fiitjee mock test-8 · mock test-8–paper-1 (100398.1)-cmp-iitjee-4fiitjee ltd., fiitjee house, 29...

FIITJEE MOCK TEST-8 IIIITT –– JJEEEE,, 22001199

PAPER-I

Time: 3 Hours Maximum Marks: 210

A. Question Paper Format: 1. The question paper consists of 3 Parts (Chemistry-Part-I, Mathematics-Part-II and Physics-Part-III). 2. Section A contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,

out of which one or more is/are correct. 4. Section C contains 10 questions. The answer to each of the questions is a single – digit integer, ranging from 0 to

9. The answer will have to be appropriately bubbled in the ORS as per the instructions given at the beginning of the section.

B. Marking Scheme: 5. For each question in Section A, you will be awarded 4 marks if you darken the bubble(s) corresponding to the

correct choice(s) for the answer, and zero mark if no bubble is darkened. In all other cases, Minus one (-1) mark will be awarded.

7. For each question in Section C, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

Enrolment No. : Name : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Batch : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Date:. . . . . . . . . . . . . . . . . . . .

Paper Code

100398.1

Mock Test-8–Paper-1 (100398.1)-CMP-IITJEE-2

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com

CChheemmiissttrryy PART – I

SECTION – A

(One or More than One Options Correct Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.

1. Which of the following order of basicity is/are correct?

(A) N

HO

<

N O

(B) N

>N

H

(C) >C NH

NH2

NH2

C NH

CH3

CH3

(D) >

NCH3CH3

NCH3CH3

CH3 CH3

2. Which of the following will form more than one dibromoproducts on reaction with Br2 in presence of

CCl4?

(A) CH3

(B)

CH3

(C) CH2

(D)

CH3

3. Which of the following statement is/are correct about the carbohydrate (A) given below?

OO

O

OHOHOHOH

OH

OH

CH2OHCH2OH

(A) (A) Compound (A) on hydrolysis produces D-Glucose and D-Galactose. (B) Compound (A) shows mutarotation. (C) Compound (A) is a reducing sugar. (D) Compound (A) has -Glycosidic linkage.

Space for Rough work



4. Which of the following statements is/are correct? (A) CHF3 is more acidic than CHCl3. (B) (SiH3)3N is less basic than (CH3)3N. (C) (SiH3)P is pyramidal. (D) (SiH3)3N is planar. 5. Which of the following reaction(s) take place in Bessemer converter for the extraction of copper? (A) 2 3FeO SiO FeSiO (B) 2 22FeS 3O 2FeO 2SO

(C) 2 2 2 22Cu S 3O 2Cu O 2SO (D) 2 2 22Cu O Cu S 6Cu SO 6. In which of the following compounds the keto form is more stable than their enol form?

(A)

O

(B)

O

(C)

O

(D)

O

7. Which of the following is/are buffer solution?

(A) 0.1 M NH4OH + 0.1 M NH4Cl (B) 0.2 M C6H5NH2 + 0.2 M 6 5 3C H NH Br

(C) 0.5 M H2CO3 + 0.5 M KHCO3 (D) 0.1 M KClO4 + 0.1 M HClO4 8. Which of the following order is/are incorrect? (A) PH3 < NH3 < AsH3 (Boiling point) (B) NF3 > NCl3 > NBr3 (Basicity)

(C) 2 2 2NO NO NO

(Bond angle) (D) 2

3 2CO CO CO (C – O bond length) 9. Which of the following statements are incorrect? (A) A solution of acetone and chloroform shows negative deviation from Raoult’s law. (B) 0.1 M glucose solution and 0.1 M urea solution are isotonic. (C) Henrey’s constant (KH) for a gas decreases with the increase in temperature. (D) Hmix is negative for a solution of n-Hexane and ethanol. 10. Which of the following statements regarding crystal defect is/are correct? (A) Due to Schottky defect lattice energy decreases. (B) Density of crystal decreases due to Frenkel defect. (C) Entropy of crystal increases due to Frenkel defect. (D) Thermal stability of crystal decreases due to Schottky defect.




SECTION – C (One Integer Value Correct Type)

This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. Total number of compounds among the following which reduce Tollen’s reagent is:

CH3 CH2 CHO, CH3 C CH3

O

, C

O

H,

CH3 C CH

O OH

CH3 , CH3 C C H , CH3 C C CH3 2. Total number of moles of formic acid formed by the oxidation of one mole of D-glucose with excess

HIO4 is 3. How many of the following molecules undergoes decarboxylation by heating?

COOH

COOH

,

COOHO

,H2C

COOH

COOH

,

H2C

H2C

COOH

COOH

H2C

CH2

CH2

COOH

COOH

,

COOHO

HOOC

, CH3 C

O

CH2 C

O

OH

4. Total number of amines among the following which react with benzene sulphonyl chloride is

NH2

,

NH CH3

, ,

NH2

N

CH3

CH3 NHCH3

CH3 ,CH

CH3

CH3

NH2

, ,N

CH3

CH3

5. How many of the following precipitate are insoluble in yellow ammonium sulphide? HgS, PbS, CdS, CuS, SnS




6. A mixture containing 1 mole each of LiNO3, NaNO3, KNO3, Ca(NO3)2, Mg(NO3)2, Pb(NO3)2, NH4NO3, AgNO3 is strongly heated. Total number of moles NO2(g) evolved is

7. At 800 K, the rms speed of a gas ‘A’ (MW = 20) is equal to the most probable speed of a gas ‘B’ at

120 K. The molecular weight of the gas ‘B’ is 8. At 400 K and one atm pressure 1 litre of N2O4(g) is heated to 800 K at constant pressure, 25% of

N2O4(g) is dissociated according to the reaction 2 4 2 2N O g N g 2O g Final volume of the gaseous mixture in litre is 9. Total number of compounds among the following which on hydrolysis produce HOCl. NCl3, PCl3, AsCl3, SbCl3, BiCl3, POCl3. 10. 25 ml of a solution containing 2 10x gram of NaOH and y × 10-2 gram of Na2CO3 when titrated

using phenolphthalein indictor required 25 ml N HCl10

. The same volume of the solution when titrated

using methyl orange indicator required 30 ml of N HCl.10

The value of x is




MMaatthheemmaattiiccss PART – II

SECTION – A

(One or More than One Options Correct Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. 1. Let PM be the perpendicular from the point (1, 2, 3) to x–y plane. It OP makes an angle with the

positive direction of the z-axis and OM makes an angle with the positive direction of x-axis, where O is the origin then ( and are acute angles)

(A) 5tan3

(B) 2sin sin14

(C) tan = 2 (D) 1cos cos14

2. If a

and b

are two vectors such that a b 5 2

and ˆ ˆ ˆ ˆ ˆ ˆa 4i j 2k 4i j 2k b

, and

ˆ ˆ ˆa b 3i 2 j k 10

then

(A) sum of values of = 487

(B) product of values of = 847

(C) no possible values of (D) two possible values of 3. The integral value of p which satisfies the inequality 10 10

p 1 pC 2 C is (A) 7 (B) 8 (C) 9 (D) 10

4. f(x) is the function such that

x 0

f xlim 1

x if

3x 0

x 1 acosx bsinxlim 1

f x

. Then the value of a and b is

(A) 5a2

(B) 3b2

(C) 7a2

(D) 5b2

Space for rough work



5. If y = (Ax + B)e3x is a solution of the differential equation 2

2d y dym ny 0

dxdx , m, n I, then

(A) m = –6 (B) n = –6 (C) m = 9 (D) n = 9 6. A die is rolled three times. Let E1 denote the event of getting a number larger than the previous

number each time and E2 denote the event that the numbers (in order) form an increasing A.P., then

(A) p(E2) p(E1) (B) 1 21p E E

36

(C) 1 210p E p E3

(D) none of these

7. If x + y + z = , tan x tan y = 2, tan x + tan y + tan z = 6, then

(A) x m , m I4

(B) y = n + tan–1 2, n I

(C) z = k + tan–1 3, k I (D) all are correct 8. In a triangle ABC, if ex – radii, r1 = 8, r2 = 12 and r3 = 24, then (A) in-radius r = 8 (B) a = 12 (C) side b = 16 (D) side c = 20

9. If 5sin3x A sin2x Bsinxf x

x

for x 0 is continuous at x = 0, then

(A) f(0) = 1 (B) A = 4 (C) A = –4 (D) B = –5

10. If the curve 627 2 2f x x 1 x x 6x 5x 4 dx passes through (0, 0), then

(A) 73f 1

7 (B)

72f 17

(C) 1f 17

(D) 73f 1

14





This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. An arc PQ of a circle subtends a central angle . Let A() be the area between the chord PQ and arc

PQ (in the direction of angle ). Let B() be the area between the tangent lines PR and QR and the

arc PQ, then the value of 0

Alim

B

is _____

2. Let f: [1, ) be a differentiable function such that f(e) = 1.

If x

2

1

4 f t dt 2xf x x x 1 then the value of [f(3)] is (where [.] denotes the greatest integer

function) (Given n 3 1.098 ) _____

3. When 1 1,2 2

, then the number of roots of equation 100x3 – 99x + = 0 in the interval

[–1, 1] is/are _____ 4. Let ‘t’ be a positive real number and let

t 1 2 t 2 2 t 2

A 2 t 2 1 t 2

2 t 2 t 2 1

,

0 t 1 t 2

B t 1 0 2 t 2

t 2 2 t 2 0

If det(adj tA) + det(adj tB) = 106, then value of ‘t’ can be _____




5. Let (p) and (p) be the roots of the equation 26 3 91 p 1 x 1 p 1 x 1 p 1 0 where

p > –1 then p 0lim p p

is equal to _____

6. Let y2(x) g(x) g(x) + y(x) y(x) = g(x) g(x), y(0) = 0, x R where f(x) denotes d f xdx

and g(x) is a

given non-constant differential function on R with g(0) = g(e) = 1. Then the value of y(e) is _____ 7. Let f be a real valued differential function on R such that f(2) = 3. If the y intercept of the tangent at

any point P(x, y) on curve y = f(x) is equal to square of the abscissa of P, then value of |f(4)| is _____ 8. Latus rectum of the parabola which has axis parallel to y-axis and which passes through points (0, 2),

(–1, 0) and (1, 6) is _____ 9. If (10!) is divisible by (2!)k·(5!) the maximum value of k is _____ 10. Total number of two digit numbers formed using the digits of ninth (9th) term of the sequence, 1, 4, 11,

26, 57 and so on is/are _____




PPhhyyssiiccss PART – III

SECTION – A

(One or More than One Options Correct Type) This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. 1. A 1 kg block is kept on an L shaped block of mass 2 kg as shown.

The coefficient of friction between the blocks is = 0.3. There is no friction between the L shaped block and the horizontal surface below it. A force F = 2N is applied on the massless string which connected to 1 kg block. (pulley is massless and frictionless). Then which of the following statements is/are correct.

(A) Acceleration of 1 kg block is 2/3 m/s2. (B) Acceleration of 2 kg block is zero (C) Friction force between blocks is 2/3 N (D) Net force on the 2 kg block is 4/3 N

F = 2N

frictionless

2. A metal cylinder of mass 0.5 kg is heated electrically by a 12 W heater in a room at 15C. The

cylinder temperature rises to 25C in 5 min and finally becomes constant at 45 C. Assuming that rate of heat loss is proportional to the excess temperature over the surroundings, which of the following statements is/are correct.

(A) the rate of loss of heat of the cylinder to surrounding at 20C is 2W. (B) the rate of loss of heat of the cylinder to surroundings at 45C is 12 W.

(C) specific heat capacity of metal is 240n(3 / 2)

Jkg1C1.

(D) specific heat capacity of metal is 240n2

Jkg1C1.




3. A conducting rod PQ of length initially at rest is dragged with a

constant force F along two long smooth parallel rails separated by a distance as shown in the figure. Then choose the correct statement(s).

(A) Terminal velocity of the rod, T 2 22FRvB

.

(B) Terminal velocity of the rod, T 2 2FRv

B

B

R

P

Q

C

F

(C) maximum charge on the capacitor, qmax = FCRB

(D) Maximum charge on the capacitor, qmax = 2FCRB

4. A particle of mass m and positive charge q is projected from origin with an initial velocity 0

ˆv v i

in a region in which there is uniform electric and magnetic fields given by

0ˆE E k

and 0

ˆB B k

. At the time t after projection its position vector is r

and velocity v

. Then,

(A) 20 0 0 0

0

mv qB qB qE1ˆ ˆ ˆr sin t i 1 cos t j t kqB m m 2 m

(B) 20 0 0 0

0

mv qB qB qE1ˆ ˆ ˆr cos t i 1 sin t j t kqB m m 2 m

(C) 0 0 00 0

qB qB qEˆ ˆ ˆv v sin t i v cos t j t km m m

(D) 0 0 00 0

qB qB qEˆ ˆ ˆv v cos t i v sin t j t km m m




5. An electron in He+ ion jumps from third excited state to the second excited state, and then from second excited state to the first excited state. Let the ratio of wavelength, momentum and energy of the photons emitted in these to transitions be a, b and c respectively. Then

(A) 1ca

(B) 20a7

(C) 7b20

(D) 20c7

6. P1 and P2 are identical prisms arranged as shown in figure. A ray of

white light incident on face of P1 undergoes dispersion and falls on one face of P2. The facing surfaces of the prisms are parallel to each other and separation between them is negligible. Then,

(A) Light emerging from P2 will be white

A

P2

A

P1

White Red

Violet

(B) In the light emerging from P2 dispersion will be greater (C) the direction of light emerging from P2 will be parallel to the direction of ray incident on P1 (D) the ray emerging from P2 will be white even it prisms P1 and P2 have identical geometry but

different material 7. A glass prism is immersed in a liquid. The curves showing the refractive index n as a function of

wavelength for glass and liquid are as shown in the figure. When a ray of white light is incident on the prism parallel to the base

Vertex

Base

yellow O

n

Liquid

Glass

(A) yellow ray travels without deviation (B) blue ray is deviated towards the vertex (C) red ray is deviated towards the base (D) there is no dispersion




8. Radiations of monochromatic waves of wavelength 400 nm are incident on the surface of metals Zn, Fe and Ni of work functions 3.4eV, 4.8eV and 5.9eV respectively (take hc=12400 eV-Å). Then

(A) maximum KE associated with photoelectrons from the surface of any metal is 0.3eV. (B) no photoelectrons are emitted from the surface of Ni. (C) if the wavelength of source of radiation is doubled then KE of photoelectrons is also doubled. (D) photoelectrons will emitted from the surface of all the three metals if the wavelength of incident

radiations is less than 200 nm. 9. Samples of two radioactive nuclides A and B are taken. A and B are the disintegration constants of

A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?

(A) Initial rate of decay of A is twice the initial rate of decay of B and A B. (B) Initial rate of decay of A is twice the initial rate of decay of B and A B. (C) Initial rate of decay of B is twice the initial rate of decay of A and A B. (D) Initial rate of decay of B is same as the rate of decay of A at t = 2h and B A. 10. ABC is a right-angled prism kept in air. A ray (1) is incident on the face AB

along the normal. Refractive index of the material of prism is the minimum value that will be required so that ray (1) undergoes total internal reflection at the face AC. Another ray (2) is incident on the face AB such that it emerges from face AC along the normal to AC. A third ray (3) falls on the face BC and emerges from face AC such that its angle of emergence is the same as that of incidence. Assuming light (1), (2) and (3) have the same wavelength, then

30° 1

90°

C 3

A

B 2

1

(A) Refractive index of the material of prism is 2 (B) Angle of incidence in degree of ray (2) is 90 (C) Deviation in degree suffered by ray (2) is 60 (D) Deviation in degree suffered by ray (3) is 150





This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). 1. A long rectangular slab of transparent medium of thickness d is placed on

table with length parallel to x-axis and width parallel to the y-axis. A ray of light travelling along y-axis enters at origin such that angle of incidence

( 90). The refractive index of the medium varies as x/d1 e . The refractive index of the air is 1. If the x-coordinate of the point A, where the ray intersects the upper surface of the slab-air boundary is (kd) n2, then find the value of k.

O medium

d

y A

2. A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt. 50/ Hz ac supply. If

the minimum time lag between maximum alternating voltage and maximum current is n ×10–2 sec,

then find the value of n. 3. A semicircular disc of radius R and mass M is pulled by a

horizontal force F so that it moves with uniform velocity. The

coefficient of friction between disc and ground is = 43

. If the

angle = /n radians, then find the value of n.

F




4. A ring of radius r (made of wire of density ) placed on a smooth

horizontal surface is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in figure. Determine the angular velocity in rad/sec at which the ring breaks. The wire breaks at a tensile stress .

(given 9

N-m/kg and r = 1m)

5. A positively charged particle of charge q and mass m is suspended from a

point by a string of length . In the entire space a uniform horizontal electric field E exists. The particle is drawn aside so that string becomes vertical and then it is projected horizontally with velocity v such that particle starts to move along a circle with same constant speed v. If v

equals nqE3m g

, find the value of n.

v

6. Intensity observed in an interference pattern is 2

0I I sin . At = 30°, intensity

I = 5 0.0020 W/m2. If I0 = 20 W/m2 and percentage error in angle is 2n 3 10

%, then the value

of n is




7. A bead of mass 5 kg is free to slide on a smooth ring of radius r = 20 cm

fixed in a vertical plane. The bead is attached to one end of a spring whose other end is fixed to the topmost point O of the spring. Initially the bead is held at rest at a point A of the ring such that OCA = 60°, C being the centre of the ring. The natural length of the spring is also equal to r. After the bead is released and slides down the ring, the contact force between the bead and the ring becomes zero when it reaches the lowest position B. If the force constant of the spring (in N/m) equals. n × 100, find n.

60° A

O

C

B 8. A disc is projected with velocity v0 down an inclined plane of inclination .

The coefficient of friction between the disc and inclined plane is 1 tan .2

If the time elapsed when the disc stops slipping on the inclined plane is 0nv

,gsin

the value of n is

v0

9. On a smooth horizontal surface, two particles of mass m each,

travelling with a velocity v0 in opposite directions, strike the ends of a rigid massless rod of length , kept perpendicular to their velocity. The particles stick to the rod after the collision. If the

tension in the rod during subsequent motion is 20nmv

, then find

the value of n.

v0

v0

m

m 10. A small sphere of mass m = 1kg is moving with a velocity ˆ ˆ(4i j) m/s. It hits a fixed smooth wall and

rebound with velocity ˆ ˆ(i 3 j) m/s. If the coefficient of restitution between the sphere and the wall is n/16, then find the value of n.


fiitjee mock test-8 · mock test-8–paper-1 (100398.1)-cmp-iitjee-4fiitjee ltd., fiitjee house, 29...

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