P A P E R - 1

READ THE INSTRUCTIONS CAREFULLY

GENERAL :

1. This sealed booklet is your Question Paper. Do not break the seal till you are toldto do so.

2. Use the Optical Response sheet (ORS) provided separately for answering the questions.

3. Blank spaces are provided within this booklet for rough work.

4. Write your name, form number and sign in the space provided on the back cover of thisbooklet.

5. After breaking the seal of the booklet, verify that the booklet contains 28 pages andthat all the 18 questions in each subject and along with the options are legible. If not,contact the invigilator for replacement of the booklet.

6. You are allowed to take away the Question Paper at the end of the examination.

OPTICAL RESPONSE SHEET :

7. The ORS will be collected by the invigilator at the end of the examination.

8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.

9. Write your name, form number and sign with pen in the space provided for this purposeon the ORS. Do not write any of these details anywhere else on the ORS. Darkenthe appropriate bubble under each digit of your form number.

DARKENING THE BUBBLES ON THE ORS :

10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.

11. Darken the bubble COMPLETELY.

12. The correct way of darkening a bubble is as :

13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correctway.

14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to eraseor "un-darken" a darkened bubble.

15. Take g = 10 m/s2 unless otherwise stated.

Time : 3 Hours Maximum Marks : 186PAPER-1

Space for Rough Work

SOME USEFUL CONSTANTSAtomic No. : H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16,

Cl = 17, Br = 35, Xe = 54, Ce = 58Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,

Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,Xe = 131, Ba=137, Ce = 140,

· Boltzmann constant k = 1.38 × 10–23 JK–1

· Coulomb's law constant pe9

0

1 = 9×104

· Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2

· Speed of light in vacuum c = 3 × 108 ms–1

· Stefan–Boltzmann constant s = 5.67 × 10–8 Wm–2–K–4

· Wien's displacement law constant b = 2.89 × 10–3 m–K· Permeability of vacuum µ0 = 4p × 10–7 NA–2

· Permittivity of vacuum Î0 = 20

1

cm· Planck constant h = 6.63 × 10–34 J–s

SYLLABUS :PHYSICS : Waves, SHM, Wave Optics, Magnetism, EMI & AC

CHEMISTRY : Inorganic- Salt analysis, Chemical bonding ; Organic- Carboxylic Acid & Derivatives,Amines & Other Nitrogen Containing Organic Compounds, Aromatic Compounds,Practical Organic Chemistry ; Physical- Chemical Kinetics, Radioactivity, Solid State,Surface Chemistry, Atomic Structure

MATHEMATICS : Quadratic Equation, Sequence & Progression, Basic Maths (Logarithm,Trigonometric Ratio & Identities, Trigonometric Equation, Modulus, Inequality),Functions, Inverse Trigonometric Functions, Limits, Continuity & Differentiability,Method of Differentiation, Complex Number, Solution of Triangle


PART-1 : PHYSICSSECTION–I(i) : (Maximum Marks : 12)

� This section contains FOUR questions.� Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options

is correct.� For each question, darken the bubble corresponding to the correct option in the ORS.� For each question, marks will be awarded in one of the following categories :

Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases

1. In the figure shown block A of mass m is rigidly attached to a light spring of stiffness k andsuspended from a fixed support. Another block B of same mass is just placed on it & blocksare in equilibrium. Suddenly the block B is removed. Choose the INCORRECT optionafterward :

BA

k

(A) Block A will perform SHM

(B) Amplitude of oscillation of block A is mg

k

(C) Maximum speed acquired by the block A is 2mg

k

(D) Time period of oscillation is m

22k

p


2. Both the strings, shown in figure are made of same material and diameter of CD is double thatof AB. The pulleys are light. The speed of a transverse wave in the string AB is n1 and in CD it

is n2, then 2

1nn is :

(A) 1 (B) 2 (C) 2 (D) 21

3. When switch S is closed, then for what value of R will the time constant will be 100 ms.

R 600W

200W

40mH

(A) 400 W (B) 300 W (C) 200 W (D) 100 W


4. A series RLC circuit is activated by an ac source of voltage VS volt and variable angularfrequency (w) as shown in the circuit. VRL and VC are the potential drops across RL and Crespectively. Select the correct statement:

VS

CR L

(A)At low frequency limit, both VRL and VC are proportional to w

(B)At high frequency limit, VRL approaches VS but VC is proportional to 21w

(C)At high frequency limit, both VRL and VC are proportional to 21w

(D)At low frequency limit, VRL is proportional to 1w

, whereas VC approaches VS

SECTION-I(ii) : (Maximum Marks: 32)� This section contains EIGHT questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of

these four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to 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,

both of which are correct options.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.

� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correctoption(s) will result in –1 marks.

5. Choose the CORRECT option(s) :-(A) Waves from two coherent sources may be in same phase always at some points.(B) Waves from two incoherent sources have fixed phase difference at a point always.(C) Initial phase difference between the waves emitted by two coherent sources may vary

with time.(D) Waves from two coherent sources may be in opposite phase always at some points.


6. Figure shows the essential parts of an apparatus to demonstrate the Hall effect. Which of thefollowing statement (s) is/are correct ?

PConstantcurrent

QN

S

(A) In the arrangement above, the Hall potential difference is developed across PQ

(B) The magnitude of the Hall potential is greater if the applied magnetic flux density(magnetic field) is increased

(C) The magnitude of the Hall potential is less if the width PQ of the specimen is decreased

(D) Hall potential is independent of material used for conductor


7. A bar magnet is moved along the axis of copper ring placed far away from the magnet. Lookingfrom the side of the magnet, an anticlockwise current is found to be induced in the ring. Which ofthe following may be true?(A) The south pole faces the ring and the magnet moves towards it.

(B) The north pole faces the ring and the magnet moves towards it.

(C) The south pole faces the ring and the magnet moves away from it.

(D) The north pole faces the ring and the magnet moves away from it.

8. It is given that SS1 – SS2 = 2l

and 2 1S P S P2l

- = . Intensity from slit S2 is I0 then which are

INCORRECT.

SS2

S1

d

P

O

D

(A) Central maxima will form at point P.

(B) Central maxima will form at point O.

(C) Resultant intensity at P is less than 4I0.

(D) Resultant intensity at P is zero.Space for Rough Work

9. Consider a rope AB of non-uniform density as shown in figure. If we consider direction A toB as the direction of increasing x, with x = 0, at A, linear mass density of rope is given by

æ öm = mç ÷è øl

0

nx where n is a constant (n ³ 0) and l is the length of the rope.

xx = 0

A B

Now the rope is hanged vertically from a roof keeping end B attached to the roof and onepulse is produced at the lower end A and another pulse is produced at upper end B as shownin figure.

A

B

Choose the CORRECT statement(s) :-(A) Time taken by both pulse to reach other end is same.(B) Time taken by pulse to reach other end increases as value of n increases.(C) Acceleration of both pulses is constant during their journey from A to B or B to A for all

values of n.(D) Acceleration of pulses does not depend on value of n.

10. For the AC circuit shown, the reading of ammeter and voltmeter are 5A and 550 voltsrespectively, then

20mH10W 50mF

A

V

~

(A) average power delivered by the source is 250W(B) rms value of AC source is 50 volts(C) rms value of AC source is 100 volts(D) frequency of ac source is 100/2p Hz


11. A wave is represented by the equation :

y A sin 20 x 30 t6

pé ù= p + p +ê úë ûWhere x is in meters and t is in seconds. The expression represents :-

(A) Wave is travelling in the positive x direction with velocity of 1.5 m/s

(B) Wavelength of the wave is 10 cm

(C) Frequency of the wave is 15 Hz

(D) Wave is travelling along positive y-direction with velocity of 2

3 m/s.

12. A capacitor with charge Q on it is connected to an inductor L as shown in diagram at t = 0.When the switch is flipped from position 1 to 2, the current in the circuit is observed to be athalf of its maximum value. Then :-

C L L

12

(A) Charge on capacitor at the time was Q

2(B) Charge on capacitor at that time was

Q 3

2

(C) Total energy lost is 2Q

4C(D) Total energy lost is

2Q

8C


SECTION-II : (Maximum Marks: 18)� This section contains SIX questions.� The answer to each question is a NUMERICAL VALUE.� For each question, enter the correct numerical value (in decimal notation, truncated/rounded-

off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is 11.36777. ...then both 11.36 and 11.37 will be correct) by darken the corresponding bubbles in the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

•

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•

•

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0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

•

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� Answer to each question will be evaluated according to the following marking scheme:Full Marks : +3 If ONLY the correct numerical value is entered as answer.Zero Marks : 0 In all other cases.

1. In a Young's double slit experiment the light source is at distance l1 = 5 µm and l2 = 10 µmfrom the slits. The light of wavelength l = 500 nm incident on slits separated at a distanced = 10 µm. A screen is placed at a distance D = 2m way from the slits as shown in the figure.If 10 k maxima appear on the screen, the find the value of k. Round off your answer to thenearest integer, if required.

q

l1

l2

S S1

S2D

C

P

d


2. A particle of mass 'm' can move along x-axis of co-ordinate frame in a force field of stationarysources. Potential energy 'U' of system varies with position x of the particle according to theequation U K x= , where k is a positive constant. If the particle is projected from the origin

with a kinetic energy k', and its period of bounded motion is N mk'K 2

. Find the value of N?

3. A steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wireback and forth. A standing wave with three antinodes is created when the spring is stretched8.0 cm. What stretch of the spring (in cm) produces a standing wave with two antinodes ?

steel wire Pull

Spring

4. In the circuit shown power factor of box is given by 0.5 and power factor of circuit is given by32

. Current leading the voltage. The effective resistance of the box is made by using 5

resistances of equal value. Find the value of each resistance (Assume all the combination arein series).

Box

10W

~Space for Rough Work

5. In the figure circuit, if E = 20V, R1 = 2 ohm, R2 = 3 ohm, R3 = 6 ohm and L = 5 Henry. The ratioof current I1 just after pressing the switch S and long time after pressing the switch S is x/10.Find the value of x.

S

E R2

I3

I2I1

R3

L

R1

6. A superconducting current carrying ring of mass m = 40 gm and R = 2cm floats in the magneticfield of a magnet. If the field lines make an angle q = 30° with vertical and the ring is placed

co-axially, assuming i = 10A, find the magnetic field Br

. if answer is n

3p. Write the value of n.

N

B q

R



PART-2 : CHEMISTRYSECTION–I(i) : (Maximum Marks : 12)




1. 80 mCi [4ml aq. solution, t1/2 = 6 hrs] is given in the blood of an insect. After 6 hrs, activityobserved is 40000 dps/ml. Assuming that there is no loss of fluid from the blood of the insectin 6 hrs then calculate initial Volume of blood (in ml) in the insect is -(A) 29 (B) 33 (C) 76 (D) 37.5

2. If uncertainity in velocity of ground state electron in Bohr's hydrogen atom is 1%, thenminimum uncertainity in its position according to Heisenberg's uncertainity principle is.[mc = 9 × 10–31 kg, h = 6.6 × 10–34 J-sec.](A) 2.7Å (B) 2.7 nm (C) 2.7 pm (D) 2.7 cm

3. Which of the following statement is INCORRECT?(A) In the clear solution of BiCl3, when large quantity of water is added the white turbidity

of BiOCl is obtained(B) One of the final product of hydrolysis of XeF4 & XeF6 is same(C) Al4C3 produce C3H4 on hydrolysis(D) Hydrolysed product of BeCl2 undergoes polymerization

4. Which of the following is not suitable for synthesis of ethanoic acid?

(A) CH3–Br MgDry ether¾¾¾¾® 2

3

COH OÅ¾¾¾¾® (B) CH – C – O – CH3 3

O3H OÅ

¾¾¾¾®

(C) CH3 – Cl Ag C N- º¾¾¾¾¾® 3H OÅ¾¾¾¾® (D) CH – C – H3

O4 3(i)NH OH,AgNO(ii) HÅ¾¾¾¾¾¾¾¾®








5. Phenol react with CH – C – Cl3

O in presence of NaOH to form product A. A reacts with Br2 to

form products. Products react with HNO3 + H2SO4 followed by acidic hydrolysis gives finalproducts. All possible final products can be

(A)

OHO2N

Br

(B)

OH

NO2

Br(C)

OHO2N Br

(D) CH – C – OH3

O


6. CH – C – H3 CH –2

O

(A)

CF CO H33

B NH3 CDKOH, Br2 DD

NaNO + HCl2 E PCC F

B + CF CO H3 2

Find out the correct statement(s) using above reactions and products?(A) Reactant A and final product F can be differentiated by Iodoform test.(B) F is homologous of A(C) A and F are isomers(D) A and F both give positive Tollen's test with Ammonical silver nitrate.

7. OH CrO / H3 HD

H N – OH (PH = 4 to 5)2 H3 4POD

(X) + (Y)

If acidic hydrolysis of y give positive Azodye test with benzenediazonium chloride.

The correct statement(s) about final product X and Y is/are

(A) X is

O

NH

(B) Y is NH

O

(C) Y is

O

NH

(D) Y is more reactive than X towards electrophilic substitution reaction

8. B2H6 + NH3 ¾® Ionic product T 200 C= °¾¾¾¾® 'X'Select CORRECT option for 'X'.

(A) 'X' is aromatic

(B) 'X' is known as inorganic benzene

(C) Back bonding takes place in 'X'

(D) 'X' has only two types of bond length data

9. Among the given following cations :-

Zn2+, Fe2+, Fe3+, Cu2+

Which can produce coloured ppt./solution with K4[Fe(CN)6]?

(A) Zn2+ (B) Fe3+ (C) Fe2+ (D) Cu2+

10. Solution of Na S O + aqueous solution of CuSO 2 2 3 4 'Y'white ppt.

excess of Na S O

solution2 2 3

'Z' soluble

Which of the following statement is/are CORRECT for above reaction?(A) Redox reaction take place when 'Y' reacts with excess Na2S2O3

(B) Z Þ Na4[Cu6(S2O3)5]

(C) Y Þ CuS2O3

(D) Anhydrous form of CuSO4 is colourlessSpace for Rough Work

11. Select the correct statement(s) about nucleus -

(A) Higher binding energy suggest more stability of the nucleus

(B) Higher binding energy per nucleon suggest more stability of the nucleus

(C) High n/p suggest high probability of 01- b decay

(D) High n/p suggest high probability of 01+ b decay

12. In a rock salt structure of A+B– , select the correct options(s)

(A) A+ is forming fcc while B– is going to all octahedral void location(B) B– is forming fcc while A+ is going to all octahedral void location

(C) a r r2 + -= + must be correct

(D) 2a 4r-= must be correctSpace for Rough Work


off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

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+

0

–

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1. Find the total number of chemical species which are non planar & lone pair of central atomoccupy equitorial orbital.SF4, 5XeF1 , 3I1 , BrF5, XeO2F2, ClF3, XeO3

2. Find the total number of sulphide ppt. which are soluble in yellow ammonium sulphideCuS, HgS, CdS, SnS, SnS2, As2S5, Sb2S5, Bi2S3, PbS, Sb2S3

3. Calculate total number of natural amino acids which gives positive Isocyanide test

(a)

COOH

HH N2

CH3

(b)

COOH

HH N2

CH2

Ph

(c)

COOH

HH N2

Ph

(d) NH

C – COOHH

(e)

COOH

HH N2

CH3

C OHH


4. Find out the total number of compounds which undergoes acetylation with excess of

CH – C – Cl3

O and increased in molecular weight by 126.

(i)

OHNH2

CH2 – OH

(ii)

NH – C – CH3

NH2

HO

O

(iii)

CHO

OHHCH2 – OH

HHO

(iv) NH2

CH2 – OH

NH2

(v)

OHH

HHOOHH

CH2 – OH

CHO

OHH(vi)

C – OH

OHHCH3

HH N2

O

5. Electron is present in nth excited state of He+. When electron comes to ground state, theemitted photon is absorbed by metal of work function (1eV). Emitted photoelectron has aminimum de-Broglie wavelength of 1.73 Å. Hence 'n' is_____.

6. 5 mol A (t1/2 = 10 min) is introduced into a closed container where it converts into B & C by

parallel first order kinetics with effective energy of activation 7.6 kcal/mol as : A

B

C

B

A

6kcal

3kcal

2kcal

10kcal

Reaction

En

C

What would be the mole fraction of B in the mixture after 20 min. from beginning.Space for Rough Work


PART-3 : MATHEMATICSSECTION–I(i) : (Maximum Marks : 12)




1. ( )®¥

æ öp + pæ ö+ -ç ÷ç ÷+ +è øè øx

x 3 2 xlim 2x 3 cos sin6x 1 6x 1 equals

(A) 6

12p +

(B) 6

24p +

(C) 6

12p -

(D) p - 624

2. Number of complex numbers satisfying |z| = 1 and z z 1z z+ = is

(A) 2 (B) 4 (C) 6 (D) 8


3. Complete set of values of a for which quadratic equation x2 – (5 – a)x + a2 – 11a + 22 = 0 has oneroot greater than 2 and another less than 2 is

(A) 9 17 9 17,2 2

æ ö- +ç ÷è ø

(B) 11 33 11 33,2 2

æ ö- +ç ÷è ø

(C) 9 17 9 17,2 2

æ ö- + -ç ÷è ø

(D) 11 33 11 33,2 2

æ ö- + -ç ÷è ø

4. If ( )( )

cos m 1sin m 1

q - a +=

q + a - then m is

(A) tan tan4 4p pæ ö æ ö- q - aç ÷ ç ÷

è ø è ø(B) tan tan

4 4p pæ ö æ ö- q + aç ÷ ç ÷

è ø è ø

(C) tan tan4 4p pæ ö æ ö+ q - aç ÷ ç ÷

è ø è ø(D) tan tan

4 4p pæ ö æ ö+ q + aç ÷ ç ÷

è ø è ø








5. The area of equilateral triangle ABC is 1 cm2. Points E, F and G are one sides AB, BC and CArespectively such that AE : EB = BF : FC = CG : GA = 3 : 1. If area of DFEB is D1 and area ofDEFG is D2 then

(A) 21

1 cm4

D = (B) 21

3 cm16

D = (C) 22

7 cm16

D = (D) 22

1 cm4

D =

6. Given ( )

ì pæ ö- ç ÷ï è ø ¹ï= pæ öí - ç ÷ï è øï

=î

n

n

n x sin4x x 0

ƒ x n x cos4x

1 x 0

, then the values of n for which function ƒ(x) is continuous

at x = 0 is/are(A) –2 (B) 0 (C) 2 (D) 3

7. A complex number 'z' can be expressed in polar form as (|z|, arg(z)), where |z| representsmodulus and arg z represents argument of complex number z. I f arg z Î [0, 2p), then which ofthe following represents cube roots of z = 1 + i in polar form

(A) 6 2,12pæ ö

ç ÷è ø

(B) 6 32,4pæ ö

ç ÷è ø

(C) 6 112,12pæ ö

ç ÷è ø

(D) 6 172,12pæ ö

ç ÷è ø

8. If a, b, c, d are lth, mth, nth and pth terms respectively of a sequence and roots of equation(a2 + b2 + c2) x2 – 2(ab + bc + cd) x + b2 + c2 + d2 = 0 are real then

(A) a,b,c,d are in GP. (B) l, m, n, p are in AP.

(C) b2 + c2 = ac + bd (D) b2 + c2 = ad + bc

9. For which values of 'm' the line y = mx cuts the graph of y = sin–1(sin x) in exactly 5 points ?

(A) 15 (B)

14

- (C) 18

- (D) 19

-

10. The number of ordered pairs (x, y) such that sin3x = 12 siny and cos3x =

12 cosy

where x Î [0, 2p] and y Î [0, 4p] is greater than(A) 2 (B) 4 (C) 6 (D) 8

11. If x1, x2 are the solutions of the equation 22

ax px 0p

+ - = where 1a2 2

=+

and p is a non-zero

real number then possible values of 4 41 2x x+ can be

(A) 1 (B) 4 (C) 19 (D) 200

12. Let z be a complex number such that |z – 1| = 1 then possible values of arg 1 1z 2

æ ö-ç ÷è ø

can be

(A) p

-2 (B) 3

p- (C) 3

p(D) 2

p



off to the second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is11.36777..... then both 11.36 and 11.37 will be correct) by darken the corresponding bubblesin the ORS.For Example : If answer is –77.25, 5.2 then fill the bubbles as follows.

0 0 0

+

0

–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

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–

0 01 1 1 1 1 12 2 2 2 2 23 3 3 3 3 34 4 4 4 4 45 5 5 5 5 56 6 6 6 6 67 7 7 7 7 78 8 8 8 8 89 9 9 9 9 9

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1. Given ƒ(x) = x2 – 2|x| and a and b are number of points of discontinuity and non differentiability

of g(x) respectively, where g(x) is defined as ( )( )( )

min ƒ t ; 2 t x for 2 x 0g xmax ƒ t ; 0 t x for 0 x 3ì - £ £ - £ <

= í£ £ £ £î

then value of a + b equals

2. Let ƒ(x3 + y3) = xƒ(x2) + yƒ(y2) for all x, y Î ¡ and ƒ(x) is differentiable. If ƒ'(0) = 5, then findvalue of ƒ'(5).

3. If function ( )( )22

1 cos x ; x 1x 1

ƒ x ax b ; 1 x 1x 1 ; x 1n x

+ pì < -ïp +ïï= + - £ £íï -ï >ïî l

is continous at all x Î ¡ then find value of ab .



4. If tan–1x + tan–1y = cot–1z such that x + y + z = 3 , then value of 1xyz

is

5. Find the value of 3/21 1 1 1y 6 log 4 4 4 ...

3 2 3 2 3 2 3 2

é ùê ú= + - - -ê úë û

6. Let function ƒ(x) = x4 + ax3 + bx2 + cx + d such that ƒ(–1) = 100, ƒ(–2) = 200, ƒ(–3) = 300 then

the value ( ) ( )ƒ 10 ƒ 14

16+ - equals

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