FIITJEE REVIEW TEST - 10

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PHYSICS, CHEMISTRY & MATHEMATICS

Time Allotted: 3 Hours Maximum Marks: 174

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the OMR sheets. 2. This question paper contains Three Parts. 3. PART–I is Physics, PART–II is Chemistry and PART–III is Mathematics. 4. Each part is further divided into two section: Section – A & C 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for

rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any

form, are not allowed.

B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and

write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All One Part. Section–A (01 – 08) contains FOUR (08) questions. Each question has FOUR options. ONLY ONE of these four

options is the correct answer. Each question will be evaluated according to the following marking scheme. Full Marks : +3 If only (all) the correct option(s) is (are) chosen; Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks : –1 In all other cases.

Section–A (09 – 12) contains EIGHT (04) questions. Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s). Each question will be evaluated according to the following marking scheme. Full Marks : +4 If only (all) the correct option(s) is (are) chosen; Partial Marks : +3 If all the four options are correct but ONLY three options are chosen; Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of which

are correct; Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option; Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks : –1 In all other cases.

Section–C (01 – 06) contains SIX (06) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer using the mouse and the on-screen

virtual numeric keypad in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places and each question carries +3 marks for correct answer and –1 mark for wrong answer.

Name of the Candidate :______________________________________________________ Batch :______________________________ Date of Examination :___________________ Enrolment Number :_________________________________________________________

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FIITJEE REVIEW TEST - 10

REVIEW TEST-10JEE(Advanced)/Sol


4

PPhhyyssiiccss PART – I

SECTION – A

Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Two metallic spheres, each of radius R having

charges 2Q and Q are joined through a capacitor of capacitance C as shown in the figure. Assuming R < < d, the charge on the capacitor long time after the key “K” is closed is

Q,R2 Q,R

d

K C

(A) 0

Q4 R

1C

(B)

0

Q4 R

2C

(C) 0

Q4 R

3C

(D)

0

Q4 R

4C

2. A standing wave is produced in a vapour of an element of atomic mass 127 (g mol-1) at 400 K.

Nodes are found to be 6.77 cm apart when frequency of source was 1000 Hz. The vapour used for the experiment is (R = 8.31 JK-1mol-1)

(A) monatomic (B) diatomic (C) polyatomic (D) cannot be determined 3. In a Coolidge tube, the potential difference used to accelerate the electrons is increased from

12.4 kV to 24.8 kV. As a result, the difference between the wavelengths of K -line and minimum

wavelength increases two times. The wavelength of the K line is hc 12.4 kVÅe

(A) 1 Å (B) 0.5 Å (C) 1.5 Å (D) 1.25 Å

Space for rough work



5

4. An electron in a hydrogen atom makes a transition from first excited state to ground state. The equivalent current due to circulating electron

(A) increases 2 times (B) increases 4 times (C) increases 8 times (D) remains the same 5. The frequency of a sonometer wire is f. The frequency becomes f/2 when the mass producing the

tension is completely immersed in water and on immersing the mass in a certain liquid, frequency becomes f/3. The relative density of the liquid is

(A) 1.32 (B) 1.03 (C) 1.41 (D) 1.18 6. A particle moves with speed u along the normal of a plane mirror

towards the mirror. The mirror is moving towards the particle with speed v0 as shown in the figure. The speed of the image of the particle is

(A) v + 2v0 (B) v + v0 (C) v – v0 (D) v – 2v0

u v0

7. A body is fired from point P and strikes at Q inside a smooth

circular wall as shown in the figure. It rebounds to point S (diametrically opposite to P). The coefficient of restitution will be

(A) cot (B) 1 (C) tan (D) tan2

P

Q

S

8. In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing

photons of various energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission spectrum will be (assume that all transitions take place)

(A) 5 (B) 10 (C) 15 (D) 20




6

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 9. A micro-ammeter has a resistance 100 and full scale deflection current 50 A. It can be used as

a voltmeter or as a higher range ammeter provided a resistance is added to it. Choose the correct range and resistance combinations from the following

(A) 50 V range with 10 k resistance in series (B) 10 V range with 200 k resistance in series (C) 5 mA range with 1 resistance in parallel (D) 10 mA range with 1 resistance in parallel 10. Light from a monochromatic source is incident normally on a small photo sensitive surface S

having work function . If power of the source is W and a is the distance between the source and S, then

(A) the number of photons striking the surface per unit time will be 2W S

4 hca

(B) the maximum energy of the emitted electrons will be 1 (hc )

(C) the stopping potential needed to stop the most energetic photons will be e (hc )

(D) photo emission occurs only if 0 (hc / ) 11. In a longitudinal stationary displacement wave (A) there is no transfer of energy in the direction of propagation of wave but the phase of

oscillation travels in the forward direction (B) maximum increase of pressure occurs at nodes (C) maximum decrease of pressure occurs at nodes (D) the pressure at antinode is same as what is would be in absence of the wave 12. For a curved track of radius R, banked at angle (A) a vehicle moving with a speed 0 Rgtan is able to negotiate the curve without calling

friction into play at all (B) a vehicle moving with any speed 0 is able to negotiate the curve with calling friction into

play (C) a vehicle is moving with any speed 0 must also have the force of friction into play (D) the minimum value of the angle of banking for a vehicle parked on the banked road can stay

there without slipping, is given by 1stan (s = coefficient of static friction)




7

SECTION –C Integer Answer Type

This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1. Find the minimum number of capacitors of 2F capacitance each, required to obtain a

capacitance of 5F. 2. Young’s double slit experiment is performed with light consisting of two wavelengths 1 = 6000Å

and 2 = 4800Å. It is observed that the maximum of the 16th order corresponding to 1 = 6000 Å coincides with the maximum of the nth order corresponding to 2 = 4800 Å. The value of n is 10K. Find K.

3. Three rods of equal length are joined to from an equilateral ABC.

The temperature coefficient of linear expansion is 1 for AB, 2 for AC and BC. For 1 = k2, ABC remains constant for small changes in temperature. Find K.

B A

C 4. The resistance of a series combination of two resistances is S. When they are joined in parallel,

the equivalent resistance is P. Find the minimum value of SP

.

5. A force ˆ ˆF yi xj N

acts on a particle which undergoes counterclockwise circular motion in

x-y plane in a circle of radius 4 m and with the centre at the origin. The work done by the force when the particle undergoes one complete revolution is (assume x, y are in m) 4K Joule. Find K.

6. An object is placed at a distance 3 from a thin equi-

convex lens at a point on its optical axis. Its image is formed at 2 m from the lens as shown in the figure.

If lens is cut into two halves along the plane perpendicular to the optical axis and one of the halves is

removed, then the image is formed at a distance 24K

m

from the lens. Find K.

Object image

3m 2m




8

CChheemmiissttrryy PART – II

SECTION – A

Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. A certain transition in H-spectrum from an excited state to ground state in one or more steps gives rise to total 10 lines. How many of them will belong to UV spectrum?

(A) 3 (B) 4 (C) 5 (D) 6 2. Which of the following structure is a representation of following type of sugars (i) hemiacetal form of sugar (ii) pyranose sugar (iii) D-sugar (iv) reducing sugar (v) anomer

(A) O

OH

H

H

OHH

OH

H

OH

H

CH2OH

(B)

O OH

CH2OHH

OH

H OH

H

CH2OH

(C) O

OH

H

H

OHOH

H

OH

H

H

CH2OH

(D)

O

OH

H

H

OHOH

H

OH

H

H

CH2OH

3. In the reaction

N OO

H

2

3

1. Br /KOH,2. H O

P

Which of the following is true about (P) (A) ‘P’ is a diamine (B) ‘P’ is a amino acid (C) ‘P’ is a amino acid (D) ‘P’ is a lacto acid 4. Potassium dichromate in acidic medium reacts with H2S to oxidize it as per given unbalanced

equation. How much g of K2Cr2O7 must be required if 1000 kg of sulphur is to be produced by following reaction?

2 2 7 2 4 2 2 4 2 4 23K Cr O H SO H S K SO Cr SO S H O

(A.W. Cr = 52, K = 39, S = 32, O = 16, H = 1) (A) 6250.5 kg (B) 9375.5 kg (C) 3062.5 g (D) 3062.5 kg

Space for Rough work



9

5. Nitrous oxide (N2O) used in whipped cream containers as the gas that makes the cream foam. Some experiments to use CO2 instead have proven unsuccessful. What does this suggest about the relative sizes of Henry’s law constant for N2O and CO2 in cream and about solubilities of two gases in cream?

(A) 2 2N O is more soluble in cream than CO and has higher value of Henry’s constant (B) 2 2 2Henry’s constant is larger for N O than CO but is less soluble than CO (C) 2CO is more soluble in cream and can make more foam so not suitable for whipped creams

(D) 2N O is less soluble in cream hence can make more foams and thus has lower value for Henry’s constant

6. A 1.0 m solution of chloroacetic acid freezes at -1.93oC. The acid dissociation constant will be: 1

fK of water 1.86 K kg mol

(A) 0.00126 (B) 0.0227 (C) 0.529 (D) 0.00142

7. Which of the following statement is incorrect? (A) All spontaneous process increases entropy of universe (B) Both sysS and surrS are zero at equilibrium

(C) The boiling of water at 100oC and 1 atm pressure is spontaneous (D) The reverse of a spontaneous process under the identical set of condition is non-

spontaneous. 8. A thin circular-disk earrings 5.0 cm in diameter is plated with a coating of gold 0.20 mm thick from

an Au3+ bath. How many days (approx.) does it take to deposit the gold on one side of one earring if the current is 0.02 A (M.W. of Au = 197 g, density of Au = 19.3 g/cm3)?

(A) 13.6 days (B) 6.45 days (C) 9.85 days (D) 10.2 days




10

Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONE OR MORE is/are correct. 9. Which of the following statement(s) is/are true for given reaction sequence?

3O

7 14 ZnP

C H Q R Both Q and R gives ve iodoform test

2NH OH reacting with Q

5PClT S Does not exhibit geometrical isomers Where (P), (Q), (R), (S) and (T) are organic compounds (A) There can be only one possible structure for compound (P) which will fulfill above condition (B) Molecular weight of (T) can be more than 75 g (C) Compound (S) has to be a ketone (D) Compound (T) can exhibit H-bonding when dissolved in water 10. Which of the following compounds can give carbylamine test as well as Hoffmann mustard oil

reaction with mustard oil smell?

(A) NH2

(B) NH

(C) NH2

O

(D) N

CH3

11. Which of the following reactions will not give any acidic gas in product (A) 2 3Li CO (B) 3NaNO (C) 2 4Na SO 4C (D) 3 2Li N 3H O 12. Which of the following is not an aromatic annulene?

(A)

(B)

(C)

(D)




11

SECTION –C Integer Answer Type

This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1. For the reaction:

x 24 3 2

1M MnO MO Mn O2

If 1 mol of 4MnO oxidizes 1.67 mol of Mx+ to 3MO , then the value of x in the reaction is:

2. How many of the following alcohols can exhibit geometrical as well as optical isomerism:

OH

OHA

,

OH

OH

B

,

OH

OHC

,

OH

OH

,

D

OH

OHE

CH3

F

,

OH

OHOHG

,

OH

OH OHH

,

OH

OH

OH

OH

I

3. How many of the following species can exhibit resonance?

(A) (B) (C)O

(D)NH

(E)

(F)

(G) CH2(H)

O

(I)




12

4. How many of the given ligands are exclusively bidentate ligands with identical donor atom.

en, gly, ox, dien, phen, dipy, py, SCN

, trien, EDTA 5. Glyphosate (below) is a common herbicide that is relatively harmless to animals but deadly to

most plants. How many atoms are in sp3 hybridization in the molecule of Glyphosate?

POH

NHOH

O

OH

O

6. How many of the following graphs are correct? (P = pressure, V = volume, T = temperature, a =

initial concentration, t1/2 = half life)

P

1/V

(at constant T & n)

(A)

P

V

(B)

P

V

(at constant T & n)

(C)

(at constant T & n)

P

1/V

(D)

P

ToC

(E)

P

T (K)

(F)

T1

T2

T1 >T2

(at constant V & n)V1

V2

V2 > V1

t1/2a

(G) (H) (I)

t1/2t1/2

(For first order kinetics) (For zero order kinetics) (For second order kinetics)a

a




13

MMaatthheemmaattiiccss PART – III

SECTION – A

Single Correct Choice Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. Line segments AK1, AK2, ….., AKn are drawn from A(1, 1) where K1, K2, K3, ….. Kn are points in

1st quadrant on 22

2 2y 1x 1 1

a b

(a > b) such that chord AKr makes an angle of r2n with the

positive x–axis. The value of n

2rn

r 1

1lim AKn

is

(A) ab2 (B) 2 ab

(C) ab (D) 1ab

2. If a curve is such that line joining origin to any point P(x, y) on the curve and line parallel to y–axis through P are equally inclined to tangent to curve at P, then the differential equation of the

curve is

(A) 2dy dyx 2y x

dx dx

(B) 2dy dy2y x

dx dx

(C) 2dy dyy 2y x

dx dx

(D) 2dy dyy 2y y

dx dx

3. If the letters of the word ‘MATHEMATICS’ are arranged around the circle randomly, then the probability that alike letters are not together is

(A) 3790

(B) 4990

(C) 4790

(D) none of these




14

4. The number of ways of arranging n boys (B1, B2, ..... Bn) and n girls (G1, G2 ..... Gn) around a circle

such that boys and girls should sit alternatively and B1 and G1 are not together is (A) (n – 1)! (n – 2)! (B) (n – 1)! (n – 2)! 2n n 2 (C) (n – 1)! (n – 2)! 2n 2 (D) (n – 1)! (n – 2)! 2n 3n 2

5. The value of n

2nk 1

klimn n 2k

is

(A) 0 (B) 13

(C) 1 (D) 12

6. Two identical blue balls, three identical red balls and four identical green balls are distributed randomly among three students. The probability that each student receives atleast one ball is

(A) 729900

(B) 723900

(C) 725900

(D) 177900

7. The value of

3 2

3 2

r 1 ! r 2r 2r 1n

r 1 r 1 ! r 2r 2r 1

cos x sin x dx

is equal to, where [.] denotes the greatest integer

function (A) (n + 2)! + n! 3 (B) 2((n + 2)! + n! 3) (C) 4((n + 2)! + n! 3) (D) none of these

8. If equation log(x2 + 2ax) = log(4x – 4a – 13) has only one solution, then the exhaustive set of values of ‘a’ is

(A) 13 , 04

(B) 13 13, { 1}4 12

(C) 13 13, { 1}14 10

(D) none of these




15

Multiple Correct Answer(s) Type This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

9. Let position vector of the orthocentre of ABC be r

. Then, which of following statement(s) is/are correct (Given position vector of points A, B, C are ˆai , ˆbj , ˆck and abc 0)

(A)

2 2 2

aˆr i1 1 1

a b c

(B)

2 2 2

1ˆr i1 1 1a

a b c

(C) ˆ ˆ ˆr i r j r k a b cˆ ˆ ˆ b c ar j r k r i

(D)

ˆ ˆ ˆr i r j r k b c aˆ ˆ ˆ a b cr j r k r i

10. A right angle triangle ABC, right angle at A is inscribed in hyperbola xy = c2 (c > 0) such that slope of BC is 2. If distance of point A from centre of xy = c2 is 10 , then which of the following is/are correct for xy = c2

(A) the value of c is 2 (B) the value of c is 4 (C) the equation of normal at point A can be y = 2x 3 2 (D) the equation of normal at point A can be y = 3x + 8 2

11. Let f (x) = x3 + 2x2 x + 1, then which of the following statement(s) is/are correct (A) 1 1sin sin cos cos 6 (where is real root of f(x) = 0 and [.] denotes the

G.I.F.) (B) f (x) = 0 has three distinct real roots (C) y = f (x) is increasing function (D) 1 1sin sin cos cos 5 2 (where is real root of f(x) = 0 and [.] denotes the

G.I.F.)

12. Let l = 2 2n

b

ndxlim1 n x

, where b R. The value of ‘l’ can be

(A) (B) 2

(C) 0 (D) 34




16

SECTION –C

Integer Answer Type This section contains 6 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

1. All 4 digit numbers of the form x1x2x3x4 are formed by using digits 1, 2, 3, 4, 5, 6, 7, 8, 9 such that x1 x2 x3 x4, and written in ascending order. If the number with rank 460 is abcd, then a b c d

4 is equal to __________.

2. If all chords of the parabola y2 = 4x + 4 which subtends a right angle at point 1, 2 2 passes

through a fixed point (, ), then the value of | + + 2 2 + 3| is equal to __________

3. The value of tan 1º tan 2º + tan 2º tan 3º + ..... + tan 88º tan 89º is equal to cot2 1 n, where n is a two digit number ab, then the value of b a is _________

4. The value of

tan A tan B tan C18 18 182 2 2tan A tan B tan C9 9 9

13 13 13tan A tan B tan C18 18 18

is equal to __________, where A, B,

C are angles of a triangle.

5. If p, q, r are complex numbers and all roots of the equation z3 + pz2 + qz + r = 0 lies on a circle with centre (0, 0) and radius 1, then the number of distinct real roots of equation z3 + |p|z2 + |q|z + |r| = 0 is/are ______

6. Let 1

1a 2i

, 2

1a 2i

, 3

1a 2i

, 4

1a 2i

, 5

1a 2i

, 6

1a 2i

, 7

1a 2i

, 8

1a 2i

are vertices of regular

octagon. If the area of octagon is A, then the value of 8 2A is (where aj R for j = 1, 2, 3, 4, 5, 6, 7, 8 and i = 1 ) _______




17

ANSWERS

PPhhyyssiiccss ((PART – I)

1. B 2. B 3. C 4. C 5. D 6. A 7. D 8. C 9. B, C 10. A, B, D 11. B, C, D 12. A, D 1. 4 2. 2 3. 1 4. 4 5. 8 6. 2

CChheemmiissttrryy ((PART – II)

1. B 2. C 3. C 4. D 5. D 6. D 7. C 8. B 9. A, C, D 10. A, C 11. B, C, D 12. B, C, D 1. 2 2. 1 3. 6 4. 4 5. 7 6. 6

MMaatthheemmaattiiccss ((PART – III)

1. C 2. A 3. C 4. D 5. D 6. B 7. B 8. B 9. B, D 10. A, C 11. A 12. A, B, C 1. 8 2. 8 3. 1 4. 0 5. 1 6. 2



18

HINTS & SOLUTIONS

PPhhyyssiiccss ((PART – I)

1. B

0

1 2Q q Q q q4 R R c

0

Qq4 R

2c

Q q2 Q q

v1 v2

q q

v1 v2 2. B

26.77 102

v = 1000 × 2 × 6.77 × 10-2 m/s

also 2RT MVv 1.4

M RT

diatomic 3. C 4. C

eiT

Now 2 3T r and 2 3r n T n 5. D

w

0

f dw 11f d 2

a

f d1 1f 3 d

d 1.18dw

6. A use the concept of relative velocity. 7. D Let 1 and 2 be the speed of the body before and after striking. 1 2sin cos (as there is no friction)

1 2e cos cos2

22

1

sine tan

cos



19

8. C

9. B, C

10V 50 A200k

gives full scale deflection.

5 mA through 1 gives 5 mV drop, which across 100 micro-ammeter gives 50 A. 10. A, B, D

Energy received at photo sensitive surface per unit time 2WS4 a

.

Number of photons = energy per unit time energy of a photon. 11. B, C, D In longitudinal stationary waves, displacement node is pressure antinode, while displacement

antinode is pressure node. 12. A, D If speed > 0, then friction is required to provide necessary centripetal force. But as the frictional force has a limitation, it cannot negotiate at any speed.

SECTION –C

1. 4 2. 2 3. 1 4. 4 Use the expressions, S = R1 + R2 & P-1 = R1

-1 + R2-1

5. 8 The force acts along the tangential direction

6. 2 For plane convex lens

1 1 11f R

; 12f

5 ; 1 1 1 1 1 5

u f 3 12

1 1 12m12

.

CChheemmiissttrryy ((PART – II) 1. 10 lines are obtained as a result of electronic transition from 5th level to lower levels and lines

corresponding to UV spectrum are as follows: 5 → 1, 4 →1, 3 →1, 2→ 1 2. (A) is not -anomer (B) is not a pyranose sugar (D) is not a D-sugar While (C) follows all criteria. 3. 2 2 2‘P’ is H N CH CH COOH (Hoffmann Bromamide reaction)



20

4. 2 2 7 2 4 2 2 4 2 4 23K Cr O 4H SO 3H S K SO Cr SO 7H O 3S

Every 294 g 2 2 7K Cr O gives 96 g of S, so 3062.5 kg of K2Cr2O7 is required to produce 1000 kg of sulphur.

5. Foam comes from gas bubbles trapped in the cream. The best gas for making the cream would be one that is not very soluble in cream. Henry’s constant is lower for a gas that is less soluble.

6. 2 2ClCH COOH ClCH COO H

1 x x x

So i = 1 + x f fT i K m

1.93i 1.0371.86 1

hence x=0.037,

a0.037 0.037K 0.00142

0.963

7. The boiling of water at 100oc and 1 atm P is in equilibrium so uniS 0

8. E I tw96500

w d V 3 319.3 gcm 2.5 2.5 0.02 cm

w = 7.575 g

7.575 96500 3t197 0.02

= 556589.5 sec 6.45 days 9.

CH3

CH3

3OZn O

O

2NH OH

N

OH

5PCl

Beckmann rearrangement

CH3 C

O

NH CH3

MW 73 g 11. 2 3 2 2Li CO Li O CO only acidic gas

3 2 21NaNO NaNO O2

2 4 2Na SO 4C Na S 4CO 3 2 3Li N 3H O 3LiOH NH 12. Annulenes are conjugated monocyclic hydrocarbon (B) is antiaromatic annulene (C) is not an annulene as it is not monocyclic (D) is aromatic but it is not an annulene. Integer Answer Type 1. equ. of 4MnO = equ. of Mx+



21

1 mol × 5 = 1.67 mol × (5 – x) x = 2 2. Compounds (C), (F) are only optically active Those which can exhibit only geometrical isomerism are compound (A), (B),(D), (G), (H) and (I). Compound which can exhibit both kind of isomerism is only (E). 3. Species C, G and I cannot exhibit resonance. 4. en, ox, phen, dipy are bidentate ligands with identical donor atoms? gly – is bidentate but with different donor atoms. dien – tridentate trien – tetradentate py – monodentate

SCN

– ambidentate 5.

CH2P

O CH2NH

OC

O

O

O

H

H H

12

4

5

6 7

3

6. (A), (C), (D), (F), (G) & (H) are correct.

MMaatthheemmaattiiccss ((PART – III) SECTION –A

1. C

22

2 2

y 1x 1 1a b

The coordinates of the point Kr will be (1 + R cos , 1 + R sin ), where R is AKr and

r2n

2 2 2 2

2 2R cos R sin

a b = 1

n

2rn

r 1

1lim AKn

(1, 1) R

Kn Kr K1

(1+ Rcos, 1+ Rsin)

n

2 2nr 1

2 2

1 1limn cos r / 2n sin (r / 2n)

a b

1 2 2

2 2 2 20

a b dxb cos x a sin x

2 2

2. A



22

1 2

1 22

1 2 122

2 122

P(x, y)

O(0, 0) 1

2

22

12

2tan 1tan1 tan

2

dy2 xdxydy1

dx

2dy dy2y x x

dx dx

2dy dyx 2y x

dx dx

3. C

Total arrangement = 10!2! 2! 2!

The number of arrangement if atleast one kind of alike letter are together

= 9! 8!3 3 7!2! 2! 2!

4. D (n – 1)!n! – (n – 2)!(n – 1)! 2n 2

1C = (n – 1)!(n – 2)! {n(n – 1) – (2n – 2)} = (n – 1)!(n – 2)! {n2 – 3n + 2}

5. D

n 2 2 21 2 nS ..........

n n 2 n n 4 n n 2n

2 2 21 2 n..........

n 3n n 3n n 3n

< n 2

1S 1 2 ..... nn n 2

nn

1 1lim S2 2

6. B Total number of ways of distribution without condition is 4C2 5C2 6C2 and number of ways each receives atleast one ball is 4C2 5C2 6C2 [3 3C1 4C1 5C1 3].

7. B

Let Tr =

3 2

3 2

r 1 ! r 2r 2r 1

r 1 ! r 2r 2r 1

cos x sin x dx

= 2 (r 1)! (r3 + 2r2 + 2r 1) = 2 {(r + 2)! (r + 1)! + r! (r 1)!}.

8. B



23

Let f(x) = x2 + 2ax, g(x) = 4x – 4a – 13 both f(x) > 0, g(x) > 0 to define log now two possibilities are there Let a < 0

4a 130 2a4

0 < 4a + 13 < – 8a

13 a4

and –12a > 13 13a12

So 13 13a4 12

and f(x) and g(x) touch each other for f(x) and g(x) touch each other discriminant of x2 + 2ax = 4x – 4a – 13.

i.e. x2 + (2a – 4) x + 4a + 13 = 0 D = 0 (2a – 4)2 – 4 × 1 (4a + 13) = 0 a2 – 4a + 4 – 4a – 13 = 0 a2 – 8a – 9 = 0 (a – 9) (a + 1) = 0 a = 9, a = 1 rejecting a = 9.

9. B, D Let orthocentre ˆ ˆ ˆr i j k

So a = b = c

a

, b

, c

and point (, , ) is on plane

x y z 1a b c

So 2 2 2 1a b c

2 2 2

11 1 1

a b c

So

2 2 2

11 1 1a

a b c

,

2 2 2

11 1 1b

a b c

,

2 2 2

11 1 1c

a b c

10. A, C Let the coordinates of point A are (ct, c/t) So, the slope of normal at A will be t2. And normal will be parallel to BC. So, t will be 2 c = 2.

11. A f ( 2) = 3 and f ( 3) is negative So, equation has one real root in between ( 3, 2).

12. A, B, C

I = 1, b 0

tan bn / 2, b 02

0, b 0



24

SECTION –C

1. 8 Number is 5999

2. 8 Shifting origin at (1, 2 2 )

2

Y 2 2 4 X 1 4 Let chord is Y = mX + c

2 Y mX Y mXY 4 2Y 4 0c c

Coefficient of X2 + coefficient Y2 = 0

4 2 4m1 0c c

c + 4 2 + 4m = 0 Y = mX – 4 2 – 4m (Y + 4 2 ) – m(X – 4) = 0 X = 4, Y = – 4 2 x = 5, y = 2 2 4 2 .

3. 1

r

sinrº sin r 1 ºT 1 1cosrº cos 1 r º

= cos1º 1

cosrºcos(r 1)º

=

sin (r 1)º rcos1º 1sin1º cosrº cos(r 1)º

= cot1º tan r 1 º tanrº 1 1 2 88T T .....T cot1º(tan89º tan1º ) 88 = 2cot (1º ) 89

4. 0

5. 1 |r| = 1 |p| = |q| So, the equation z3 + |p|z2 + |q|z + |r| = 0 (z + 1) (z2 + (|p| 1)z + 1) = 0.

6. 2

r2

r

a 2iX iy

a 4

r2r

aX

a 4

, 2

r

2Ya 4

X2 + Y2 = 1 Y2

2 2 1X Y Y 02

So all points lies on circle x2 + y2 – y 02

1r4



25

Area of regular octagon = 21 28 r sin2 8

= 1 1 1 18

2 16 2 4 2 .

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