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JEE (ADVANCED) 2018 PAPER 1

PART-I PHYSICS

ΣΕΧΤΙΟΝ 1 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΣΙΞ (06) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ φορ χορρεχτ ανσωερ(σ). ΟΝΕ ΟΡ ΜΟΡΕ ΤΗΑΝ ΟΝΕ οφ τηεσε φουρ

οπτιον(σ) ισ (αρε) χορρεχτ οπτιον(σ).

Φορ εαχη θυεστιον, χηοοσε τηε χορρεχτ οπτιον(σ) το ανσωερ τηε θυεστιον.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪想 Ιφ ονλψ (αλλ) τηε χορρεχτ οπτιον(σ) ισ (αρε) χηοσεν.

Παρτιαλ Μαρκσ : 髪惣 Ιφ αλλ τηε φουρ οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τηρεε οπτιονσ αρε χηοσεν.

Παρτιαλ Μαρκσ : 髪匝 Ιφ τηρεε ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τωο οπτιονσ αρε χηοσεν, βοτη οφ

ωηιχη αρε χορρεχτ οπτιονσ.

Παρτιαλ Μαρκσ : 髪層 Ιφ τωο ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ ονε οπτιον ισ χηοσεν ανδ ιτ ισ α

χορρεχτ οπτιον.

Ζερο Μαρκσ : 0 Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐匝 Ιν αλλ οτηερ χασεσ.

Φορ Εξαmπλε: Ιφ φιρστ, τηιρδ ανδ φουρτη αρε τηε ΟΝΛΨ τηρεε χορρεχτ οπτιονσ φορ α θυεστιον ωιτη σεχονδ

οπτιον βεινγ αν ινχορρεχτ οπτιον; σελεχτινγ ονλψ αλλ τηε τηρεε χορρεχτ οπτιονσ ωιλλ ρεσυλτ ιν +4 mαρκσ.

Σελεχτινγ ονλψ τωο οφ τηε τηρεε χορρεχτ οπτιονσ (ε.γ. τηε φιρστ ανδ φουρτη οπτιονσ), ωιτηουτ σελεχτινγ ανψ

ινχορρεχτ οπτιον (σεχονδ οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +2 mαρκσ. Σελεχτινγ ονλψ ονε οφ τηε τηρεε

χορρεχτ οπτιονσ (ειτηερ φιρστ ορ τηιρδ ορ φουρτη οπτιον) ,ωιτηουτ σελεχτινγ ανψ ινχορρεχτ οπτιον (σεχονδ

οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +1 mαρκσ. Σελεχτινγ ανψ ινχορρεχτ οπτιον(σ) (σεχονδ οπτιον ιν τηισ χασε),

ωιτη ορ ωιτηουτ σελεχτιον οφ ανψ χορρεχτ οπτιον(σ) ωιλλ ρεσυλτ ιν −2 mαρκσ.

Q.1 The potential energy of a particle of mass 兼 at a distance 堅 from a fixed point 頚 is given by 撃岫堅岻 噺 倦堅態【に, where 倦 is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius 迎 about the point 頚. If 懸 is the speed of the particle and 詣 is the magnitude of its angular momentum about 頚, which of the following statements is

(are) true?

(A) 懸 噺 謬 賃態陳 迎

(B) 懸 噺 謬 賃陳 迎

(C) 詣 噺 ヂ兼倦 迎態

(D) 詣 噺 謬陳賃態 迎態

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Q.2 Consider a body of mass な┻ど 倦訣 at rest at the origin at time 建 噺 ど. A force 繋王 噺 岫糠建 続┏ 髪 紅 卒┏岻

is applied on the body, where 糠 噺 な┻ど 軽嫌貸怠 and 紅 噺 な┻ど 軽. The torque acting on the body

about the origin at time 建 噺 な┻ど 嫌 is 酵王. Which of the following statements is (are) true?

(A) 】酵王】 噺 怠戴 軽 兼

(B) The torque 酵王 is in the direction of the unit vector + 倦侮

(C) The velocity of the body at 建 噺 な 嫌 is v屎王 噺 怠態 岫続┏ 髪 に卒┏岻 兼 嫌貸怠

(D) The magnitude of displacement of the body at 建 噺 な 嫌 is 怠滞 兼

Q.3 A uniform capillary tube of inner radius 堅 is dipped vertically into a beaker filled with water.

The water rises to a height 月 in the capillary tube above the water surface in the beaker. The

surface tension of water is 購. The angle of contact between water and the wall of the capillary

tube is 肯. Ignore the mass of water in the meniscus. Which of the following statements is

(are) true?

(A) For a given material of the capillary tube, 月 decreases with increase in 堅

(B) For a given material of the capillary tube, 月 is independent of 購

(C) If this experiment is performed in a lift going up with a constant acceleration, then 月

decreases

(D) 月 is proportional to contact angle 肯

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Q.4 In the figure below, the switches 鯨怠 and 鯨態 are closed simultaneously at 建 噺 ど and a current

starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive

force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between

the inductors. The current 荊 in the middle wire reaches its maximum magnitude 荊陳銚掴 at time 建 噺 酵. Which of the following statements is (are) true?

(A) 荊陳銚掴 噺 蝶態眺 (B) 荊陳銚掴 噺 蝶替眺 (C) 酵 噺 挑眺 ln に (D) 酵 噺 態挑眺 ln に

Q.5 Two infinitely long straight wires lie in the 捲検-plane along the lines 捲 噺 罰迎. The wire

located at 捲 噺 髪迎 carries a constant current 荊怠 and the wire located at 捲 噺 伐迎 carries a

constant current 荊態. A circular loop of radius 迎 is suspended with its centre at 岫ど┸ ど┸ ヂぬ迎岻

and in a plane parallel to the 捲検-plane. This loop carries a constant current 荊 in the clockwise

direction as seen from above the loop. The current in the wire is taken to be positive if it is

in the 髪卒┏ direction. Which of the following statements regarding the magnetic field 稽屎王 is (are)

true?

(A) If 荊怠 噺 荊態, then 稽屎王 cannot be equal to zero at the origin 岫ど┸ ど┸ ど岻

(B) If 荊怠 伴 ど and 荊態 隼 ど, then 稽屎王 can be equal to zero at the origin 岫ど┸ ど┸ ど岻

(C) If 荊怠 隼 ど and 荊態 伴 ど, then 稽屎王 can be equal to zero at the origin 岫ど┸ ど┸ ど岻

(D) If 荊怠 噺 荊態, then the 権-component of the magnetic field at the centre of the loop is 岾伐 禎轍 彫態眺 峇

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Q.6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure

(where V is the volume and T is the temperature). Which of the statements below is (are)

true?

(A) Process I is an isochoric process

(B) In process II, gas absorbs heat

(C) In process IV, gas releases heat

(D) Processes I and III are not isobaric

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ΣΕΧΤΙΟΝ 2 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΕΙΓΗΤ (08) θυεστιονσ. Τηε ανσωερ το εαχη θυεστιον ισ α ΝΥΜΕΡΙΧΑΛ ςΑΛΥΕ.

Φορ εαχη θυεστιον, εντερ τηε χορρεχτ νυmεριχαλ ϖαλυε (ιν δεχιmαλ νοτατιον, τρυνχατεδ/ρουνδεδ−οφφ το

τηε σεχονδ δεχιmαλ πλαχε; ε.γ. 6.25, 7.00, −0.33, −.30, 30.27, −127.30) υσινγ τηε mουσε ανδ τηε ον−

σχρεεν ϖιρτυαλ νυmεριχ κεψπαδ ιν τηε πλαχε δεσιγνατεδ το εντερ τηε ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ νυmεριχαλ ϖαλυε ισ εντερεδ ασ ανσωερ.

Ζερο Μαρκσ : ど Ιν αλλ οτηερ χασεσ.

Q.7 Two vectors 畦王 and 稽屎王 are defined as 畦王 噺 欠 続┏ and 稽屎王 噺 欠 岫cos 降建 続┏ 髪 sin 降建 卒┏岻, where 欠 is a

constant and 降 噺 講【は 堅欠穴 嫌貸怠. If 弁畦王 髪 稽屎王弁 噺 ヂぬ弁畦王 伐 稽屎王 弁 at time 建 噺 酵 for the first time,

the value of 酵, in 嫌結潔剣券穴嫌, is __________.

Q.8 Two men are walking along a horizontal straight line in the same direction. The man in front

walks at a speed な┻ど 兼 嫌貸怠 and the man behind walks at a speed に┻ど 兼 嫌貸怠. A third man is

standing at a height なに 兼 above the same horizontal line such that all three men are in a

vertical plane. The two walking men are blowing identical whistles which emit a sound of

frequency なねぬど 茎権. The speed of sound in air is ぬぬど 兼 嫌貸怠. At the instant, when the moving

men are など 兼 apart, the stationary man is equidistant from them. The frequency of beats in 茎権, heard by the stationary man at this instant, is __________.

Q.9 A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes

an angle はどソ with the horizontal. They start to roll without slipping at the same instant of

time along the shortest path. If the time difference between their reaching the ground is 盤に 伐 ヂぬ匪 【ヂなど 嫌, then the height of the top of the inclined plane, in 兼結建堅結嫌, is __________.

Take 訣 噺 など 兼 嫌貸態.

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Q.10 A spring-block system is resting on a frictionless floor as shown in the figure. The spring

constant is に┻ど 軽 兼貸怠 and the mass of the block is に┻ど 倦訣. Ignore the mass of the spring.

Initially the spring is in an unstretched condition. Another block of mass な┻ど 倦訣 moving with

a speed of に┻ど 兼 嫌貸怠collides elastically with the first block. The collision is such that the に┻ど 倦訣 block does not hit the wall. The distance, in 兼結建堅結嫌, between the two blocks when

the spring returns to its unstretched position for the first time after the collision is _________.

Q.11 Three identical capacitors 系怠┸ 系態 and 系戴 have a capacitance of な┻ど 航繋 each and they are

uncharged initially. They are connected in a circuit as shown in the figure and 系怠 is then

filled completely with a dielectric material of relative permittivity 香追. The cell electromotive

force (emf) 撃待 噺 ぱ 撃. First the switch 鯨怠 is closed while the switch 鯨態 is kept open. When

the capacitor 系戴 is fully charged, 鯨怠 is opened and 鯨態 is closed simultaneously. When all the

capacitors reach equilibrium, the charge on 系戴 is found to be の 航系. The value of 香追 噺____________.

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Q.12 In the 捲検-plane, the region 検 伴 ど has a uniform magnetic field 稽怠倦侮 and the region 検 隼 ど has

another uniform magnetic field 稽態倦侮. A positively charged particle is projected from the

origin along the positive 検-axis with speed 懸待 噺 講 兼 嫌貸怠 at 建 噺 ど, as shown in the figure.

Neglect gravity in this problem. Let 建 噺 劇 be the time when the particle crosses the 捲-axis

from below for the first time. If 稽態 噺 ね稽怠, the average speed of the particle, in 兼 嫌貸怠, along

the 捲-axis in the time interval 劇 is __________.

Q.13 Sunlight of intensity な┻ぬ 倦激 兼貸態 is incident normally on a thin convex lens of focal length にど 潔兼. Ignore the energy loss of light due to the lens and assume that the lens aperture size

is much smaller than its focal length. The average intensity of light, in 倦激 兼貸態, at a distance にに 潔兼 from the lens on the other side is __________.

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Q.14 Two conducting cylinders of equal length but different radii are connected in series between

two heat baths kept at temperatures 劇怠 噺 ぬどど 計 and 劇態 噺 などど 計, as shown in the figure.

The radius of the bigger cylinder is twice that of the smaller one and the thermal

conductivities of the materials of the smaller and the larger cylinders are 計怠 and 計態

respectively. If the temperature at the junction of the two cylinders in the steady state is にどど 計, then 計怠【計態 噺__________.

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ΣΕΧΤΙΟΝ 3 (Μαξιmυm Μαρκσ: 12)

Τηισ σεχτιον χονταινσ ΤWΟ (02) παραγραπησ. Βασεδ ον εαχη παραγραπη, τηερε αρε ΤWΟ (02) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ. ΟΝΛΨ ΟΝΕ οφ τηεσε φουρ οπτιονσ χορρεσπονδσ το τηε χορρεχτ ανσωερ.

Φορ εαχη θυεστιον, χηοοσε τηε οπτιον χορρεσπονδινγ το τηε χορρεχτ ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ οπτιον ισ χηοσεν.

Ζερο Μαρκσ : ど Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐な Ιν αλλ οτηερ χασεσ.

ΠΑΡΑΓΡΑΠΗ ╉X╊

In electromagnetic theory, the electric and magnetic phenomena are related to each other.

Therefore, the dimensions of electric and magnetic quantities must also be related to each

other. In the questions below, 岷継峅 and 岷稽峅 stand for dimensions of electric and magnetic

fields respectively, while 岷香待峅 and 岷航待峅 stand for dimensions of the permittivity and

permeability of free space respectively. 岷詣峅 and 岷劇峅 are dimensions of length and time

respectively. All the quantities are given in SI units.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.15 The relation between 岷継峅 and 岷稽峅 is

(A) 岷継峅 噺 岷稽峅 岷詣峅 岷劇峅

(B) 岷継峅 噺 岷稽峅 岷詣峅貸怠 岷劇峅

(C) 岷継峅 噺 岷稽峅 岷詣峅 岷劇峅貸怠

(D) 岷継峅 噺 岷稽峅 岷詣峅貸怠 岷劇峅貸怠

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ΠΑΡΑΓΡΑΠΗ ╉X╊

In electromagnetic theory, the electric and magnetic phenomena are related to each other.

Therefore, the dimensions of electric and magnetic quantities must also be related to each

other. In the questions below, 岷継峅 and 岷稽峅 stand for dimensions of electric and magnetic

fields respectively, while 岷香待峅 and 岷航待峅 stand for dimensions of the permittivity and

permeability of free space respectively. 岷詣峅 and 岷劇峅 are dimensions of length and time

respectively. All the quantities are given in SI units.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.16 The relation between 岷香待峅 and 岷航待峅 is

(A) 岷航待峅 噺 岷香待峅 岷詣峅態 岷劇峅貸態

(B) 岷航待峅 噺 岷香待峅 岷詣峅貸態 岷劇峅態

(C) 岷航待峅 噺 岷香待峅貸怠 岷詣峅態 岷劇峅貸態

(D) 岷航待峅 噺 岷香待峅貸怠 岷詣峅貸態 岷劇峅態

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ΠΑΡΑΓΡΑΠΗ ╉A╊

If the measurement errors in all the independent quantities are known, then it is possible to

determine the error in any dependent quantity. This is done by the use of series expansion

and truncating the expansion at the first power of the error. For example, consider the relation 権 噺 捲【検. If the errors in 捲, 検 and 権 are ッ捲┸ ッ検 and ッ権, respectively, then 権 罰 ッ権 噺 掴罰ッ掴槻罰ッ槻 噺 掴槻 岾な 罰 ッ掴掴 峇 岾な 罰 ッ槻槻 峇貸怠.

The series expansion for 岾な 罰 ッ槻槻 峇貸怠, to first power in ッ検【検, is な 噛 岫ッ検【検岻. The relative

errors in independent variables are always added. So the error in 権 will be ッ権 噺 権 岾ッ掴掴 髪 ッ槻槻 峇.

The above derivation makes the assumption that ッ捲【捲 企1, ッ検【検 企1. Therefore, the higher

powers of these quantities are neglected.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.17 Consider the ratio 堅 噺 岫怠貸銚岻岫怠袋銚岻 to be determined by measuring a dimensionless quantity 欠.

If the error in the measurement of 欠 is ッ欠 岫ッ欠【欠 企 な岻 , then what is the error ッ堅 in

determining 堅?

(A) ッ銚岫怠袋銚岻鉄

(B) 態ッ銚岫怠袋銚岻鉄

(C) 態ッ銚岫怠貸銚鉄岻

(D) 態銚ッ銚岫怠貸銚鉄岻

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ΠΑΡΑΓΡΑΠΗ ╉A╊

If the measurement errors in all the independent quantities are known, then it is possible to

determine the error in any dependent quantity. This is done by the use of series expansion

and truncating the expansion at the first power of the error. For example, consider the relation 権 噺 捲【検. If the errors in 捲, 検 and 権 are ッ捲┸ ッ検 and ッ権, respectively, then 権 罰 ッ権 噺 掴罰ッ掴槻罰ッ槻 噺 掴槻 岾な 罰 ッ掴掴 峇 岾な 罰 ッ槻槻 峇貸怠.

The series expansion for 岾な 罰 ッ槻槻 峇貸怠, to first power in ッ検【検, is な 噛 岫ッ検【検岻. The relative

errors in independent variables are always added. So the error in 権 will be ッ権 噺 権 岾ッ掴掴 髪 ッ槻槻 峇.

The above derivation makes the assumption that ッ捲【捲 企1, ッ検【検 企1. Therefore, the higher

powers of these quantities are neglected.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.18 In an experiment the initial number of radioactive nuclei is 3000. It is found that などどど 罰 ねど

nuclei decayed in the first な┻ど 嫌. For 】捲】 企 な, ln岫な 髪 捲岻 噺 捲 up to first power in 捲. The error ッ膏, in the determination of the decay constant 膏, in 嫌貸怠, is

(A) 0.04 (B) 0.03 (C) 0.02 (D) 0.01

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PART II-CHEMISTRY

ΣΕΧΤΙΟΝ 1 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΣΙΞ (06) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ φορ χορρεχτ ανσωερ(σ). ΟΝΕ ΟΡ ΜΟΡΕ ΤΗΑΝ ΟΝΕ οφ τηεσε φουρ

οπτιον(σ) ισ (αρε) χορρεχτ οπτιον(σ).

Φορ εαχη θυεστιον, χηοοσε τηε χορρεχτ οπτιον(σ) το ανσωερ τηε θυεστιον.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪想 Ιφ ονλψ (αλλ) τηε χορρεχτ οπτιον(σ) ισ (αρε) χηοσεν.

Παρτιαλ Μαρκσ : 髪惣 Ιφ αλλ τηε φουρ οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τηρεε οπτιονσ αρε χηοσεν.

Παρτιαλ Μαρκσ : 髪匝 Ιφ τηρεε ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τωο οπτιονσ αρε χηοσεν, βοτη οφ

ωηιχη αρε χορρεχτ οπτιονσ.

Παρτιαλ Μαρκσ : 髪層 Ιφ τωο ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ ονε οπτιον ισ χηοσεν ανδ ιτ ισ α

χορρεχτ οπτιον.

Ζερο Μαρκσ : 0 Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐匝 Ιν αλλ οτηερ χασεσ.

Φορ Εξαmπλε: Ιφ φιρστ, τηιρδ ανδ φουρτη αρε τηε ΟΝΛΨ τηρεε χορρεχτ οπτιονσ φορ α θυεστιον ωιτη σεχονδ

οπτιον βεινγ αν ινχορρεχτ οπτιον; σελεχτινγ ονλψ αλλ τηε τηρεε χορρεχτ οπτιονσ ωιλλ ρεσυλτ ιν +4 mαρκσ.

Σελεχτινγ ονλψ τωο οφ τηε τηρεε χορρεχτ οπτιονσ (ε.γ. τηε φιρστ ανδ φουρτη οπτιονσ), ωιτηουτ σελεχτινγ ανψ

ινχορρεχτ οπτιον (σεχονδ οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +2 mαρκσ. Σελεχτινγ ονλψ ονε οφ τηε τηρεε

χορρεχτ οπτιονσ (ειτηερ φιρστ ορ τηιρδ ορ φουρτη οπτιον) ,ωιτηουτ σελεχτινγ ανψ ινχορρεχτ οπτιον (σεχονδ

οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +1 mαρκσ. Σελεχτινγ ανψ ινχορρεχτ οπτιον(σ) (σεχονδ οπτιον ιν τηισ χασε),

ωιτη ορ ωιτηουτ σελεχτιον οφ ανψ χορρεχτ οπτιον(σ) ωιλλ ρεσυλτ ιν −2 mαρκσ.

Q.1 The compound(s) which generate(s) N2 gas upon thermal decomposition below 300C

is (are)

(A) NH4NO3

(B) (NH4)2Cr2O7

(C) Ba(N3)2

(D) Mg3N2

Q.2 The correct statement(s) regarding the binary transition metal carbonyl compounds is (are)

(Atomic numbers: Fe = 26, Ni = 28)

(A) Total number of valence shell electrons at metal centre in Fe(CO)5 or Ni(CO)4 is 16

(B) These are predominantly low spin in nature

(C) Metal–carbon bond strengthens when the oxidation state of the metal is lowered

(D) The carbonyl C−O bond weakens when the oxidation state of the metal is increased

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Q.3 Based on the compounds of group 15 elements, the correct statement(s) is (are)

(A) Bi2O5 is more basic than N2O5

(B) NF3 is more covalent than BiF3

(C) PH3 boils at lower temperature than NH3

(D) The N−N single bond is stronger than the P−P single bond

Q.4 In the following reaction sequence, the correct structure(s) of X is (are)

(A)

(B)

(C)

(D)

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Q.5 The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)

(A)

(B)

(C)

(D)

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Q.6 A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure,

volume and temperature, respectively. The thermodynamic parameters q, w, H and U are

heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

(A) 圏凋寵 噺 ッ戟喋寵 and 拳凋喋 噺 鶏態岫撃態 伐 撃怠岻

(B) 拳喋寵 噺 鶏態岫撃態 伐 撃怠岻 and 圏喋寵 噺 ッ茎凋寵

(C) ッ茎寵凋 隼 ッ戟寵凋 and 圏凋寵 噺 ッ戟喋寵

(D) 圏喋寵 噺 ッ茎凋寵 and ッ茎寵凋 伴 ッ戟寵凋

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ΣΕΧΤΙΟΝ 2 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΕΙΓΗΤ (08) θυεστιονσ. Τηε ανσωερ το εαχη θυεστιον ισ α ΝΥΜΕΡΙΧΑΛ ςΑΛΥΕ.

Φορ εαχη θυεστιον, εντερ τηε χορρεχτ νυmεριχαλ ϖαλυε (ιν δεχιmαλ νοτατιον, τρυνχατεδ/ρουνδεδ−οφφ

το τηε σεχονδ δεχιmαλ πλαχε; ε.γ. 6.25, 7.00, −0.33, −.30, 30.27, −127.30) υσινγ τηε mουσε ανδ τηε

ον−σχρεεν ϖιρτυαλ νυmεριχ κεψπαδ ιν τηε πλαχε δεσιγνατεδ το εντερ τηε ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ νυmεριχαλ ϖαλυε ισ εντερεδ ασ ανσωερ.

Ζερο Μαρκσ : ど Ιν αλλ οτηερ χασεσ.

Q.7 Among the species given below, the total number of diamagnetic species is ___.

H atom, NO2 monomer, O2− (superoxide), dimeric sulphur in vapour phase,

Mn3O4, (NH4)2[FeCl4], (NH4)2[NiCl4], K2MnO4, K2CrO4

Q.8 The ammonia prepared by treating ammonium sulphate with calcium hydroxide is

completely used by NiCl2.6H2O to form a stable coordination compound. Assume that both

the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl2.6H2O

are used in the preparation, the combined weight (in grams) of gypsum and the nickel-

ammonia coordination compound thus produced is ____.

(Atomic weights in g mol-1: H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

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Q.9 Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit

cell is constructed from the unit cell of MX following the sequential instructions given

below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of number of anions

number of cations

in Z is ____.

Q.10 For the electrochemical cell,

Mg(s) Mg2+ (aq, 1 M) Cu2+ (aq, 1 M) Cu(s)

the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg2+ is changed

to 姉 M, the cell potential changes to 2.67 V at 300 K. The value of 姉 is ____.

(given, 庁眺 = 11500 K V−1, where 繋 is the Faraday constant and 迎 is the gas constant,

ln(10) = 2.30)

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Q.11 A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal

gas). The partition separating the two compartments is fixed and is a perfect heat insulator

(Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat

but does NOT allow the gas to leak across (Figure 2), the volume (in m3) of the compartment

A after the system attains equilibrium is ____.

Q.12 Liquids A and B form ideal solution over the entire range of composition. At temperature T,

equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same

temperature, a new solution of A and B having mole fractions 捲凋 and 捲喋, respectively, has

vapour pressure of 22.5 Torr. The value of 捲凋【捲喋 in the new solution is ____.

(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)

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Q.13 The solubility of a salt of weak acid (AB) at pH 3 is Y×103 mol L−1. The value of Y is ____.

(Given that the value of solubility product of AB (計鎚椎) = 2×1010 and the value of ionization

constant of HB (計銚岻 = 1×108)

Q.14 The plot given below shows 鶏 伐 劇 curves (where P is the pressure and T is the temperature)

for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely

dissociates in both the solvents.

On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of

these solvents, the elevation of boiling point of solvent X is three times that of solvent Y.

Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is

0.7 in solvent Y, the degree of dimerization in solvent X is ____.

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ΣΕΧΤΙΟΝ 3 (Μαξιmυm Μαρκσ: 12)

Τηισ σεχτιον χονταινσ ΤWΟ (02) παραγραπησ. Βασεδ ον εαχη παραγραπη, τηερε αρε ΤWΟ (02) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ. ΟΝΛΨ ΟΝΕ οφ τηεσε φουρ οπτιονσ χορρεσπονδσ το τηε χορρεχτ ανσωερ.

Φορ εαχη θυεστιον, χηοοσε τηε οπτιον χορρεσπονδινγ το τηε χορρεχτ ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ οπτιον ισ χηοσεν.

Ζερο Μαρκσ : ど Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐な Ιν αλλ οτηερ χασεσ.

ΠΑΡΑΓΡΑΠΗ ╉X╊

Treatment of benzene with CO/HCl in the presence of anhydrous AlCl3/CuCl

followed by reaction with Ac2O/NaOAc gives compound X as the major product.

Compound X upon reaction with Br2/Na2CO3, followed by heating at 473 K with

moist KOH furnishes Y as the major product. Reaction of X with H2/Pd-C, followed

by H3PO4 treatment gives Z as the major product.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.15 The compound Y is

(A)

(B)

(C)

(D)

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ΠΑΡΑΓΡΑΠΗ ╉X╊

Treatment of benzene with CO/HCl in the presence of anhydrous AlCl3/CuCl

followed by reaction with Ac2O/NaOAc gives compound X as the major product.

Compound X upon reaction with Br2/Na2CO3, followed by heating at 473 K with

moist KOH furnishes Y as the major product. Reaction of X with H2/Pd-C, followed

by H3PO4 treatment gives Z as the major product.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.16 The compound Z is

(A) (B)

(C)

(D)

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ΠΑΡΑΓΡΑΠΗ ╉A╊

An organic acid P (C11H12O2) can easily be oxidized to a dibasic acid which reacts with

ethyleneglycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic

ketone as one of the products. P undergoes the following reaction sequences to furnish

R via Q. The compound P also undergoes another set of reactions to produce S.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.17 The compound R is

(A) (B)

(C)

(D)

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ΠΑΡΑΓΡΑΠΗ ╉A╊

An organic acid P (C11H12O2) can easily be oxidized to a dibasic acid which reacts with

ethyleneglycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic

ketone as one of the products. P undergoes the following reaction sequences to furnish

R via Q. The compound P also undergoes another set of reactions to produce S.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.18 The compound S is

(A) (B)

(C)

(D)

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JEE (ADVANCED) 2018 PAPER 1

PART-III MATHEMATICS

ΣΕΧΤΙΟΝ 1 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΣΙΞ (06) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ φορ χορρεχτ ανσωερ(σ). ΟΝΕ ΟΡ ΜΟΡΕ ΤΗΑΝ ΟΝΕ οφ τηεσε φουρ οπτιον(σ)

ισ (αρε) χορρεχτ οπτιον(σ).

Φορ εαχη θυεστιον, χηοοσε τηε χορρεχτ οπτιον(σ) το ανσωερ τηε θυεστιον.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪想 Ιφ ονλψ (αλλ) τηε χορρεχτ οπτιον(σ) ισ (αρε) χηοσεν.

Παρτιαλ Μαρκσ : 髪惣 Ιφ αλλ τηε φουρ οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τηρεε οπτιονσ αρε χηοσεν.

Παρτιαλ Μαρκσ : 髪匝 Ιφ τηρεε ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ τωο οπτιονσ αρε χηοσεν, βοτη οφ

ωηιχη αρε χορρεχτ οπτιονσ.

Παρτιαλ Μαρκσ : 髪層 Ιφ τωο ορ mορε οπτιονσ αρε χορρεχτ βυτ ΟΝΛΨ ονε οπτιον ισ χηοσεν ανδ ιτ ισ α

χορρεχτ οπτιον.

Ζερο Μαρκσ : 0 Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐匝 Ιν αλλ οτηερ χασεσ.

Φορ Εξαmπλε: Ιφ φιρστ, τηιρδ ανδ φουρτη αρε τηε ΟΝΛΨ τηρεε χορρεχτ οπτιονσ φορ α θυεστιον ωιτη σεχονδ

οπτιον βεινγ αν ινχορρεχτ οπτιον; σελεχτινγ ονλψ αλλ τηε τηρεε χορρεχτ οπτιονσ ωιλλ ρεσυλτ ιν +4 mαρκσ.

Σελεχτινγ ονλψ τωο οφ τηε τηρεε χορρεχτ οπτιονσ (ε.γ. τηε φιρστ ανδ φουρτη οπτιονσ), ωιτηουτ σελεχτινγ ανψ

ινχορρεχτ οπτιον (σεχονδ οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +2 mαρκσ. Σελεχτινγ ονλψ ονε οφ τηε τηρεε

χορρεχτ οπτιονσ (ειτηερ φιρστ ορ τηιρδ ορ φουρτη οπτιον) ,ωιτηουτ σελεχτινγ ανψ ινχορρεχτ οπτιον (σεχονδ

οπτιον ιν τηισ χασε), ωιλλ ρεσυλτ ιν +1 mαρκσ. Σελεχτινγ ανψ ινχορρεχτ οπτιον(σ) (σεχονδ οπτιον ιν τηισ χασε),

ωιτη ορ ωιτηουτ σελεχτιον οφ ανψ χορρεχτ οπτιον(σ) ωιλλ ρεσυλτ ιν −2 mαρκσ.

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Q.1 For a non-zero complex number 権, let arg岫権岻 denote the principal argument with

伐 講 隼 arg岫権岻 判 講┻ Then, which of the following statement(s) is (are) FALSE?

(A) arg岫伐な 伐 件岻 噺 訂替 , where 件 噺 ヂ伐な

(B) The function 血┺ 温 蝦 岫伐講┸ 講峅, defined by 血岫建岻 噺 arg岫伐な 髪 件建岻 for all 建 樺 温, is

continuous at all points of 温, where 件 噺 ヂ伐な

(C) For any two non-zero complex numbers 権怠 and 権態, arg 岾佃迭佃鉄峇 伐 arg岫 権怠岻 髪 arg岫 権態岻

is an integer multiple of に講

(D) For any three given distinct complex numbers 権怠, 権態 and 権戴, the locus of the

point 権 satisfying the condition arg 岾岫佃貸佃迭岻 岫佃鉄貸佃典岻岫佃貸佃典岻 岫佃鉄貸佃迭岻峇 噺 講,

lies on a straight line

Q.2 In a triangle 鶏芸迎, let 乾鶏芸迎 噺 ぬどソ and the sides 鶏芸 and 芸迎 have lengths などヂぬ and など,

respectively. Then, which of the following statement(s) is (are) TRUE?

(A) 乾芸鶏迎 噺 ねのソ (B) The area of the triangle 鶏芸迎 is にのヂぬ and 乾芸迎鶏 噺 なにどソ (C) The radius of the incircle of the triangle 鶏芸迎 is 10ヂぬ 伐 なの

(D) The area of the circumcircle of the triangle 鶏芸迎 is などど 講

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Q.3 Let 鶏怠: に捲 髪 検 伐 権 噺 ぬ and 鶏態: 捲 髪 に検 髪 権 噺 に be two planes. Then, which of the

following statement(s) is (are) TRUE?

(A) The line of intersection of 鶏怠 and 鶏態 has direction ratios な┸ に┸ 伐な

(B) The line ぬ捲 伐 ねひ 噺 な 伐 ぬ検ひ 噺 権ぬ

is perpendicular to the line of intersection of 鶏怠 and 鶏態

(C) The acute angle between 鶏怠 and 鶏態 is はどソ

(D) If 鶏戴 is the plane passing through the point 岫ね┸ に┸ 伐に岻 and perpendicular to the line

of intersection of 鶏怠 and 鶏態, then the distance of the point 岫に┸ な┸ な岻 from the plane

鶏戴 is 態ヂ戴

Q.4 For every twice differentiable function 血┺ 温 蝦 岷伐に┸ に峅 with 岫血岫ど岻岻態 髪 盤血嫗岫ど岻匪態 噺 ぱの,

which of the following statement(s) is (are) TRUE?

(A) There exist 堅┸ 嫌 樺 温┸ where 堅 隼 嫌┸ such that 血 is one-one on the open interval 岫堅┸ 嫌岻

(B) There exists 捲待 樺 岫伐ね┸ ど岻 such that 】血嫗岫捲待岻】 判 な

(C) lim掴蝦著血岫捲岻 噺 な

(D) There exists 糠 樺 岫伐ね┸ ね岻 such that 血岫糠岻 髪 血嫗嫗岫糠岻 = 0 and 血嫗岫糠岻 塙 ど

Q.5 Λετ 血┺ 温 蝦 温 ανδ 訣┺ 温 蝦 温 βε τωο νον−χονσταντ διφφερεντιαβλε φυνχτιονσ. Ιφ 血嫗岫捲岻 噺 盤結岫捗岫掴岻貸直岫掴岻岻匪訣旺岫捲岻 φορ αλλ 捲 樺 温,

ανδ 血岫な岻 噺 訣岫に岻 噺 な, τηεν ωηιχη οφ τηε φολλοωινγ στατεmεντ(σ) ισ (αρε) ΤΡΥΕ?

(A) 血岫に岻 隼 な 伐 log奪 に (B) 血岫に岻 伴 な 伐 log奪 に (C) 訣岫な岻 伴 な 伐 log奪 に (D) 訣岫な岻 隼 な 伐 log奪 に

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Q.6 Λετ 血┺ 岷ど┸ タ岻 蝦 温 βε α χοντινυουσ φυνχτιον συχη τηατ 血岫捲岻 噺 な 伐 に捲 髪 豹 結掴貸痛血岫建岻穴建掴

φορ αλλ 捲 樺 岷ど┸ タ岻. Τηεν, ωηιχη οφ τηε φολλοωινγ στατεmεντ(σ) ισ (αρε) ΤΡΥΕ?

(Α) Τηε χυρϖε 検 噺 血岫捲岻 πασσεσ τηρουγη τηε ποιντ 岫な┸ に岻

(Β) Τηε χυρϖε 検 噺 血岫捲岻 πασσεσ τηρουγη τηε ποιντ 岫に┸ 伐な岻

(Χ) Τηε αρεα οφ τηε ρεγιον 版岫捲┸ 検岻 樺 岷ど┸ な峅 抜 温 柑 血岫捲岻 判 検 判 ヂな 伐 捲に 繁 ισ 訂貸態替

(D) Τηε αρεα οφ τηε ρεγιον 版岫捲┸ 検岻 樺 岷ど┸な峅 抜 温 柑 血岫捲岻 判 検 判 ヂな 伐 捲に 繁 ισ 訂貸怠替

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ΣΕΧΤΙΟΝ 2 (Μαξιmυm Μαρκσ: 24)

Τηισ σεχτιον χονταινσ ΕΙΓΗΤ (08) θυεστιονσ. Τηε ανσωερ το εαχη θυεστιον ισ α ΝΥΜΕΡΙΧΑΛ ςΑΛΥΕ.

Φορ εαχη θυεστιον, εντερ τηε χορρεχτ νυmεριχαλ ϖαλυε (ιν δεχιmαλ νοτατιον, τρυνχατεδ/ρουνδεδ−οφφ

το τηε σεχονδ δεχιmαλ πλαχε; ε.γ. 6.25, 7.00, −0.33, −.30, 30.27, −127.30) υσινγ τηε mουσε ανδ τηε

ον−σχρεεν ϖιρτυαλ νυmεριχ κεψπαδ ιν τηε πλαχε δεσιγνατεδ το εντερ τηε ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ νυmεριχαλ ϖαλυε ισ εντερεδ ασ ανσωερ.

Ζερο Μαρκσ : ど Ιν αλλ οτηερ χασεσ.

Q.7 The value of 岫岫log態 ひ岻態岻 迭嶋搭塔鉄 岫嶋搭塔鉄 纏岻 抜 盤ヂば匪 迭嶋搭塔填 店

is ______ .

Q.8 The number of 5 digit numbers which are divisible by 4, with digits from the set 岶な┸ に┸ ぬ┸ ね┸ の岼 and the repetition of digits is allowed, is _____ .

Q.9 Let 隙 be the set consisting of the first 2018 terms of the arithmetic progression

な┸ は┸ なな┸ ┼ , and 桁 be the set consisting of the first 2018 terms of the arithmetic

progression ひ┸ なは┸ にぬ┸ ┼ . Then, the number of elements in the set 隙 姦 桁 is _____.

Q.10 The number of real solutions of the equation sin貸怠 蕃布 捲沈袋怠著

沈退怠 伐 捲 布 岾捲に峇沈著沈退怠 否 噺 講に 伐 cos貸怠 蕃布 岾伐 捲に峇沈 伐著

沈退怠 布岫伐捲岻沈著沈退怠 否

lying in the interval 岾伐 怠態 ┸ 怠態峇 is _____ .

(Here, the inverse trigonometric functions sin貸怠捲 and cos貸怠捲 assume values in 峙伐 訂態 ┸ 訂態峩 and 岷ど┸ 講峅, respectively.)

Q.11 For each positive integer 券, let 検津 噺 怠津 盤岫券 髪 な岻岫券 髪 に岻 橋 岫券 髪 券岻匪迭韮 .

For 捲 樺 温, let 岷捲峅 be the greatest integer less than or equal to 捲┻ If lim津蝦著検津 噺 詣, then the

value of 岷詣峅 is _____ .

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Q.12 Let 欠王 and 決屎王 be two unit vectors such that 欠王 糾 決屎王 噺 ど. For some 捲┸ 検 樺 温, let 潔王 噺 捲 欠王 髪 検 決屎王 髪 盤欠王 抜 決屎王匪. If 】潔王】 噺 に and the vector 潔王 is inclined at the same angle 糠 to

both 欠王 and 決屎王, then the value of ぱ cos態 糠 is _____ .

Q.13 Let 欠┸ 決┸ 潔 be three non-zero real numbers such that the equation

ヂぬ 欠 cos 捲 髪 に 決 sin 捲 噺 潔, 捲 樺 峙伐 訂態 ┸ 訂態峩,

has two distinct real roots 糠 and 紅 with 糠 髪 紅 噺 訂戴. Then, the value of 長銚 is _____ .

Q.14 A farmer 繋怠 has a land in the shape of a triangle with vertices at 鶏岫ど┸ ど岻┸ 芸岫な┸ な岻 and 迎岫に┸ ど岻. From this land, a neighbouring farmer 繋態 takes away the region which lies

between the side 鶏芸 and a curve of the form 検 噺 捲津 岫券 伴 な岻. If the area of the region

taken away by the farmer 繋態 is exactly ぬどガ of the area of ッ鶏芸迎, then the value of 券 is

_____ .

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ΣΕΧΤΙΟΝ 3 (Μαξιmυm Μαρκσ: 12)

Τηισ σεχτιον χονταινσ ΤWΟ (02) παραγραπησ. Βασεδ ον εαχη παραγραπη, τηερε αρε ΤWΟ (02) θυεστιονσ.

Εαχη θυεστιον ηασ ΦΟΥΡ οπτιονσ. ΟΝΛΨ ΟΝΕ οφ τηεσε φουρ οπτιονσ χορρεσπονδσ το τηε χορρεχτ ανσωερ.

Φορ εαχη θυεστιον, χηοοσε τηε οπτιον χορρεσπονδινγ το τηε χορρεχτ ανσωερ.

Ανσωερ το εαχη θυεστιον ωιλλ βε εϖαλυατεδ αχχορδινγ το τηε φολλοωινγ mαρκινγ σχηεmε:

Φυλλ Μαρκσ : 髪ぬ Ιφ ΟΝΛΨ τηε χορρεχτ οπτιον ισ χηοσεν.

Ζερο Μαρκσ : ど Ιφ νονε οφ τηε οπτιονσ ισ χηοσεν (ι.ε. τηε θυεστιον ισ υνανσωερεδ).

Νεγατιϖε Μαρκσ : 伐な Ιν αλλ οτηερ χασεσ.

PARAGRAPH ╉X╊

Let 鯨 be the circle in the 捲検-plane defined by the equation 捲態 髪 検態 噺 ね.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.15 Let 継怠継態 and 繋怠繋態 be the chords of 鯨 passing through the point 鶏待 岫な┸ な岻 and parallel to the

x-axis and the y-axis, respectively. Let 罫怠罫態 be the chord of S passing through 鶏待 and

having slope 伐な. Let the tangents to 鯨 at 継怠 and 継態 meet at 継戴, the tangents to 鯨 at 繋怠 and 繋態 meet at 繋戴, and the tangents to 鯨 at 罫怠 and 罫態 meet at 罫戴. Then, the points 継戴┸ 繋戴┸ and 罫戴 lie on the curve

(A) 捲 髪 検 噺 ね (B) 岫捲 伐 ね岻態 髪 岫検 伐 ね岻態 噺 なは

(C) 岫捲 伐 ね岻岫検 伐 ね岻 噺 ね (D) 捲検 噺 ね

ΠΑΡΑΓΡΑΠΗ ╉X╊

Let 鯨 be the circle in the 捲検-plane defined by the equation 捲態 髪 検態 噺 ね.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉X╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.16 Let 鶏 be a point on the circle 鯨 with both coordinates being positive. Let the tangent to 鯨 at 鶏 intersect the coordinate axes at the points 警 and 軽. Then, the mid-point of the line

segment 警軽 must lie on the curve

(A) 岫捲 髪 検岻態 噺 ぬ捲検 (B) 捲態【戴 髪 検態【戴 噺 に替【戴

(C) 捲態 髪 検態 噺 に捲検 (D) 捲態 髪 検態 噺 捲態 検態

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Q.17 The probability that, on the examination day, the student 鯨怠 gets the previously allotted seat 迎怠, and NONE of the remaining students gets the seat previously allotted to him/her is

(A) 戴替待 (B)

怠腿 (C) 胎替待 (D)

怠泰

ΠΑΡΑΓΡΑΠΗ ╉A╊

There are five students 鯨怠┸ 鯨態┸ 鯨戴┸ 鯨替 and 鯨泰 in a music class and for them there are

five seats 迎怠┸ 迎態┸ 迎戴┸ 迎替 and 迎泰 arranged in a row, where initially the seat 迎沈 is

allotted to the student 鯨沈, 件 噺 な┸ に┸ ぬ┸ ね┸ の. But, on the examination day, the five

students are randomly allotted the five seats.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)

Q.18 For 件 噺 な┸ に┸ ぬ┸ ね, let 劇沈 denote the event that the students 鯨沈 and 鯨沈袋怠 do NOT sit adjacent

to each other on the day of the examination. Then, the probability of the event 劇怠 堪 劇態 堪 劇戴 堪 劇替 is

(A) 怠怠泰 (B)

怠怠待 (C) 胎滞待 (D)

怠泰

END OF THE QUESTION PAPER

PARAGRAPH ╉A╊

There are five students 鯨怠┸ 鯨態┸ 鯨戴┸ 鯨替 and 鯨泰 in a music class and for them there are

five seats 迎怠┸ 迎態┸ 迎戴┸ 迎替 and 迎泰 arranged in a row, where initially the seat 迎沈 is

allotted to the student 鯨沈, 件 噺 な┸ に┸ ぬ┸ ね┸ の. But, on the examination day, the five

students are randomly allotted the five seats.

(Τηερε αρε τωο θυεστιονσ βασεδ ον ΠΑΡΑΓΡΑΠΗ ╉A╊, τηε θυεστιον γιϖεν βελοω ισ ονε οφ τηεm)