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Ltd., House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 16, Ph: 26515949, 26854102, Fax: 26513942.

MOCK TEST-7IIIITT –– JJEEEE,, 22001199

PAPER-II

Time: 3 Hours Maximum Marks: 228

A. Question Paper Format

1. The question paper consists of 3 parts (Physics-Part-I, Chemistry-Part-II, and Mathematics-Part-III) and each part consists of four sections.

2. Section – A(i) contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is

correct.

3. Section – A(ii) contains 3 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 – A(iii) contains 2 groups of questions. Total 5 questions based on two paragraphs. Each question has 4 choices (A), (B), (C) and (D)

for its answer, out of which only one is correct.

5. Section B contains 2 questions. Each question has four statements (A, B, C and D) given in column I and five statements (p, q, r, s and t) in

Column II. Any given statement in column I can have correct matching with one or more statements(s) given in column II. For example, if for

a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the

bubbles corresponding to q and r in the ORS.

6. Section - C contains 5 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:

7. For each question in Section – A(i), you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero

mark if no bubbles are darkened. In all other cases, minus one ( 1) mark will be awarded.

8. For each question in Section – A(ii), you will be awarded 4 marks if you darken only the bubble corresponding to the correct answer and zero

mark if no bubbles are darkened. No negative marks will be awarded in this Section.

9. For each question in Section – A(iii), you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and zero

mark if no bubbles are darkened. In all other cases, minus one ( 1) mark will be awarded.

10. For each question in Section B, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the

correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for this

section.

11. 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. No negative marks will be awarded for in this Section

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

Paper Code

100397.1

Mock Test-7–Paper-2 (100397.1)-CMP-IITJEE-2

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

PART – I

SECTION – A

Straight Objective Type

This section contains 6 multiple choice questions numbered 1 to 6. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

1. Two positive point charges 1q and 2q of magnitude 16 nC and 144

nC are placed at point A and B as shown in figure. The potential at each point of the given equipotential surface is 640 Volt. Then the separation between the point charges is (A) 3.6 m (B) 2.7 m(C) 1.8 m (D) 0.9 m

q1 q2

A B

2. A lamp post is fixed at point (0, 0, 5m). A man is moving with constant velocity 6 m/s along a line

y 3x. Height of man is 2m and initially the man is at origin. The velocity of edge of his shadow

along the line of motion of man is

(A) ˆ ˆ8i 6 j (B) ˆ ˆ6i 8 j

(C) ˆ ˆ5 3 i 5 j (D) ˆ ˆ5i 5 3j

3. A plank of mass M and sphere of mass 2 M are kept on a smooth inclined plane as shown in the figure. The coefficient of friction between sphere and plank is ‘ ’. If system is released from rest then choose the INCORRECT alternative at t = 0. (A) Friction force between sphere and plank is 2 Mg cos . (B) Acceleration of plank with respect to sphere is zero. (C) Friction force between sphere and plank is zero. (D) Acceleration of plank and sphere is same.

M

2M

Space for Rough work



4. A plane mirror is rotating about point ‘O’ with constant angular velocity 4 rad/sec in anticlockwise direction. A point ‘P’ is moving in a circle of radius 50 cm with constant speed 3 m/s in anticlockwise direction about point O. At a given instant as shown in figure, the angular velocity of image is (A) 6 rad/sec in clockwise (B) 6 rad/sec anticlockwise direction (C) 2 rad/sec in anticlockwise (D) 2 rad/sec in clockwise direction

4 rad/s

x

y

P

O

5. Three long wires are placed in xy plane in a gravity free space ‘i’ is the current flowing in each wire. The currents are constant in magnitude. Distance between each wire is ‘d’ and ‘ ’ is the mass per unit length of each wire. Wire ‘A’ and wire ‘C’ are fixed and wire ‘B’ is slightly displaced along ‘z’ axis. The period of oscillation of wire ‘B’ is

(A) 0

d

i(B)

0

2 d

i

(C) 0

d

2i (D)

0

4 d

i

i i i

d d

x

y

A B C

6. Figure (i) shows a galvanometer without shunt and figure (ii) shows same galvanometer with a shunt which is connected in parallel to the galvanometer. The resistance of shunt is 1/n times the resistance of galvanometer. If the sensitivity of galvanometer in figure (i) is ‘S’ then sensitivity of ammeter in figure (ii) is (sensitivity is defined as the deflection per unit current)

i

G

Figure-1

S

i

G

Figure-2

(A) nS (B) 1

Sn

(C) (n + 1) S (D) 1

Sn 1




Multiple Correct Choice Type

This section contains 3 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

7. Three capacitors A, B, and C of capacitance 2 F , 2 F and 4 F

respectively are connected with a resistance of 4 as shown. Initially potential difference across capacitor A is 5 V, while capacitor B and C are uncharged. Now switch is closed at t = 0. Choose the correct statement(s).

S

B

A

C

(A) The magnitude of current in the circuit at t = 0 is zero.(B) After a long time the magnitude of charge on each capacitor is equal. (C) After a long the magnitude of charge on capacitor B is 4 C. (D) After a long time energy stored in capacitor C is 2 J.

8. A block of mass 1 kg is released from the top of a wedge of mass 2 kg. Height of wedge is 10 meter and all the surfaces are frictionless. Then(A) Displacement of centre of mass of system in vertical direction is zero. (B) Displacement of centre of mass of system, vertically downward, is

10m.

3

2 kg10m

1 kg

(C) Ratio of normal reaction between block and wedge to the acceleration of wedge w.r.t. ground is 4 (in kg).

(D) Momentum of system will be conserved in horizontal direction.

9. Three concentric spherical shells of radius a, 2a and 4a having positive charges Q1 and Q2 and Q3 respectively are placed as shown. Now, shell of radius ‘a’ and ‘4a’ are earthed through switch S1 and S2. A point ‘P’ lies at a distance 5a from the centre of shell and a point R inside the inner most shell. Now, choose the correct option(s) when switch S1 and S2 are closed. (A) The magnitude of electric field at ‘P’ and at ‘R’ is equal. (B) The potential of inner most shell and outermost shell

must be equal

Ra

P

2a 4a

S2 S1

5a

(C) The magnitude of charge on shell of radius 2a remain unchanged. (D) Potential must drop in moving from inner most shell to middle shell




Comprehension Type

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

Paragraph for Question Nos. 10 and 11

One mole of an ideal diatomic gas undergoes a process AB as shown. Pressure at A and B are 5P0 and P0 while volumes are V0 and 5 V0 respectively. On the basis of the given information answer the following question(s).

V0 5V0

V

P

5P0

P0 B

A

10. Choose the correct option regarding the process A B. (A) Work done by the gas from A B is negative.(B) Change in internal energy of the gas from A B is positive.(C) Work done by the gas from A B is zero (D) Change in internal energy of the gas from A B is zero

11. During the process from A B, pressure and volume of the gas, where the direction of flow of heat is reversed, is

(A) 0 0

5 7P , V

2 2(B) 0 0P ,5V

(C) 0 04P , 2V (D) 0 0

9 3P , V

2 2




Paragraph for Question Nos. 12 and 14

Five equal resistances, a capacitor and two batteries are connected in a circuit as shown in the figure. The capacitor is initially uncharged and each battery has negligible internal resistance. It is given that R = 1 , C = 1 F and V = 8 volt. On the basis of above information answer the following questions, if switch ‘S’ is closed at t = 0. (assume e 1 = 0.37, if required)

E C

V A

RD

2V

S

C R

R

R

R

B

12. Current in the branch of capacitor at t = 5/8 s is (approximately) (A) 6 A (B) 3 A (C) 12 A (D) 10 A

13. Current in the branch AB at t = 5/8 s is (approximately) (A) 1.7 A (B) 4.3 A (C) 3.4 A (D) 8.6 A

14. Potential difference between points A and C at t = 5/8 s is (approximately) (A) 1.7 V (B) 2.5 V(C) 6 V (D) 9.3 V




SECTION – B

(Matching List Type)

This section contains 2 multiple choice questions. Each question has matching Column(s). The codes for the Column(s) have choices (A), (B), (C) and (D) out of which only ONE OR MORE is/are correct

1. A narrow slit S transmitting light of wavelength is placed a distance d above a large plane mirror as shown in the figure. The light coming directly form the slit and that coming after the reflection interfere at a screen placed at a distance D from the slit. Assume that the mirror is 100% reflecting and d << D. Match the quantities in Column–I with their corresponding values in Column –II. (given D = 1m, d = )

d

S

D

O

Column–A Column–B

(A) Distance from O, where first interference maximum is formed on screen

(p)

0

(B) Distance from O, where closest interference minimum is formed on screen

(q) 1/4

(C) Fringe width of the interference pattern (r) 1/2

(D) Closest point to O on screen where waves interfere with a phase difference of /2

(s) 1

(t) 1/8

2. A frame ABCD is rotating with angular velocity about an axis which passes through the point O perpendicular to the plane of

paper as shown in the figure. A uniform magnetic field B is applied into the plane of the paper in the region as shown. Match the following.

A

B C

D

L

L

O LL

B

B

Column–I Column–II

(A) Potential difference between A and O (p) zero

(B) Potential difference between O and D (q) B L2/2

(C) Potential difference between C and D (r) B L2

(D) Potential difference between A and D (s) 2B L2

(t) 8B L2




SECTION – C(One Integer Value Correct Type)

This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

1. A light beam of power 12 watt and wavelength 6000 Å falls normally on a partially reflecting plate. If reflecting plate absorb 80% of light falling on it then force exerted on the plate is 4.8 10 n Newton. Find the value of + n.

2. Two infinitely long wires are placed perpendicular to the plane of paper. Current in wire A is 4 i0 outward the plane of paper and current in ‘B’ is i0 inward the plane of paper.

The –

B d along the QP is 0 0

Ki

2. Find the value of K.

A

B

Q –

+ P

3. Four blocks A, B, C and D of equal mass are placed on the belt of conveyor at equal distances as shown. Mass of each block is 2 kg and distance between blocks (d) is 400 mm. Assume masses of rollers and conveyor are negligible. Friction is sufficient to prevent the slipping between blocks and belt. A constant force of 1000 N is applied parallel to the belt as shown. Neglect the radius of roller as compare to d. The magnitude of velocity of block B when it leave the roller

at point ‘T’ is 7

10 m/s. Find the value of .

A B C D

P

roller rollerF=1000 N

U T

d d d d

4. The reflecting surface of two mirrors M1 and M2 are at angle = 50 as shown in the figure. A ray of light, parallel to M2, is incident on M1. The emerging ray intersects the incident ray at an angle = 10 (in degree). Find the value of .

M1

M2

5. The length of a simple pendulum, measured by an instrument of least count 4 mm, is found to be 40 cm. Its time period is measured by taking 200 oscillations using a watch of resolution 2s. The time period is found to be 0.4 s. Find the percentage error in the determination of the acceleration due to gravity using this data.




PART – II

SECTION – A



1. Which of the following is correct order of stability of given species?

OH

(I) (II)

OH

(III) (IV) H2C NH2 (V) CH2OH

(A) I > III > II (B) I > II > III(C) IV < V (D) I < V

2. Compare the C – O bond lengths in the following?

(a)

O

O

(b)

O

OO

(c) O

(d)

O

(e) 23CO (f) RCOO

(A) b > e > f > c > d > a (B) e > b > f > d > c > a (C) b > e > f > d > a > c (D) d > c > a > b > f > e




3. Some of the inorganic compounds when subjected to transformations from gaseous phase to liquid or

solid phases, they ionize themselves and consequently hybridization of central atom changes. Match

the following columns in this refrence.Column I

(Species in gas phase)Column II

(Hybridisation of central atom in gas phase)

Column III (Hybridisation

in solid/liquid phase) (a) N2O5 (p) sp3d (w) sp, sp2

(b) BrF3 (q) sp2 (x) sp3d, sp3d2 (c) Cl2O6 (r) sp3d2 (y) Sp2, sp3 (d) IF5 (s) sp3 (z) sp3, sp3d2

(A) (a, q, w); (b, p, z); (c, s, z); (d, r, y) (B) (a, q, z); (b, p, x); (c, s, w); (d, r, y) (C) (a, q, w); (b, p, z); (c, s, y); (d, r, x) (D) (a, p, w); (b, q, z); (c, s, x); (d, r, y)

4. The following reversible reaction starts only with A;1

1

12

K sec

K secA B;

What is the time taken by the reaction to achieve equilibrium?

(A) 1

1 2

K1n 1

K K (B) 1

2 2

K1n 1

K K

(C) 2 1

1 1

K K1n

K K (D) 2

2 1

K1n 1

K K

5. Which of the following give an acidic gas on heating?(A) (NH4)2CO3 (B) N2H5NO2

(C) AgNO3 (D) All of these

6. Which of the following set of polymers belongs to condensation polymer?(A) Nylon-66, Kevlar, orlon (B) Orlon, Perlon, Nylon-66(C) Polytetrafluoroethylene, Nylon-66, Bakelite (D) Bakelite, Nylon, Kevlar






7. Which of the following acquire bent shape upto appreciable extent?(A) CH3NCS (B) H3Si – NCS (C) PH2NCS (D) I3

+

8. Which of the following is/are correct combination about cellulose and starch?

Cellulose StarchI II III IV

(A) Natural polymer Linear polymer Natural polymer Cross linked polymer(B) Natural polymer Cross linked polymer Natural polymer Linear polymer (C) Homo polymer Condensation

polymer Co polymer Condensation polymer

(D) Randum polymer

Imparts blue colour to KI solution

Graft polymer Imparts blue colour to KI solution

9. Which of the following is/are correct about the product (P) of the following process?NH2

ProlongedProduct P ;2 4

o

1 H SO dil.

2 heating at 180 C

(A) M.P. of P is very high. (B) P is soluble in aqueous NaOH.(C) P is insoluble in HCl solution. (D) It is electrically neutral.




Comprehension Type


Paragraph for Question Nos. 10 to 11

In case of alkanes anticonformers are more stable than Gauche and other conformations. However, in case of the groups at adjacent positions, strong van der Waals forces of attraction or hydrogen bonding are more stabilized in Gauche form instead of anti form. In E2 reactions anti elimination occurs while in E1 & E1cB it is not necessary.

10. In the following reaction which ‘H’ eliminates preferentially from alkyl fluoride?

CH3

NO2

F

NaOHEtOH

alkeneaH

bH

cHdH

(A) Ha (B) Hb (C) Hc (D) Hd

11. For which of the following compound, Gauche conformation is more stable than its anticonformation? (A) C C

H

C2H5

H

Cl

CH3CH3 1 2For C H& C Clbond1 2

(B)

C

H

C2H5

H NH2 For .p. & C H bond

(C) CH2CH2

Cl Cl

In aqueous solution

(D) CH2CH2

HOOC SH

COOH & SH at high pH





Solubility of salts in water is mainly depends upon the hydration energy and lattice energy. It hydration energy is greater than lattice energy then the salt becomes soluble. However, if the metallic part of the salt form soluble complex in some specific conditions then again it becomes soluble under those conditions, not in pure water. Hydration energy and lattice energy both are directly proportional to q+ and q (charges on the cationic and anionic part of the salts respectively) and both of those depend on the size of cations and anions as follows:

hydration

1 1H ; r radius of cation

r r

r = radius of anion.

Lattice energy1

U ;r r

In this case if r >> r+ then lattice energy is less dominant than hydration energy. Lattice energy on the other hand also depend upon packing of ions in crystal, which further depends upon the size of cation and anion, better is the packing and more is the lattice energy and less is the solubility.

12. Which of the solubility order is correct?(A) BeO < MgO < CaO < SrO < BaO (B) NaBr < KBr < RbBr < CsBr (C) NaClO3 > KClO3 > RbClO3 > CsClO3 (D) BeS2O3 < MgS2O3 < CaS2O3 < SrS2O3

13. Which of the following is correct? (A) Oxalates, Borates and Chromates of alkali metals as well as alkaline earth metals are soluble in

water. (B) All permanganate salts are soluble in water but all nitrite salts are not.(C) Permanganate salts of alkali metals are soluble in water however solubility of permanganates of

alkaline earth metals increases down the group. And Ba(MnO4)2 is insoluble in water.

(D) 2o

H O2 3 3 2boiled above 300 C

Na CO AgNO Brown precipitate of Ag O.

14. Which of the following is correct? (A) 3 4 3Na PO aq. AgNO Light yellow precipitate

(B) 3 2KHCO HgCl

Cold

Boiled

Reddish brown precipitate

No precipitate

(C) On adding HgCl2 to KHCO3 solution in cold, pH decreases drastically.

(D) 2 3 2Na CO aq. BaCl aq. White precipitate

Excess of NaOH solution

Clear solution




SECTION – B



1. Match the following columns for P & R:

R P

Column I (P)

Column II(R)

(A)

(p) 3Na,NH

(B) (q) H2, Pd/BaSO4/quinoline

(C)

O

(r) H2O/Hg2+/H2SO4

(D)

(s) Excess H2/Ni/

(t) (i) B2H6/THF (ii) H2O2/OH

2. Match the Column – I with Column II:

Column – I Column – II

(A) Isothermal process (reversible) (p) 1

2

PW 2.303nRTlog

P

(B) Adiabatic process (q) PV constant

(C)2 1

nRW T T

1

(r)1

2

VW 2.303nRTlog

V

(D) Irreversible isothermal process (s) W = -Pext(V2 – V1)




SECTION – C

(One Integer Value Correct Type)


1. Number of bond in Fe2(CO)9 is X and X

3n

, then value of ‘n’ will be.

2. 100 ml of ‘x’ normal H2O2 gives 3 litre of O2 gas under the conditions when 1-mole occupies 24 litre. What is the value of x?

3. A complex is represented by CoCl3yNH3. It’s 0.1 molal solution freezes at –0.558°C. Kf H2O = 1.86 K Kg mol–1. Coordination number of Co(III) is six. Assuming 100% ionization, what is the value of y ?

4. How many of the following bear unpaired electron in sp3 hybridised orbitals? ClO2; ClO3; NO2; NO; 3CH ; 3CF ; ICl2;

5. How many gases/vapours are involved either as reactants or products in Serpeck’s process used for concentration of bauxite (Al2O3.2H2O) ?




PART – III

SECTION – A



1. The number of ways in which three couples can sit around a rectangular table with three seats each along the opposite length of table, such that no couple sit in front of each other is ___ (seats are numbered)

(A) 63P 2 (B) 384

(C) 424 (D) none of these

2. If there exists atleast one z satisfying |z – ki| = k + 4 and |z – 3| 4, then which of following can not be the value of k (A) 4 (B) 0 (C) 10 (D) none of these

3. Let f(x) = 27 + x + x3. The values of x which satisfy f f f f x f f f x is

(A) –10 < x < –4 (B) x < –10(C) x > –3 (D) none of these

4. Let p, q, r are three vectors such that p r q p and p r 1 then which of following is true

(A) 2

p q2

p (B)

2

p p qr

p

(C) 2

2

2 p qp q r

p (D) none of these

5. If f(x) be a differentiable function in interval (– , ) such that f(x) = f(10 – x), then the value of 2

54 x

5

f ' 5 x x e dx is

(A) 5e2 – 1 (B) 25e 1

3

(C) 0 (D) 1

3

Space for rough work



6. The degree of differential equation for the family of curves such that the tangent at any point P on curve divides the OPN in the ratio 1 : 2, where PN is perpendicular to x-axis and O is origin, is (A) 1 (B) 2 (C) 3 (D) none of these



7. If A BA = 0 for all 3 1 column matrices A, then which of the following statement(s) is/are correct (where A represents transpose of matrix A)(A) B is a skew symmetric matrix (B) B is a non singular matrix(C) B is a singular matrix (D) |B| = 0

8. If f: [0, 27] R be a differentiable function such that f(0) = 0, f(10) = 1 and f(27) = 1, then which of the following statement(s) is/are correct

(A) there exist some where 1

f '10

(B) there exist some where f ( ) = 0 (C) f (x) < 0 x (0, 27)

(D) there exist some , (0, 3) such that 27

2 3 2 3

0

2 f t dt 9 f f

9. If f(x) be twice differentiable function such that f (x) is positive in [0, 4], then which of the following statement(s) is/are correct (A) f(0) + f(4) = 2f(c) for atleast one c (0, 4) (B) f(0) + f(4) < 2f(2)

(C) f(0) + f(4) > 2f(2) (D) 2f(0) + f(4) > 4

3f3




Comprehension Type



Read the following write up carefully and answer the following questions: For the equation (2x2 – 1)2 + 2ax(2x2 – 1) + x2(4a2 – 1) = 0

10. The values of a for which above equation has all roots positive(A) (– , –1) (B) (–1, 2) (C) (2, ) (D) none of these

11. The values of a for which above equation has two positive and two negative roots (A) (– , –4) (B) (5, )

(C) 1 1

,3 3

(D) none of these





Read the following write up carefully and answer the following questions: The differentiable function y = f(x) has property that chord joining any two points A( , f( )) and B( , f( )) always intersects the y-axis at (0, 3 ). If f(1) = 2 then

12. 1

0

f x dx is

(A) 1 (B) 5

2

(C) 3

2 (D) none of these

13. If the area bounded by y = f(x) and y = mx – 2 is minimum, then the value of m is(A) 5 (B) 6 (C) 3 (D) none of these

14. The equation of circle which touches y = f(x) at (1, 2) and passes through (0, 0) is (A) (x – 1)2 + (y – 2)2 + 5(y + x – 3) = 0 (B) (x – 1)2 + (y – 2)2 + 4(y + x – 3) = 0 (C) (x – 1)2 + (y – 2)2 + (y + x – 3) = 0 (D) 3(x – 1)2 + 3(y – 2)2 + 5(y + x – 3) = 0




SECTION – B



1. Match the following Column-I with Column-II

Column – I Column – II(A) If 210·20C0·

20C10 – 29·20C1·19C9 + 28·20C2·

18C8 – … + 20C10·10C0

= 20Ck, then the value of k is

(p) 10

(B) If the product of all divisors of 240 is 2 3 5 , then the value

of 6

is (q) 12

(C) If the number of divisors of the number n = 23 3

5 57 79 of the

form 4k + 3 is t then t

20 is (r) 6

(D) Let set A has 4 elements and a subset P is randomly formed from set A. Set A is reconstructed and again a subset Q is randomly formed from set A. The probability that number of elements in set P are greater than number of elements of set Q is

(s)93

256

(t)93

128

2. Match the following Column-I with Column-II

Column – I Column – II

(A) If f : R R, x 2m , if x 1

f xmx 4 , if x 1

, then for all

values of m (– , –2) f(x) is

(p) one-one function

(B) If f : R – { , } R, x x

f xx x

. < < < ,

then f(x) is

(q) many-one function

(C) If f : R (– , 0], x

x

2f x ln

2 1, then f(x) is (r) into function

(D) If f : R R, f(x) = 3 21x 2x 6x sinx 1

3, then f(x)

is(s) onto function

(t) invertible function




SECTION – C

(One Integer Value Correct Type)


1. If L =

2nn

n

nlim ln e

n 1, then

1

L is _____

2. The line y + x = 2 intersects ellipse 2 2x y

116 9

at A and B. A circle with diameter AB is drawn to

intersect the same ellipse at two more points C and D. If equation of line CD is y = mx + c, then the value of m is _____

3. The value of 3

1/33 2

1

1 x 1 x 1 dx is _____

4. Let points A, B, C be (0, 0), (1, 0), (2, 0) respectively. A point P moves in the xy-plane such that

maximum {PA + PB, PB + PC} 2. If the area of region bounded by point P is 3

k3 4

, then the

value of k is _____

5. The slope of the tangent at ( 1, f( 1)) to the continuous and differentiable

function

2

2

2

x 10x 6 , x 2

f x ax bx c , 2 x 0

x 4x , x 0

is _____


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