Fulltest i\\Main\\Paper\\Question\\Paper Aits 2013 Ft i Jeem

ALL INDIA TEST SERIES

From Long Term Classroom Programs and Medium / Short Classroom Program 4 in Top 10, 10 in Top 20, 43 in Top 100, 75 in Top 200, 159 in Top 500 Ranks & 3542 t o t a l s e l e c t i o n s i n I I T - J E E 2 0 1 2 FIITJEE St d t h b d d th R k i IIT JEE 2012

JEE (Main), 2013

FIITJEE

FULL TEST – I

Time Allotted: 3 Hours ƒ ƒ

Maximum Marks: 432

P l e a s e r e a d t h e i n s t r u c t i o n s c a r e f u l l y. Y o u a r e a l l o t t e d 5 m i n u t e s specifically for this purpose. Y o u a r e n o t a l l o we d t o l e a v e t h e E x a m i n a t i o n H a l l b e f o r e t h e e n d o f the test.

INSTRUCTIONS A. General Instructions 1. 2. 3. 4. 5.

Attempt ALL the questions. Answers have to be marked on the OMR sheets. This question paper contains Three Parts. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. Each part has only one section: Section-A. 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 black pen for each character of your Enrolment No. and write 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 Three Parts. (i)

Section-A (01 to 03 and 10 to 12) contains 6 multiple choice questions which have only one correct answer. Each question carries +8 marks for correct answer and – 2 mark for wrong answer. Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and – 1 mark for wrong answer.

Name of the Candidate Enrolment No.

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Useful Data

PHYSICS Acceleration due to gravity

g = 10 m/s2

Planck constant

h = 6.6 ×10−34 J-s

Charge of electron

e = 1.6 × 10−19 C

Mass of electron

me = 9.1 × 10−31 kg

Permittivity of free space

ε0 = 8.85 × 10−12 C2/N-m2

Density of water

ρwater = 103 kg/m3

Atmospheric pressure

Pa = 105 N/m2

Gas constant

R = 8.314 J K−1 mol−1 CHEMISTRY

Gas Constant

R

Avogadro's Number Na Planck’s constant h 1 Faraday 1 calorie 1 amu 1 eV

= = = = = = = = = =

8.314 J K−1 mol−1 0.0821 Lit atm K−1 mol−1 1.987 ≈ 2 Cal K−1 mol−1 6.023 × 1023 6.625 × 10−34 J⋅s 6.625 × 10–27 erg⋅s 96500 coulomb 4.2 joule 1.66 × 10–27 kg 1.6 × 10–19 J

Atomic No:

H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8, N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.

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3

Physics

AITS-FT-I-PCM-JEE(Main)/13

PART – I SECTION – A Single Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

Which of the following curves correctly represents the variation of capacitive reactance (XC) with frequency n? XC (A) XC (B)

n

(C)

XC

n XC

(D)

n

2.

n

Three rods of the same mass are placed as shown in the figure. What will be the co-ordinates of the center of mass of the system?  a a  (A) (a/2, a/2) (B)  ,   2 2  2a 2a  (C)  ,   3 3  

Y (0, a) O

(a, 0)

X

a a (D)  ,  3 3

Rough work

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3.

4.

If switch S is closed at t = 0 then the time at which power supplied by battery is equal to rate of energy storage in capacitor is (A) t = 0 (B) t = 4RC (C) t = 5RC (D) It never happens (except t → ∞) because resistor always consume energy Two conducting spheres of radii a and b are separated by a large distance. The capacity of this system between points A and B is

(A)

4πε 0 1 1 + a b

(C) 2πε0(a + b) 5.

4

a

A

ε

S

b

B

(D) None of the above A 1

E1 A 2 = E2 A1

B

l1

In the given circuit diagram, the key K is switched on at t = 0. The ratio of the current i through the cell at t = 0 and t = ∞ will be (A) 3 : 1 (B) 1 : 3 (C) 1 : 2 (D) 2 : 1

l2

L

A

C

+ − + 3 + 2 + + + + + + + E1+ +E2 + + + + + + + − − + −

(C) E1A1 > E2A2 (D) none of these 6.

C

(B) 4πε0(a + b)

Suppose Electric field between plate (A) and (B) is E1 and between (B) and (C) is E2 then E A (A) 1 = 1 E2 A 2 (B)

R

3R C

i

B

R

6R

ε

K

Rough work

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7.

The density ρ of a liquid varies with depth h from the free surface as ρ = kh. A small body of density ρ1 is released from the surface of liquid. The body will 2ρ1 from the free surface (A) come to a momentary rest at a depth k ρ (B) execute simple harmonic motion about a point at a depth 1 from the surface k ρ1 (C) execute simple harmonic motion of amplitude k (D) all of the above

8.

Dimensional formula of modulus of rigidity is (A) M2L−1T −2 (C) MLT −1

(B) ML−2 T −2 (D) ML−1T −2

9.

At the center of a non-uniform ring of radius R, made up of two uniform halves of mass 2M and M (G : Newton’s gravitational constant) (A) field and potential both are zero −3GM (B) field is zero but potential is R −GM (C) field is zero but potential is R 2GM 3GM (D) magnitude of field is and potential is − 2 R πR

10.

For a satellite of mass m orbiting the earth very close to earth’s surface (mass of earth = M, radius of earth = R) total energy is (A) zero (B) greater than zero GMm GMm (D) − (C) R 2R

11.

An ideal gas has initial volume V and pressure P. In doubling its volume the minimum work done will be in the following process (of given processes) (A) Isobaric process (B) Isothermal process (C) Adiabatic process (D) None of the above Rough work

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12.

13.

6

A particle moving in the positive x-direction has initial velocity v0. The particle undergoes retardation kv2, where v is its instantaneous velocity. The velocity of the particle as a function of time is given by 2v 0 (A) v = v0/(1 + kv0t) (B) v = 1 + kt v v0 (C) v = 0 (D) v = kt (1 + k 2 v 02 t) G Velocity of a particle at any instant is given by the equation v = 2tiˆ + 3t 2 ˆj m/s and radius of the

(

)

curvature of the path is 2m. Centripetal acceleration of the particle at t = 2 s is (B) 160 m/s2 (A) 80 m/s2 2 (D) 100 m/s2 (C) 40 m/s 14.

A car accelerates on a horizontal road due to the force exerted (A) by the engine of the car (B) by the driver of the car (C) due to the earth’s gravity (D) by the friction of the road

15.

A current carrying wire frame is in the shape of digit eight (8). It is carrying current i0. If the radius of each loop is R0, then the net magnetic dipole moment of the figure is (A) (i0 πR02 ) 2 (B) zero (C) i0 × 2πR02 (D) i0 × 4πR0

y-axis

R0 x-axis i0

Rough work

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16.

AITS-FT-I-PCM-JEE(Main)/13

Suppose that a material emits X–rays of wavelengths: λK α , λKβ , λLα when it is excited by fast moving electrons; the wavelengths corresponding to K α , K β , L α respectively. Then we can write : (A) λKβ = λK α + λLα (C)

1 1 1 = + λ K β λ Kα λ L α

(B) (D)

X–rays of the material

λK β = λK α + λL α 1 λK β

=

1 λ Kα

+

1 λLα

.

17.

An excited hydrogen atom in the state n (principal quantum number of electron : n) is moving with a velocity v (v SB > SC (D) SB = SC > SA (C) SA = SB = SC

F0 θ

I II III

π/3 π/4

π/6

Rough work

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t

11

Chemistry

AITS-FT-I-PCM-JEE(Main)/13

PART – II SECTION – A Single Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

()  → (B ) cold alkaline KMnO4 I

( )  → (C) OsO4 /NaHSO3 II

H HOOC

COOH

( )  → (D ) PhCO3H/H2 O

H

( )  → (E ) MMPP + C2H5 OH/H2 O

III

IV

( )  → (F ) H2 O2 + OsO4 V

( )  → (G) H2 O2 + SeO2 VI

Which of the following reaction will yield racemic mixture? (A) (I), (III), (V) (B) (I), (II), (V) (C) (I), (II), (IV) (D) (III), (IV), (V) 2.

A gas behaving ideally was allowed to expand reversibly and adibatically to twice its volume. Its 5 initial temperature was 25oC and CV = R . Calculate ∆H (Given 22/5 = 1.32) 2 (A) 1499.84 J (B) 2102.4 J (C) 8671.5 J (D) Zero

3.

Which of the following ions are expected to be paramagnetic to the same extent? (II) [MnCl4]-2 (I) [FeF6]-3 -2 (III) [NiCl4] (A) I, II and III (B) I and II (C) I and III (D) II and III Rough work

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4.

O

O

O +

H3 O + C2H5MgBr  → Product

(Excess )

Me

The major product is: O (A)

C2H5

(B)

COOH

COOH

H 5 C2 Me

(C)

C2H5

HO

Me H3C OH

(D) COOH

O

COOH

H5C2

Me

Me

Me

NO2

5.

O3 Li in liquid  → ( A )  → (B ) + ( C ) NH3 Zn/H2 O

The compounds (B) and (C) are respectively: NO2

(A) H

O

H H O

(C)

NH2

(B)

O

H

H

O

O

O NH2

(D) O

O H

O

H

H

O

NO 2

O

H

H

O H

O O

O

H

O

H

H

Rough work

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13 6.

AITS-FT-I-PCM-JEE(Main)/13

Consider a reaction: Me Me K 2 Cr2 O7 ∆  → (B )  → (C) H+

Me

Me

Me

The product (C) is: COOH

(A)

O

(B)

O

COOH

O

Me

(C)

Me

Me

Both (A) and (B)

Me

(D)

Me

Me

None of these

7.

Which among the following compounds will not give effervescence with sodium bicarbonate: (B) C6H5SO3H (A) C6H5CO2H (D) picric acid (C) C6H5OH

8.

When glycolic acid is subjected to reduction with HI, the product formed is: (A) Acetic acid (B) Formic acid (C) Iodoacetic acid (D) None of these

9.

Which one is the correct statement: (A) The boiling points of alkyl halides are more than those of the corresponding alkanes. (B) In water, solubility of C2H5OH > CH3OH > C6H5OH (C) C6H5NH2 is stronger base than NH3 (D) All of the above statements are correct Rough work

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10.

14

Which of the following compounds can undergo nucleophilic substitution easily? O C

O

O

C O

C

(I)

(II)

O

O

C

C CCl 3

NH2

(IV)

(III)

F O C (V)

(A) Only (II) (C) Only (IV)

(B) (I), (II), (III) and (IV) (D) (II), (III) and (V)

11.

When conc. HNO3 acts on our skin, the skin becomes yellow, because (A) HNO3 acts as an oxidizing agent (B) HNO3 acts as a dehydration agent (C) Nitro-cellulose is formed (D) the proteins are converted into xanthoproteins

12.

Which one of the following is a correct statement (A) When a liquid is transferred from a small container to large container at the same temperature; vapour pressure remains constant (B) Viscosity increases with increase in temperature (C) Addition of detergent to water increases its surface tension (D) Surface tension increases with increase in temperature Rough work

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AITS-FT-I-PCM-JEE(Main)/13

Consider the following reaction: dry HI+ P Barium adipate  → ( A )  → (B ) distillation Compound (B) is: (A)

(C)

(B)

OH

OH

(D)

14.

What is the de-Broglie wavelength associated with He atom at room temperature 25oC (B) 6.34 × 10-8 m (A) 6.34 × 10-11 m -11 (D) 7.34 × 10-8 m (C) 7.34 × 10 m

15.

Entropy of system depends upon (A) Volume and pressure only (C) Temperature and volume only

(B) Pressure and temperature only (D) Pressure, volume and temperature

16.

Which forces of attraction are responsible for liquefication of H2? (A) Coloumbic forces (B) Hydrogen bonding (C) Dipole forces (D) All of these

17.

Which of the following salt is basic? (A) HOCl (C) NaHSO4

18.

(B) NaOCl (D) NH4NO3

For the reaction: −

K 4 Fe ( CN)6  → Fe +3 + CO2 + NO3

19.

The n-factor is: (A) 1 (C) 5/3

(B) 11 (D) 61

Dopping of AgCl crystals with CdCl2 results in: (A) Schottky defect (C) Substitutional cation vacancy

(B) Frenkel defect (D) Formation of F-centres

Rough work

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20.

Freshly obtained SnO2 is added to water containing a little HCl. The solution obtained would be……..due to preferential absorption of ……ions. (B) negatively charged, SnO32 − (A) positively charged, H+ +4 (D) positively charged Sn2+ (C) positively charged, Sn

21.

The product formed, when Mg(NH4)PO4 is heated (B) MgO (A) Mg(NH4)2PO4 (C) PbO (D) Mg2P2O7

22.

Carbon cannot be used in the reduction of Al2O3 because (A) the enthalpy of formation of CO2 is more than that of Al2O3 (B) pure carbon is not easily available (C) the enthalpy of formation of Al2O3 is very high (D) both (B) and (C)

23.

A + CH3 COOH → B + CO2 + H2 O ( Soluble )

B + (NH4 )2 C2 O4 → White ppt.

A and B may contain (A) Ni2+ (C) Sr2+

(B) Ba2+ (D) Ca2+

24.

Racemic acid + optically active alcohol then the product will be: (A) Optically inactive mixture (B) Meso compound (C) Diastereomeric mixture (D) Racemic mixture

25.

Bad conductor of electricity is (A) H2F2 (C) HBr

(B) HCl (D) HI Rough work

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26.

Cryolite is: (A) Na3AlF6 and is used in the electrolysis of alumina for decreasing electrical conductivity (B) Na3AlF6 and is used in electrolysis of alumina for lowering the melting point of alumina (C) Na3AlF6 and is used in the electrolytic purification of alumina (D) Na3AlF6 and is used in the electrolysis of alumina

27.

An organic compound consumes 4 moles of periodic acid to form following compounds per mole of the starting compound HCHO, 3HCOOH and CHOCOOH. The organic compound is: (A) Glucose (B) Fructose (C) Gluconic acid (D) Sorbitol

28.

For which of the following species d – d transition does not account for its colour? (B) CrO4−2 (A) Cr2 O7−2 (D) All of the above (C) CrO2Cl2

29.

Which one is the correct statement: (A) Lactose is a disaccharide and is a non reducing sugar (B) methyl-α-D-glucopyranoside has a acetal structure and a reducing sugar (C) α-D-glucopyranose has a hemiacetal structure and is reducing sugar (D) All of the above

30.

Which one of the following is a correct relation on the basis of Bohr’s theory 1 Z (B) radius of orbit ∝ 2 (A) velocity of electron ∝ 2 n n 1 (C) frequency of revolution ∝ 3 (D) All of the above n Rough work

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Mathematics

18

PART – III SECTION – A Single Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.

G G G G G G The points represented by a , b , c , d are coplanar and ( sin A ) a + ( 2 sin 2B ) b G G G ( 3 sin3C ) c − 4d = 0 then, the least value of 21 ( sin2 A + sin2 2B + sin2 3C ) is 8 (A) 1 (B) 2 (C) 4 (D) 3

+

2.

A and B are two non–singular square matrices of each 3 × 3 such that AB = A and BA = B and |A + B| ≠ 0 then (A) |A + B| = 0 (B) |A + B| = 8 (C) |A – B| = 1 (D) |A + B| = 2

3.

For integer n > 1, the digit at units place in the number

20

∑ r! + 2

2n

is

r =0

(A) 0 (C) 6 4

4.

If

∑(x

(B) 4 (D) 9 2 i

+ yi2 ) ≤ 2x1x 3 + 2x 2 x 4 + 2y 2 y3 + 2y1y 4 then points (x1, y1), (x2, y2), (x3, y3), (x4, y4) are

i=1

(A) vertices of a rectangle (C) concyclic 5.

(B) collinear (D) none of these

If (a cos θ1, a sin θ1), (a cos θ2, a sin θ2), (a cos θ3, a sin θ3) represent the vertices of an equilateral triangle inscribed in a circle, the (A) sec θi = 0 (B) sin θi = 0

∑ (C) ∑ tan θ = 0 i

∑ (D) ∑ cot θ = 0 i

Rough work

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19

6.

d2 y  x  then x 3 2 is equal to If y = x log    a + bx  dx

 dy  (A)  x − y  dx   dy  − y (C)   dx 

7.

AITS-FT-I-PCM-JEE(Main)/13

2

(B)

2

a2 x

( a + bx )2

 dy  + y (D)  x  dx 

x2

y2

= 1 in points whose eccentric angles are 30º a2 b2 and 60º subtends right angle at the origin then its equation is x2 y2 x2 y2 + =1 (B) + =1 (A) 8 4 16 4 If the line x + 2y + 4 = 0, cutting the ellipse

(C)

x2 y2 + =1 4 16

+

2

(D) none of these

8.

If the two roots of the equation (c – 1)(x2 + x + 1)2 – (c + 1)(x4 + x2 + 1) = 0 are real and distinct   1  1− x and f(x) = then f ( f ( x ) ) + f  f    is 1+ x   x  (A) –c (B) c (C) 2c (D) –2c

9.

Let W denotes the set of words in the English dictionary. Define the relation R by R = {(x, y) ∈ W × W; the words x and y have as least one letter in common}. Then R is (A) reflexive, symmetric not transitive (B) reflexive, symmetric and transitive (C) reflexive, not symmetric, and transitive (D) Not reflexive, symmetric and transitive 1

10.

If α and β are the roots of the equation tan x = 2x; then the value of

∫ sin αx sin βx dx(α, β > 0) is

−1

(A) 0 (C) 2

(B) 1 (D) 3 Rough work

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11.

Let A = {1, 2, 3, 4, 5}. Then the number of one–one onto functions from A to A in which at least three elements have self image, is equal to (A) 10 (B) 11 (C) 120 (D) 55 – 5!

12.

Let f and g be two functions with f″ and g″ existing everywhere. If f(x)g(x) = 2 ∀ x and f "(x) g"(x) = f '(x), g'(x) ≠ 0 . Then f '(x) g'(x) (A) has at least one real root (B) may have real roots (C) has at most one real root (D) has no real roots

13.

If 2x + 3y = 7 and x – y = 1 are two normals of a parabola y2 = 4ax from a point then third normal may be (A) x – 3y + 1 = 0 (B) x + 3y = 5 (C) x + 3y + 1 = 0 (D) x – 3y – 7 = 0

14.

If [.] denotes the greatest integer function then domain of the real valued function log[ x +1/ 2] x 2 + x − 6 is 1 (A)  , 2 3 (C)  , 2

15.

 1 ∪ (1, ∞ )   2  ∪ (2, ∞ ) 

 3 (B) 0,  ∪ (2, ∞ )  2 3  (D) ( 0, 1] ∪  , ∞  2 

The length of sub tangent, ordinate and subnormal to the parabola y2 = 4ax at a point (different from origin) are in (A) AP (B) GP (C) HP (D) AGP 1 2

2p

3

2

16.

If p, q ∈ R and p + q – pq – p – q + 1 ≤ 0 then 3q −1 −5p is equal to p q p (A) 1 (B) –1 (C) –2 (D) 0

17.

If the standard deviation of x1, x2 ….., xn is 3.5, the standard deviation of –2x1 – 3, –2x2 – 3, ….., –2xn – 3 is (A) –7 (B) –4 (C) 7 (D) 1.75 Rough work

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21

18.

The line (A) ±1 (C) ± 5

19.

AITS-FT-I-PCM-JEE(Main)/13

x − 2 y +1 z −1 = = intersects the curve xy = c 2 , z = 0 if c is equal to 3 2 −1 1 (B) ± 3

(D) ±2

Sum of first n terms of an AP (having positive terms) is given by Sn = (1 + 2Tn )(1 − Tn ) (where Tn is the nth term of the series). Then the value of 2T12 is (A) 2 (B) 4 (C) 1 (D) 6

20.

If p = ∆ABC is equilateral and q = each angle is 60º. Then symbolic form of statement (A) p ∨ q (B) p Λ q (C) p ⇒ q (D) p ⇔ q

21.

The locus of the middle points of chords of hyperbola 3x2 – 2y2 + 4x – 6y = 0 parallel to y = 2x is (A) 3x – 4y = 4 (B) 3y – 4x + 4 = 0 (C) 4x – 4y = 3 (D) 3x – 4y = 2

22.

If A and B represent the complex numbers z1 and z2 such that |z1 – z2| = |z1 + z2| the circumcentre of ∆AOB, O being origin is z + 2z2 (A) 0 (B) 1 3 z1 + z2 z1 − z2 (C) (D) 2 2

23.

24.

 c   b  If ∠A = 90º in ∆ABC, then tan−1  + tan−1  is equal to  a + b   a + c  (A) 0 (B) 1 π π (C) (D) 6 4 The number of real values of a such that a2 – 2a sin x + 1 = 0 for any x, is (A) 1 (B) 2 (C) 3 (D) 4 Rough work

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AITS-FT-I-PCM-JEE(Main)/13

25.

26.

27.

∫

( x 4 − x )1/ 4 x5

22

dx is equal to 5/4

(A)

4  1 1− 3   15  x 

(C)

4  1 1+ 3   15  x 

5/4

+c

(B)

4 1 1− 3   5 x 

+c

(D)

4 1 1+ 3   5 x 

5/4

+c 5/4

+c

If x, y, z are angles of a triangle and tan x = 2 cot y and tan x + tan y + tan z = 6 then value of z is π (B) nπ + tan−1 2 ; n ∈ I (A) nπ + ; n ∈ I 4 (D) nπ; n ∈ I (C) nπ + tan−1 3 ; n ∈ I  x 3  x 3  lim−  −    ( a > 0 ) ; where [.] represent G.I.F. x →a  a a  (A) a2 – 3 (B) a2 – 1 2 (D) a2 + 1 (C) a

28.

Out of 40 consecutive integers two are chosen at random then the probability that their sum is odd, is 14 20 (A) (B) 29 39 1 1 (D) (C) 3 2

29.

The area bounded by the curves y = x2 – 2x + 2 and its inverse is given by 1 2 (A) (B) 3 3 5 4 (D) (C) 3 3

30.

Given a triangle with sides 17, 15 and 19 cm long. If a circle touching two smaller sides has its centre on the largest side, then the radius of the circle is (A) 51 91 (C)

51 91 64

(B)

192 + 172 − 152

(D) 17 91 Rough work

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