05 weeklytestquestions.textmark

IIT-JEE CLASSROOM CENTRE

WEEKLY NORTH INDIA COMPETITIVE EXAMINATION-5(WNICE)

ALL RESHUFFLED BATCHES

Time: 3 Hours Maximum Marks: 264 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS: A. GENERAL

1. This booklet is your Question Paper containing 72 questions. The booklet has 26 pages. 2. No additional sheets will be provided for rough work. 3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers &

electronic gadgets in any form are not allowed to be carried inside the examination hall. 4. Write your Name and Enrollment No. in the space provided below. 5. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately. B. Filling the ORS

6. On the upper part of the ORS, write in ink, your name, enrollment number and batch number in the space provided. Do not write these anywhere else.

C. Question paper format: 7. This question paper has 3 sections: Section-A, B & C. Section-A has 60 questions

of physics, chemistry & mathematics (20 per subject), Section-B has 6 questions of matrix match type (2 per subject) & Section-C has 6 questions of single integer type (2 per subject).

8. Each subject of Section-A contains 8 questions of single correct choice type, 2 reasoning type, 2 set of paragraph type questions. The paragraph is followed by 3 questions. Each of these questions has 4 choices: (a), (b), (c) & (d), out of which only one choice is correct. Each subject also contains 4 questions of multiple correct choice type. Each of these questions has 4 choices: (a), (b), (c) & (d), out of which one or more than one choice is correct.

9. Each subject of Section-B contains 2 questions of matrix match type. Each question has four statements (A, B, C and D) given in Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II.

10. Each subject of Section-C contains 2 questions of integer answer type 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.

D. Marking Scheme: 11. In Section-A, for single correct choice type questions, you will be awarded 3 marks if you have

darkened only 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.

12. In Section-A, for multiple correct choice type questions, you will be awarded 4 marks if you darken only the bubble(s) corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded.

13. In Section-A, for reasoning type and paragraph type questions, 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.

14. For each question in Section-B, you will be awarded 8 marks if you have darkened ALL the bubbles corresponding ONLY to the correct answer or awarded 2 marks each for correct bubbling of answer in any row. No negative mark will be awarded for an incorrectly bubbled answer.

15. For each question in Section-C, you will be awarded 4 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 in this Section.

Name: Enrollment No.: Batch number:

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Brilliant Tutorials QUESTIONS WNICE-5/RB/230511/PCM 2

Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

Space for rough work

PHYSICS

SECTIONA Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

1. A block of mass m = 0.1 kg is released from a height of 4 m on a curved smooth surface. On the horizontal smooth surface, it collides with a spring of force constant 800 N/m. The maximum compression in the spring will be (g = 10 m/s2)

4m k=800N/m

m

(a) 1 cm (b) 5 cm (c) 10 cm (d) 20 cm

2. A block of mass 2 kg is lifted through a chain starting from rest. When block moves through

2m vertically upward, the velocity becomes 4 m/s. Work done by chain on the block until it moves 2m is (g = 10 ms2)

(a) 40 J (b) 24 J (c) 56 J (d) None of these

3. The electric potential V at any point P (x, y, z) in the space is given by V = 4x2 volt, here x, y and z are in meter. The electric field (in V/m) at the point Q (1 m, 0, 2 m) is

(a) i8 (b) i8 (c) i16 (d) i58

4. Three point charges +q, 2q and 2q are placed at the vertices of an equilateral triangle of

side a. The work done by external force to slowly increase their separation to 2a will be

(a) a

q0

2

2 (b) aq

0

2

4 (c) aq

0

2

43 (d) zero

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5. Two positive point charges each of magnitude 103 C are fixed at a distance 8m apart in same vertical plane. In between the two charges a third positive point charge of 103C and mass 3 kg is connected with a spring and the other end of the spring is fixed. The spring is in its natural length in the shown position. The charge in the middle is released, it travels a distance of 3m before coming to instantaneous rest. The spring constant is ( g = 10m/s2)

4m + ++

4m

Fixed charge3kg

Fixed charge

(a) 110 N/m (b) 220 N/m (c) 154 N/m (d) 100 N/m 6. If net electric field E due to a short dipole at point P makes an

angle 30 with the line OP as shown, then the value of angle is

(a)

2

1tan 1 (b) ( )2tan 1 (c)

32tan 1 (d)

23tan 1

E

P

30

q

O +q

7. A uniformly charged ring (fixed) carries positive charge +Q. A particle carrying negative charge q is released from rest from the position shown on the axis of ring. The kinetic energy of particle when it reaches the centre of the ring is

Q

r + +

+ + + + + +

+ + + +

+ + +

r22q

(a)

rqQ

04 (b)

rqQ

012 (c)

rqQ

06 (d)

rqQ

02

8. A point charge q is placed inside a neutral conducting spherical shell of inner radius 2R and

outer radius 3R, at a distance of R from the centre of the shell. The electric potential at the

centre of shell will be 04

1 times (potential at infinity is zero)

(a) Rq

2 (b)

Rq

34 (c)

Rq

65 (d)

Rq

32

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Multiple Correct Choice Type This section contains 4 multiple correct questions. Each question has 4 choices: (a), (b), (c)

and (d) for its answer, out of which ONE OR MORE may be correct.

9. Particle A having positive charge is moving directly (head on) towards initially stationary positively charged particle B. At the instant when A and B are closest, which of the following statements is/are correct.

(a) Linear momentum of A and B must be equal (b) The velocities of A and B must be equal (c) B would have gained less kinetic energy than A would have lost (d) B would have gained the same momentum as A would have lost

10. Figure show the lines of force of the electric field of a isolated positive charge (+q) and a isolated negative charge (-q) respectively.

Which of the following statements are correct? (a) Potential at P is greater than that at Q. (b) Potential at A is less than that at B. (c) Magnitude of electric field at P is less than that at Q (d) Magnitude of electric field at A is greater than that at B

Q

P +q

O

(i)

B

Aq

O

(ii)

11. A block having mass m and charge +q is connected by spring of force constant k. The other end of the spring is fixed to wall. The block lies on a frictionless horizontal track and a uniform external electric field E exists in the region as shown. The block is released from rest with spring unstretched. Then

E

+q,mk

(a) maximum stretch in the spring is kqE2

(b) at equilibrium position, stretch in the spring is k

qE

(c) amplitude of oscillation of block is k

qE

(d) amplitude of oscillation is kqE2

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12. Figure shows three concentric thin spherical shells A, B and C of

radii R, 2R, and 3R respectively. Shells A and C are given charges +q and +2q and shell B is earthed. Then

(a) charge on inner surface of shell C is + q34

(b) charge on outer surface of shell B is q34

(c) charge on outer surface of shell C is + q32

(d) charge on outer surface of shell C is + q34

A B

C

3R

R

2R

Reasoning Type This section contains 2 reasoning type questions. Each question contains Statement-1 and

Statement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

Directions: Read the following questions and choose (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for

Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

13. Statement-1: Two concentric conducting spherical shells are charged. The charge on the

outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.

Statement-2: If charge is changed on an thin conducting spherical shell, the potential at all points inside the shell changes by same amount.

(a) A (b) B (c) C (d) D

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14. Statement-1: For a non-uniformly charged thin circular ring with net charge zero, the electric

field at any point on axis of the ring is zero. Statement-2: For a non-uniformly charged thin circular ring with net charge zero, the electric

potential at each point on the axis of the ring is zero. (a) A (b) B (c) C (d) D

Paragraph Type

This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice questions have to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

Paragraph 1 Two identical large metallic plates a and b, with their faces named 1, 2, 3 and 4 are placed

parallel to each other at a small separation d as shown with switch S open. The plate a carries a net charge of +3Q while plate b carries net charge of Q. The area of each plate is A. There exists a uniform external electric field in the complete region of intensity

AQE0

= in the positive direction of x-axis.

d ba

S

31 2 4

AQE0

=

y

x

15. The potential difference (Va Vb) between plates a and b (with switch S open) is

(a) dA

Q

0 (b) d

AQ

0 (c) d

AQ

0

3 (d) dA

Q

0

3

16. Now the switch S is closed, the charge appearing on the faces 1, 2, 3 and 4 respectively are (a) +Q, 0, 0, +Q (b) 0, 0, 0, +2Q (c) 0, +Q, Q, 0 (d) +2Q, +Q, Q, +Q

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17. Charge flown through the switch after it is closed is (a) +3Q from plate a to plate b (b) +3Q from plate b to plate a (c) +2Q from plate a to plate b (d) +2Q from plate b to plate a

Paragraph 2

A non-conducting sphere of radius a is concentric with a

conducting spherical shell having inner radius 3a and outer radius 5a as shown in the figure. The charge +Q1 is uniformly distributed throughout the volume of the non-conducting sphere, and the net charge on the spherical shell is +Q2.

+Q2 (net)

+Q1a

3a5a

18. The magnitude of the electric field at a distance of 2a from the center of the sphere is

(a) 20

21

4)(

aQQ

+ (b) 2

0

1

16 aQ

(c) 20

1

4 aQ (d) None of these

19. The electric flux through a Gaussian spherical surface of radius 4a that is concentric with

the sphere and conducting shell is

(a) zero (b) 0

1

Q

(c) 0

21 )(+QQ (d) None of these

20. The surface charge density on the outer surface of the conducting shell is

(a) 22

100 aQ (b) 2

21

100)(

aQQ+

(c) 221

100)(3

aQQ

+ (d) None of these

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SECTIONB Matrix Type

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in 2 and 3, then for that particular question, against statement B, darken the bubbles corresponding to 2 and 3 in the ORS.

1. A variable force F is acting on a particle moving along

x-axis starting from rest from origin. The variation of force F with position of the particle x is shown in F-x curve. (Assuming that the particle moves under the action of this force only)

F(N)

5

10

5

10

2 4 6 8 10 x(m)

Column I Column II

(A) Net work done by the force is positive from starting position till x equal to

1. 6 m

(B) Position of particle when magnitude of force is 5 N 2. 8 m

(C) Position of particle when instantaneous power is positive (non zero)

3. 9 m

(D) Position of particle when it is retarding 4. 10 m

5. 7 m

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2. Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown.(where M is the midpoint of PQ) Let E be the electric field intensity and V be the electric potential at point M (potential at infinity is zero) due to the given charge distribution when it is at rest. p be the dipole moment of the system in this condition.

Column I Column II (A) E = 0

1.

+ +

+ P

M

Q

Charges are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon.

(B) V 0

2. + + +P

QM

Charges are on a line perpendicular to PQ at equal intervals. M is the mid-point between the two innermost charges.

(C) E 0

3.

M

P

Q+ +

+

Charges are placed symmetrically on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings.

(D) p 0

4. P Q

M

+

+

Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides.

5.

P

M

Q

+

+ +

Charges are placed symmetrically on two coplanar, identical insulating rings at equal intervals. M is mid point between the centres of the rings. PQ is perpendicular to the line joining the centers and coplanar to the rings.

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SECTION C Integer Type

This section contains TWO questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. Two identical charges are placed at the two corners of an equilateral triangle. The potential energy of the system is U. The work done in bringing an identical charge slowly from infinity to the third vertex is nU. Find the value of n.

2. A uniformly charged semi infinite rod of linear

charge density + is placed along the x-axis which on end is at origin. Electric flux associated with conical(slant) surface of a cone of radius R and

height 2R as shown in the figure, is 02

Rn . Find the value of n.

2R

R

O

y

x

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CHEMISTRY

SECTIONA Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

1.

B2D6

H2O2/OH (X). Identify the product (X).

(a) D H

OH

CH3

(b)

DH

OHCH3 (c) OD

HCH3

D (d)

OD

H CH3

D

2. (i) + OH O

(ii) I2/NaHCO3(Y). The product (Y) is

(a)

OH O I

I (b)

COOH

(c) I

O O

(d)

O O

3.

O

+ D2O long time (Z). The product (Z) is

(a)

OD

(b)

OD D

DD (c)

ODD

DD

D (d)

D DD

D D

D

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4. Which of the following pairs of structures represents conformational isomers?

(a)

and (b) and

(c) and (d) andC C 5. Find out the nature of product obtained by selective bromination of the following reactant.

CH3

CH3 CH3 h

Br2

(a) Meso (b) Diastereomers (c) Enantiomers (d) Homomers 6. Find the R, S configuration of 1 and 2 carbon atom in the following compound.

Br H

Cl 1 2

(a) R, S (b) S, R (c) R, R (d) S, S

7. The given compound (Y) is obtained when aq. KMnO4 (cold) is treated with (X).

(X) + aq. KMnO4 (cold)

HO

O

O

HO

(Y)

(X) is

(a) (b) OH

OH (c)

O

OHBr

Br (d)

8. Minimum number of C atoms an alkyne must have to show diastereoisomerism is (a) 4 (b) 5 (c) 6 (d) 7

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Multiple Correct Choice Type This section contains 4 multiple correct questions. Each question has 4 choices: (a), (b), (c)

and (d) for its answer, out of which ONE OR MORE may be correct.

9. The product(s) formed in the following reaction is (are)

Me H H

+ : CH2 (Triplet) P.Me P is (are)

(a) Me

H H Me

(b)

Me

HHMe

(c) H

Me Me

Me H

H (d) Me

H HCH2CH3

10. Acetylene can be synthesised from

(a) CaC2 (b) CH3CHBr2 (c) CHCOONa

CHCOONa (d) Be2C

11. The reaction of (A) with HCl gives more than one product. OH Products HCl

(A)

The products are

(a) Cl

(b) Cl

(c) MeCl (d) Me

Cl

12. Among the following, identify the species with an atom in + 6 oxidation state (a) 4MnO (b) 5CrO (c) 52SOH (d) 22ClCrO

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13. Statement 1 : In aqueous solution, 2SO reacts with SH2 liberating sulphur. Statement 2 : 2SO is an effective reducing agent in the above reaction. (a) A (b) B (c) C (d) D

14. Statement 1 : The addition of HCl to propene in presence of peroxide gives 1-chloropropane

Statement 2 : HBr obeys Kharasch effect. (a) A (b) B (c) C (d) D

Paragraph Type This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice questions

have to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

Paragraph 1 Both the alkenes and alkynes undergo electrophilic addition reactions, because of electron

density. They behave as electron rich species. Alkenes are more reactive towards this reaction because the intermediate formed when an E adds to an alkyne is a vinylic cation whereas the intermediate formed when an E adds to alkene is alkyl cation, which is more stable. Also addition reaction can proceed via formation of three membered cyclic transition state.

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RCCH E RC=CHE or RC=CHVinyl cation

RCH=CH2 E

RCHCH2E or RCHCH2

Alkyl cation

E

E

15.

HCl (1 mole)

(a)

Cl

(b)

Cl

(c)

Cl

(d) Cl

16. CF3CO3H

(a)

O

(b)

O

(c)

OHOH

(d)

O

O

17. CH3

C=C HH

Ph Cl2, CH3OH Major product:

(a)

H Cl

CH3 Cl

Ph

H (b)

H ClH OCH3

Ph

CH3

(c)

H Cl

H CH3

Ph

H3CO (d) H OCH3

HCH3

Ph

Cl

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Paragraph 2

A redox reaction consists of oxidation and reduction half reactions. There is a loss of electron(s) in oxidation and the species which loses electron(s) is reducing agent. Its oxidation number increases during oxidation. Similarly there is a gain of electron(s) during reduction and the species which gains electron(s) is an oxidizing agent. Its oxidation number decreases during reduction. The number of electrons released during oxidation is equal to number of electrons gained during reduction.

18. The reaction:

+ ++ e4O)aq(H4)(OH2 22 l is (a) an oxidation reaction (b) a reduction reaction (c) a redox reaction (d) a hydrolysis reaction 19. The oxidation number of sulphur in 228 FS,S and SH2 respectively are

(a) 0, + 1 and 2 (b) + 2, +1 and 2 (c) 0, +1 and +2 (d) 2, + 1 and 2 20. A mole of 42HN loses ten moles of electrons to form a new compound Y. Assuming that all

the nitrogen appears in the new compound, what is the oxidation state of nitrogen in Y? (there is no change in the oxidation number of hydrogen)

(a) 1 (b) 3 (c) + 3 (d) + 5

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SECTIONB Matrix Type


1. Match the following

Column I Column II

(A) Br

?

1. NaI + Acetone

(B) Br ? 2. Zn + CH3COOH

(C)

Me

? Br

3. EtOK + EtOH

(D) Cl

?

Cl

4. OH ONa + +

5. NaOH + CH3OH

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2. Match the following

Column I Column II

(A) Me

H H

Me

Me

H H

Me

1. Rotates plane polarized light.

(B)

Cl

Cl Br

2. Cannot rotate plane polarized light.

(C)

H CH3

H H H

H H

CH3

3. Plane of symmetry.

(D)

C = C = C CH3

CH3 ICl

4. Centre of symmetry. 5. Axis of symmetry.

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1. How many alkenes can be obtained in the following reaction?

OH H+ Alkenes

2. Compound (A) C4H6 which on reduction with Lindlars catalyst give cis-but-2-ene. (A) will

react with how many reagent(s) given below:

2NaNH , RMgX, AgNO3, Br2/H2O, KMnO4(aq.)

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MATHEMATICS

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. Number of solutions to satisfy 2112

12sintan212

xxxxx ++=++

will be

(a) zero (b) one (c) two (d) infinitely many

2. Sum of values of x such that ( )97cot1tantan 111 =+ xx

(a) 2 (b) 1 (c) 1 (d) 9

3. The value of

+

37coscos

67tantansin 11 is

(a) 0 (b) 1 (c) 1 (d) none of these 4. Two perpendicular tangents PA and PB are drawn to ,42 axy = minimum length of AB is

equal to (a) a (b) 4a (c) 8a (d) 2a 5. If 2coslogsinlog sincos =+ xx xx , then value of xtan will be (a) 1 (b) 1 (c) 2 (d) none of these

6. If baz

acy

cbx

==logloglog then the value of xyz is

(a) 1 (b) 3 (c) 2 (d) none of these

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7. Number of integral triplets ( )dcb ,, such that ( ) dcxbxxxf +++= 23 has all integral roots where ( ) ( )1,0 ff are odd integers

(a) zero (b) one (c) two (d) infinitely many

8. The least value of the expression yxyxyx 2632 22 ++ Ryx , will be (a) 11 (b) 12 (c) 10 (d) 9

Multiple Correct Choice Type This section contains 4 multiple choice questions. Each question has four choices (a), (b),

(c) and (d) out of which ONE OR MORE may be correct.

9. ( ) ,5.86sin6 21 =+ xx if (a) 1=x (b) 2=x (c) 3=x (d) 4=x

10. If ,0,0)}]tan2{cot(cos2sin[ 11 >= xx then (a) 1=x (b) 12 +=x (c) 12 =x (d) 3=x

11. If === xxx cba log,log,log and =xdlog such that 1>x and each of dcba ,,, is greater than 1, then xabcdlog

(a) 16

+++ (b) 16

+++

(c) 11111

+++= (d) =1

12. The solution of the equation 233 3loglog =+ axa x is given by

(a) aa 3log (b) 23log2

a (c) 23loga (d) a3log2

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13. Statement 1 : The conic 132

=

+

yx represents a parabola.

Statement 2 : Conic 0222 22 =+++++ cfygxbyhxyax represents a parabola if 0 and abh =2 .

(a) A (b) B (c) C (d) D 14. Statement 1 : The equation 2ammxy = is tangent to the parabola ayx 42 = for all values of

Rm . Statement 2 : A straight line cmxy += that intersects the parabola ayx 42 = at one point is

a tangent line. (a) A (b) B (c) C (d) D

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Paragraph Type This section contains 2 paragraphs. Based upon the paragraph 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 -1

As ( ) = =

==

+n

r

n

rnrr

rr

rr Nnxxxxxx

rx1 1

011

111

1

11 ,tantantantan1

tan , hence sum

of such infinite series can be obtained by repeated cancellation of alternative terms. Based upon this method answer the following questions:-

15. The sum to infinite terms of the series ...21

2tan...92tan

31tan 12

1111 +

+++

+

n

n

is

(a) 4 (b)

2 (c) (d) none of these

16. The value of ...325eccos65eccos5eccos 111 +++ to is (a) (b)

43 (c)

2 (d)

4

17. The sum to infinite terms of the series ...212cot

212cot

212cot 3

412

3121 +

++

++

+ is

(a) 4 (b)

2 (c) 2cot 1 (d) 2cot 1

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Paragraph 2 Let consider quadratic equation 02 =++ cbxax (i) Where Rcba ,, and .0a If equation (i) has roots, ,

ac

ab ==+ , and equation (i) can be written as ( )( )=++ xxacbxax 2 .

18. Let p and q be roots of the equation 022 =+ Axx and let r and s be the roots of the

equation .0182 =+ Bxx If srqp




SECTION B Matrix Type


1. Match the equations given in column I with their number of solutions in column II.

Column I Column II (A) ( )( ) ( )( ) 1cos2/14/tancos2/14/tan 11 =++ xx 1. 0 (B) 2

111 2tan14

1tan12

1tanxxx

=+++ 2. 2

(C) 02tan4tan2tan 111 =

+ x

xxx

x 3. 3

(D) =++ xxx 111 seccossin 4. 1 5. 4

2. Match the values of N and S as instructed between column I and column II.

Column I Column II (A) If N be the number of real solutions and S be the sum of all real

roots of the equation ,424 = xxx then 1. 0=S (B) If N be the number of solutions and S be the sum of all roots of the

equation ,262 += xxx then 2. 1=N (C) If N be the number of solutions and S be the sum of all roots of the

equation ,0432 = xx then 3. 2=N (D) If N be the number of real roots and S be the sum of all roots of

equation 090213 = xx then 4. 3=N 5. 4=S

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1. If number of positive integral solutions of the equation 103sin

1costan 1

2

11 =+

+y

yx

is a then find the value of a. 2. Find the value of m if the expression 2532 22 ++ yymxyx can be expressed as

( )++ yx ( )rqypx ++ ; Rrqp ,,,,,

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