) $\left[ \mathrm { Ag } \left( \mathrm { NH } _ { 3 } \right) _ { 2 } \right] ^ { + }$and $\left[ \mathrm { Ni } \left( \mathrm { NH } _ { 3 } \right) _ { 6 } \right] ^ { 2 + }$

ANSWER: C

Paragraph for Question Nos. 15 and 16

An acyclic hydrocarbon $\mathbf { P }$, having molecular formula $\mathrm { C } _ { 6 } \mathrm { H } _ { 10 }$, gave acetone as the only organic product through the following sequence of reactions, in which $\mathbf { Q }$ is an intermediate organic compound.
(i) conc. $\mathrm { H } _ { 2 } \mathrm { SO } _ { 4 }$ (catalytic amount) $\left( \mathrm { C } _ { 6 } \mathrm { H } _ { 10 } \right)$ [Figure] [Figure] [Figure]
(ii) $\mathrm { NaBH } _ { 4 }$ /ethanol
(iii) dil. acid
(ii) $\mathrm { O } _ { 3 }$
(iii) $\mathrm { Zn } / \mathrm { H } _ { 2 } \mathrm { O }$

15. The structure of compound $\mathbf { P }$ is
(A) $\mathrm { CH } _ { 3 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 2 } - \mathrm { C } \equiv \mathrm { C } - \mathrm { H }$
(B)
(C) [Figure]
(D) [Figure]
ANSWER: D

16. The structure of the compound $\mathbf { Q }$ is
(A) [Figure]
(B) [Figure]
(C) [Figure]
(D) [Figure]
ANSWER:B

SECTION - IV (Total Marks : 28)

(Integer Answer Type)

This section contains $\mathbf { 7 }$ questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9 . The bubble corresponding to the correct answer is to be darkened in the ORS.

17. The difference in the oxidation numbers of the two types of sulphur atoms in $\mathrm { Na } _ { 2 } \mathrm {~S} _ { 4 } \mathrm { O } _ { 6 }$ is
ANSWER : 5

18. Reaction of $\mathrm { Br } _ { 2 }$ with $\mathrm { Na } _ { 2 } \mathrm { CO } _ { 3 }$ in aqueous solution gives sodium bromide and sodium bromate with evolution of $\mathrm { CO } _ { 2 }$ gas. The number of sodium bromide molecules involved in the balanced chemical equation is

ANSWER : 5

1. The maximum number of electrons that can have principal quantum number, $n = 3$, and spin quantum number, $m _ { \mathrm { s } } = - 1 / 2$, is

ANSWER: 9

20. The work function ( $\phi$ ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

Metal	Li	Na	K	Mg	Cu	Ag	Fe	Pt	W
$\phi ( \mathrm { eV } )$	2.4	2.3	2.2	3.7	4.8	4.3	4.7	6.3	4.75

ANSWER: 4

1. To an evacuated vessel with movable piston under external pressure of $1 \mathrm {~atm} . , 0.1 \mathrm {~mol}$ of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm . at $0 ^ { \circ } \mathrm { C }$ ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at $0 ^ { \circ } \mathrm { C }$ is close to

ANSWER:7

1. The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is

ANSWER: 5

1. A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes $47.0 \%$ to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

ANSWER: 6

PART II: PHYSICS

SECTION-I (Total Marks : 21)

(Single Correct Answer Type)

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

24. A police car with a siren of frequency 8 kHz is moving with uniform velocity $36 \mathrm {~km} / \mathrm { hr }$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \mathrm {~m} / \mathrm { s }$. The frequency of the siren heard by the car driver is
(A) 8.50 kHz
(B) 8.25 kHz
(C) 7.75 kHz
(D) 7.50 kHz

ANSWER:A

1. 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be $T _ { 1 }$, the work done in the process is
   (A) $\frac { 9 } { 8 } R T _ { 1 }$
   (B) $\frac { 3 } { 2 } R T _ { 1 }$
   (C) $\frac { 15 } { 8 } R T _ { 1 }$
   (D) $\quad \frac { 9 } { 2 } R T _ { 1 }$

ANSWER:A

1. Consider an electric field $\vec { E } = E _ { 0 } \hat { x }$, where $E _ { 0 }$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is [Figure]
   (A) $2 E _ { 0 } a ^ { 2 }$
   (B) $\sqrt { 2 } E _ { 0 } a ^ { 2 }$
   (C) $E _ { 0 } a ^ { 2 }$
   (D) $\frac { E _ { 0 } a ^ { 2 } } { \sqrt { 2 } }$

ANSWER: C

1. The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561 \AA$. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is
   (A) $1215 \AA$
   (B) $1640 \AA$
   (C) $2430 \AA$
   (D) $4687 \AA$

ANSWER: A

28. A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m . The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N . The maximum possible value of angular velocity of ball (in radian/s) is [Figure]
(A) 9
(B) 18
(C) 27
(D) 36

ANSWER: D

1. A meter bridge is set-up as shown, to determine an unknown resistance ' $X$ ' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B . The determined value of ' $X$ ' is [Figure]
   (A) 10.2 ohm
   (B) 10.6 ohm
   (C) 10.8 ohm
   (D) 11.1 ohm

ANSWER:B

1. A $2 \mu \mathrm {~F}$ capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position 2 is [Figure]
   (A) $0 \%$
   (B) $20 \%$
   (C) $75 \%$
   (D) $80 \%$

ANSWER: D

SECTION - II (Total Marks : 16)

(Multiple Correct Answers Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct.

31. A spherical metal shell $A$ of radius $R _ { A }$ and a solid metal sphere $B$ of radius $R _ { B } \left( < R _ { A } \right)$ are kept far apart and each is given charge ' $+ Q$ '. Now they are connected by a thin metal wire. Then
(A) $\quad E _ { A } ^ { \text {mide } } = 0$
(B) $Q _ { A } > Q _ { B }$
(C) $\frac { \sigma _ { A } } { \sigma _ { B } } = \frac { R _ { B } } { R _ { A } }$
(D) $E _ { A } ^ { \text {on surface } } < E _ { B } ^ { \text {on surface } }$

ANSWER: ABCD

1. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
   (A) They will never come out of the magnetic field region.
   (B) They will come out travelling along parallel paths.
   (C) They will come out at the same time.
   (D) They will come out at different times.

ANSWER : BC, BD, BCD

33. A composite block is made of slabs $\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }$ and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat 'Q' flows only from left to right through the blocks. Then in steady state [Figure]
(A) heat flow through A and E slabs are same.
(B) heat flow through slab $E$ is maximum.
(C) temperature difference across slab E is smallest.
(D) heat flow through $\mathrm { C } =$ heat flow through $\mathrm { B } +$ heat flow through D .

ANSWER: ACD

1. A metal rod of length ' $L$ ' and mass ' $m$ ' is pivoted at one end. A thin disk of mass ' $M$ ' and radius ' R ' ( $< \mathrm { L }$ ) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true? [Figure]
   (A) Restoring torque in case $\mathrm { A } =$ Restoring torque in case B
   (B) Restoring torque in case $\mathrm { A } <$ Restoring torque in case B
   (C) Angular frequency for case $A >$ Angular frequency for case $B$.
   (D) Angular frequency for case $A <$ Angular frequency for case $B$.

SECTION - III (Total Marks : 15)

(Paragraph Type)

This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions and based on the other paragraph $\mathbf { 2 }$ multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Question Nos. 35 to 37

Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is $x ( t )$ vs. $p ( t )$ curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative. [Figure]