Name of the candidate (In Capital Letters)

I have read all the instruction and shallabide by them.

.....................................................................(Signature of the candidate)

I have verified all the information filled inby the candidate.

.....................................................................(Signature of the Invigilator)

Enrollment Number

Duration : 2 Hours Max. Marks : 360

Talent Search Exam. 2018for class XII

Please read the instructions carefully. You are alloted 5 minutes specifically for this purpose.

TEST

CODE 1201 A

INSTRUCTIONSA. General :1. This booklet is your question paper containing 90 Questions. Attempt any one of the Biology OR

Mathematics. The booklet has 20 Pages.

2. The question paper contains blank space for your rough work. No additional sheets will be provided for roughwork.

3. It is mandatory to use Blue or Black Ball Point Pen to darken to appropriate circle in the answer sheet.

4. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electron ic gadgetsin any form are not allowed to be carried inside the examination hall.

5. Fill in the boxes provided below on this page and also write your Name and Roll Number in the space provided.

6. Do not use white-fluid or any other rubbing material on answer sheet. Before handing over the answer sheet to theinvigilator, candidate should check that Roll No, Test code and Book Code have been filled and marked correctly.Immediately after the prescribed examination time is over, the Answer sheet is to be returned to the invigilator.

B. Filling the Answer Sheet :7. On Side-1 of Answer Sheet write your name, Enrollment Number and Name of the centre in the respective

boxes. Do not write anything on Side-2.8. Put your signature space provided on the Answer Sheet affirming that you have verifed this.9. All question carry +4 Marks for Right Answer and –1 for Wrong Answer.

BOOKLET

PROCEDURE OF FILLING UP THE ANSWERS IN ANSWER SHEET

Wrong Filling Right Filling

A B C D Tick mark A B C D Fully darken with Pen

A B C D Cross mark A B C D Fully darken with Pen

A B C D Half filled or semi dark A B C D Fully darken with Pen

A B C D Light filled A B C D Fully darken with Pen

You can never quit. Winners never quit, and quitters never win.

(Page No. : 2 of 20)

PHYSICS1. In the figure shown, a parallel beam of light is incident on the plane of the slits of a Young’s

double slit experiment. Light incident on the slit, S1 passes through a medium of variable refractiveindex m = 1 + ax(where ‘x’ is the distance from the plance of slits as shown), upto a distance‘ ’ before falling on S1. Rest of the space is filled with air. If at ‘O’ a minima is formed, then theminimum value of the positive constant a (in terms of and wavelength’’ in air) is :

(A) (B)

2 (C) 2

(D) None of these

2. A ray of light is incident on a thin film. As shown in figure M,N are two reflected rays and P,Qare two transmitted rays. Rays N and Q undergo a phase change of . correct order of therefracting indices is:

(A) n2 > n3 > n1 (B) n3 > n2 > n1 (C) n3 > n1 > n2 (D) None of these

3. A broad source of light (=680nm)illuminates normally two glass plates 120mm long that touchat one end and are separated by a wire 0.034 mm in diameter at the other end. The total numberof bright fringes that appear over the 120 mm distance is:

(A) 50 (B) 100 (C)200 (D) 400

Comprehension (4 to 6)All objects referred to the subsequent problems lie on the principle axis.

4. If light is incident surface 1 from left, the image formed after the first refraction is definitely:(A) Real for a real object (B) Virtual for a real object(C) Real for a virtual object (D) Virtual for a virtual object

5. In above question if the object is real, then the final image formed after two refractions:(A) may be real (B) may be virtual (C) must be virtual (D) both A and B

(Page No. : 3 of 20)

6. If light is incident on surface 2 from right then which of the following is true for image formed aftera single refraction.(A) Real object will result in a real image (B) Virtual object will result in a virtual image(C) Real object will result in a virtual image (D) Virtual object will result in a Real image

7. Switch S is closed for a long time at t = 0. It is opened, then :

(A) total heat produced in resistor R after opening the switch is 12

2

2LVR

(B) total heat produced in resistor R1 after opening the switch is 12

2

2

LVR

(C) heat produced in resistor R1 after opening the switch is 12

22

21 2

R LV(R +R )R

(D) no heat will be produced in R1

8. A magnetic field (B), uniform between two magnets can be determined measuring the induced voltagein the loop as it is pulled through the gap at uniform speed 20m/sec. Size of magnet and coil is 2cm ×1cm × 2cm and 4cm × 6cm as shown in figure. The correct variation of induced emf with time is:(Assume at t = 0, the coil enters in the magnetic field) :

Comprehension (9 to 11)An infinitely long wire lying along z-axis carries a current I, flowing towards positives z-diretion.There is no other current, consider a circle in x-y plane with centre at (2 meter, 0, 0) and radius

(Page No. : 4 of 20)

1 meter. Divide the circle in small segments and let d denote the length of a small segment in

anticlockwise direction, as shown.

9. The path integral

B.d of the total magnetic field B along the perimeter of the given circle is,

(A) 0I8 (B)

0I2 (C) 0I (D) 0

10. Consider two points A(3, 0, 0) and B(2, 1, 0) on the given circle. The path integral

B

A

B.d of the

total magnetic field B along the perimeter of the given circle from A to B is,

(A) –10I 1tan12 2 (B)

–10I 1tan2 2 (C)

–10I 1tan2 2 (D) 0

11. The maximum value of path integral

B.d of the total magnetic field B along the perimeter of the

given circle between any two points on the circle is

(A) 0I12 (B)

0I8 (C)

0I6 (D) 0

12. If i1 = 2 sin t and i2 = 4 cos t, then i3 is

(A) 5 sin (wt +530) (B) 5 sin ( t + 370) (C) 5 sin ( t + 450) (D) 5 cos ( t + 530)

13. In the circuit shown the capacitor of capacitance C is initially uncharged. Now the capacitor isconnected in the circuit as shown. The charge passed through an imgianary circular loop parallelto the plates (also circular) and having the area equal to half of the area of the plates, in onetime constant is:

(A)

1C 1–e (B)

C 11–2 e (C)

C4

(D) C

14. Two long stright with the same cross-section are arranged in air, parallel to one another. Thedistance between the axis of the wire in n timeslarger then the radius of wires' cross-section.Capacitance of the wires per unit length would be (Take >>1)

(Page No. : 5 of 20)

(A)

02I (B)

02I (C)

0I (D) Information insufficient

15. A parallel plate capacitor is immersed, in a liquid dielectric having dielectric constant as shownin the figure. Find the force acting on a unit surface of the plate from the dielectric.

(A) 2

02V

2d(B)

20

2X

– 1 V

2d(C)

2

2V

2d(D)

20

2– 1 V

2d16. When agalvanometer is shunted with a 4 resistance, the deflection is reduced to one - fifth. If the

galvanometer is further shunted with a 2 wire, the further reduction (find the ratio of decrease incurrent to the previous current in) in the deflection will be (the main current remains the same).(A) (8/13) of the deflection when shunted with 4 only(B) (5/13) of the deflection when shunted with 4 only(C) (3/4) of the deflection when shunted with 4 only(D) (3/13) of the deflection when shunted with 4 only

17. Two circular ring of identical radii and resistance of 36W each are placed in such a way that theycros each other's centre C1 and C12 as shown in figure. Conducting joints are made atintersectionpoints A and B of the rings. An ideal cell of emf 20Volts is connected across AB. Thepower delivered by cell is

(A) 80 watt (B) 100 watt (C) 120 watt (D) 200 watt

18. Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is firstconnected at point A and zero deflection is observed at length P J = 10 cm. In second case it isconnect at point C and zere deflection is observed at a length 30cm from P. Then the unknownreitance X is

(A) 2R (B) R2 (C)

R3 (D) 3R

(Page No. : 6 of 20)

19. In the figure shown, initially the spring of negligible mass is in underformed state and the block haszero velocity E is a uniform electric field. Then :

(i) The maximum speed of the block will be QEmk

(ii) The maximum speed of the block will be 2QEmk

(iii) The maximum compression of the spring will be QEK

(vi) The maximum compression of the spring will be 2QE

K(A) Only (i) and (iii) are correct (B) Only (i) and (iv) are correct(C) Only (ii) and (iii) are correct (D) Only (i) and (iv) are correct

20. Two infinitely large charged planes having uniform surface charge density + and – are placedalong x-y plane and yz plane respectively as shown in the figure. Then the nature of electric lines offorces in x-z plane is given by :

(A) (B) (C) (D)

21. Two identical small balls each have a mass m and charge q. When placed in a hemispherical bowl ofradius R with frictionless, nonconductive walls, the beads move, and at equilibrium the line joining theballs is horizontal and the distance between them is R (figure). Neglect any induced charge on the

hemispherical bowl. Then the charge on each bead is : (here K = 0

14 )

(A) q = R

1/ 2mgK 3

(B) q =

1/ 2mgRK 3

(C) q = R

1/ 23mgK (D) q =

1/ 23mgRK

22. In an particle is particle is 48 MeV and Q-value of the reaction is 50 MeV. The mass numberof the mother nucleus is:- (Assume that daughter nucleus is in ground state)(A) 96 (B) 100 (C) 104 (D) none of these

(Page No. : 7 of 20)

CHEMISTRY26. Gas A (1 mol) dissociates in a closed rigid container of volume 0.16 lit. as per following reaction.

2A (g) 3B (g) + 2C (g)If degree of dissociation of A is 0.4 and remains constant in entire range of temperature, then the correctP vs T graph is [Given R = 0.08 lit-atm/mol/K]

(A) (B) (C) (D)

27. A definite amount of solid NH4HS is placed in a flask already containing ammonia gas at a certaintemperature and 0.50 atm pressure. NH4HS decomposes to give NH3 and H2S and at equilibrium totalpressure in flask is 0.84 atm. The equilibrium constant for the reaction is :(A) 0.30 (B) 0.18(C) 0.17 (D) 0.11

28. The correct pKa order of the follwoing acids is :

23. A radioactive nucleus 'X' decays to a stable nucleus 'Y'. Then the graph of rate of formation of'Y' against time 't' will be:

24. The photon radiated from hydrogen corresponding to 2nd line of Lymn series is absorbed by ahydrogen like atom 'X' in 2nd excited state. As a result the hydrogen like atom 'X' makes atranstion to nth orbit. Then,(A) X = He+, n =4 (B) X = Li++, n = 6 (C) X = He+, n = 6 (D) X = Li++, n = 9

25. When an electron accelerated by potential difference U is bombarded on a specific metal, theemitted X-ray spectrum obtained is shown in adjoining graph. If the potential difference is reducedto U/3, the correct spectrum is

(Page No. : 8 of 20)

(A) I > II > III (B) III > II > I (C) III > I > II (D) I > III > II

29. Basicity order in following compound is :

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

30. Assuming complete precipitation of AgCl, calculate the sum of the molar concentration of all the ions if 2 litof 2M Ag2SO4 is mixed with 4 lit of 1 M NaCl solution is :(A) 4M (B) 2M (C) 3 M (D) 2.5 M

31. Consider the following Galvanic cell.

By what value the cell voltage change when concentration of ions in anodic and cathodic compartmentsboth increased by factor of 10 at 298 K(A) +0.0591 (B) –0.0591 (C) –0.1182 (D) 0

32. A 0.001 molal solution of a complex [MA8] in water has the freezing point of –0.0054°C. Assuming 100%ionization of the complex salt and Kf for H2O = 1.86 km–1, write the correct representation for thecomplex(A) [MA8] (B) [MA7]A (C) [MA6]A2 (D) [MA5]A3

33. The activation energies of two reactions are Ea1 and Ea2 with Ea1 > Ea2. If the temperature of thereacting system is increased from T1 to T2 predict which of the following alternative is correct

(A) 2

2

1

1K

'KK

'K (B)

2

2

1

1K

'KK

'K (C)

2

2

1

1K

'KK

'K (D)

2

2

1

1K

'K2K

'K

34. Which is not position isomer of A?

(Page No. : 9 of 20)

(A) (B) (C) (D)

35. Which of the indicated H in the following is most acidic ?

(A) X (B) Y (C) Z (D) p36. Which of the following compounds will not show resonance ?

(A) (B)

(C) (D)

T

0

37. Which of above curve is wrongly presented.(A) C CO2 (B) Pb PbO (C) Zr ZrO2 (D) Mg MgO

(Page No. : 10 of 20)

38. Which of the above metal oxide is having minimum thermal decomposition temperature.(A) CaO (B) FeO (C) ZrO2 (D) MgO

39. Which of the following metal's oxide can be reduced by Fe as reducing agent at temperature T1(A) Zr (B) Ca (C) Mg (D) None of these

40.. Which of the following process is not involved in extraction of Fe.(A) Gravity separation (B) Leaching(C) Roasting (D) Carbon reduction

41. Which of the following properties is the dissimilarities between NH3 and PH3.(A) Colour of product on reaction with HCHO(B) Formation of addition product with different metal chloride(C) Absorption by bleaching powder(D) Burning characteristics in air

42. Which of the following statement is correct for the following complex. [Fe(H2O)5NO]SO4.(A) The E.A.N. value of Fe in this complex depends on the charge of NO ligand.(B) The E.A.N. value of Fe in this complex does not depends on the charge of NO ligand.(C) The hybridisation of the central atom is d2sp3.(D) It is paramagnetic with = 1.73 B.M.

43.42

3

SOH

HNO (A)

,FeCl

Cl

3

2 (B) 22NHNH (C)

(C) is:

(A) (B) (C)

2

(D)

44.

Order of rate of electrophilic addition reaction with HBr will be(A) IV > I > III > II (B) I > II > III > IV(C) I > III > II > IV (D) IV > I > II > III

(Page No. : 11 of 20)

45. (a) Total number of stereoisomer in given compound are?

33 CHCCCHCHCHCHCH||

MeCl

(b) Total number of products on monochlorination of n-pentane in presence of sunlight are?(c) Number of structural isomers of C3H9N are ?(d) How many cyclic alkenes (excluding stereoisomer) will produce methyl cyclohexane on

catalytic hydrogenation.(A) 4, 4, 3, 5 (B) 1, 2, 4, 4 (C) 4, 4, 4, 4 (D) 4, 3, 2, 1

46. A reaction at 312 K with G° = – 1798 J /mol consists of 3 mole of substance 'A', 6 mole of substance 'B'and 3 mole of substance 'C'. If A, B and C are in equilbrium, then the reaction could be(A) A + B C (B) A B + 2C (C) 2A B + C (D) A + B 2C

47. Select the correct statement about FCC (ABCAB...) structure.

(A) Distance between nearest octahedral void and tetrahedral void is 4

a3

(B) Distance between two nearest octahedral void is 0.707 a

(C) Distance between layer A and B is 32r2

(D) All of these

48. Match the column and select the correct option given below:Column I Column II

(I) BF2Cl (P) Molecules in the column-I is having maximum number of atomslying in the same plane.

(II) B3N3H6 (Q) Molecules having maximum number of lone pair.(III) SF4 (R) Molecule is Non polar.(IV) XeO4 (S) Molecule is planar.

(T) px, py and pz orbitals are involved in the hybridisation of thecentral atom.

(A) I R, II P,S, III Q,R, IV R,S(B) I S, II P,R,S, III Q,T, IV R,T(C) I S, II P,R,S, III P,Q, IV R,Q(D) I P, II P,R, III Q,S, IV R,T

49. Match the column and select the correct option given below:Column I Column II

(I) [Cr(H2O)5Br]2+ (P) Paramagnetic in nature(II) [Cu(NH2CH2CH2NH2)Cl4]

2– (Q) Geometrical isomerism is exhibited(III) [Pt(OX)2]

2– (R) Optical isomerism is exhibited(IV) [Fe(OH)4]

r (S) Do not follow Sidewick E.A.N. rule(T) Complex having symmetrical bidentate ligand

(Page No. : 12 of 20)

(A) I P,S, II P,S,T, III S,T, IV P,S(B) I P,R, II P,S, III S, IV P,Q(C) I R,S, II P,R,S, III P,S, IV R,Q(D) I P, Q, II P,R,S, III Q,S, IV R,T

50. What percentage of acetic acid molecules are unionised in 5 × 10–8M-CH3COOH solution at 25°C? Ka

of CH3COOH = 1.6 × 10–5.(Take 06.225.4 )(A) 0.650 (B) 0.700 (C) 0.800 (D) 0.600

IMPORTANT INSTRUCTION :-Attempt any one in Biology OR Mathematics by following the same questionnumber given in test booklet. Leave blank circle against non-attempting subject.You are not allowed to change any question number.

BIOLOGY51. What type of tree habit is seen in Dalbergia?

(1) Caudex (2) Excurrent(3) Columnar (4) Deliquescent

52. In castor, Luffa and Vitis venation is(1) Reticulate convergent(2) Parallel convergent(3) Reticulate divergent(4) Parallel divergent

53. Calculate DPD of a fully plasmolysed cell if itsO.P. = 12 atm and T.P. is 3 atm

(1) 9 (2) 15

(3) 12 (4) 6

54. Long distance transport of substances like water,mineral and organic solute within a plant can not beby diffusion alone because

(1) Diffusion is meant only for gaseous substances

(2) It can not occur in medium separated bymembranes

(3) It is rather a slow process

(4) It shows saturation effects

55. Essential element required for uptake and utilisationof calcium, membrane functioning, cell elongationand carbohydrate translocation in plants is

(1) Zn (2) B

(3) Mo (4) Ca

56. Element which promotes synthesis of cytochromesand when deficient produce whip tip of maize is

(1) Zn (2) Mn

(3) Si (4) Fe

57. Light dependent release of CO2 from photosyntheticorgans involves

(1) Transamination of glycolate

(2) Loss of six carbons from 6 molecules ofphosphoglycolic acid

(3) Transamination of serine in peroxisome

(4) Decarboxylation occurs in mitochondria tosynthesise glycine

58. In given diagram effect of O2 concentration on therate of net photosynthesis is demonstrated for twoplant types A and B. Which of the following statementis incorrect for them?

(1) B plants have safety value protecting fromphotoinhibition

(2) A plants are adapted to tropical climate(3) B plants are evolutionary less advanced(4) A plants show dimorphic stomata with agranal

condition in mesophyll cell

59. Which of the following plant does not reproducevegetatively by leaves?

(1) Bryophyllum (2) Begonia

(Page No. : 13 of 20)

(3) Saintpaulia (4) Dalbergia

60. In which of the following group generally syngamydoes not occur inside the body?

(1) Bryophytes (2) Pteridophytes

(3) Algae (4) Gymnosperms

61. Which of the following is incorrectly matched w.r.tchromosome number in meiocyte?

(1) Ophioglossum – 630

(2) Onion – 16

(3) Zea mays – 34

(4) Pisum sativum – 14

62. The number of phenotypes and types of gametes ina trihybrid cross AaBbCc × AaBbCc will be

(1) 8 and 64 (2) 8 and 8

(3) 8 and 27 (4) 27 and 27

63. The genotypic and phenotypic ratio is same in caseof

(1) Recessive epistasis(2) Multiple alleles

(3) Incomplete dominance

(4) Dominant epistasis

64. In a typical monohybrid cross, we have crossed atall plant with another tall plants, both the parentsare heterozygous for concerned trait, which of thefollowing result cannot be expected?

(1) 25% tall homozygous

(2) 25% dwarf homozygous

(3) 50% tall heterozygous(4) 66.7% tall heterozygous

65. Backbone of a DNA polynucleotide chain is formeddue to(1) Phosphate(2) Sugar and phosphate(3) Sugar(4) Sugar and nitrogen base

66. Generally nucleosomal histones are rich in the(1) Basic amino acids like lysine and arginine(2) Acidic amino acids like aspartic acid and

glutamic acid(3) Polar amino acids like serine, threonine and

tyrosine(4) Non-polar amino acids like glycine, alanine and

valine

67. A typical nucleosome contains(1) 200 bp of DNA helix(2) 200 bp of RNA helix(3) 100 nucleotides of DNA helix(4) 400 nucleotides of RNA helix

68. First biological agents and their products used tocontrol weeds were

(1) Bacterial (2) Fungal

(3) Algal (4) Viral

69. Which step in sewage treatment rely on biologicaldegradation?

(1) Primary (2) Secondary

(3) Tertiary (4) Chlorination

70. Secondary treatment for sewage does not involves

(1) Aeration (2) Microbes

(3) Shreeding (4) Flocs

71. Which stage of Plasmodium is infective to femaleAnopheles, is

(1) Sporozoite (2) Gametocyte

(3) Merozoite (4) Cryptomerozoite

72. The causative agent of Elephantasis is

(1) Ascaris lumbricoides

(2) Fasciola hepatica

(3) Wuchereria bancrofti

(4) Ancylostoma duodenalae

73. Which one of the following is odd w.r.t. their sourceof production?

(1) Marijuana (2) Hashish

(3) Charas (4) Smack

74. Which glycoprotein of the protein coat of the HIVvirus helps in attachment with the CD4 receptors ofthe cell?

(1) GP 120 (2) GP41

(3) P-17 (4) P-24

75. Which one of the following cannot be treated as theprimitive sign of cancer?

(1) Rapid weight loss without apparent cause

(2) A blemish or mole that enlarges, bleeds or itches

(3) Persistant hoarseness of voice

(4) Angiogenesis in the secondary tumors

(Page No. : 14 of 20)

76. A mode of asexual reproduction in which nucleusdivides into several daughter nuclei, followed by thesimultaneous divisions of cytoplasm is

(1) Sporulation (2) Multiple fission

(3) Fragmentation (4) Binary fission

77. If only females are produced parthenogenetically thecondition is Thelytoky and the best example of it is

(1) Aphis (plant lice) (2) Rotifers

(3) Drones (4) Lacerta saxicola

78. Membranous part of urethra carries

(1) Only the secretion of seminal vesicle

(2) Only semen

(3) Only urine

(4) Both urine and semen

79. Entry of sperm into the ovum restarts the cell cycleby

(1) Breakdown of metaphase promoting factor

(2) Release of anaphase promoting complex

(3) Zona reaction which constitute fast block tocheck polyspermy

(4) Both (1) & (2)

80. Which gland of external genitilia in female opens onthe either side of urethral orifice?

(1) Bartholin’s gland

(2) Gland of tyson

(3) Greater vestibular glands

(4) Skene’s glands

MATHEMATICS81. If

nk

1k42

1

kk2k2tan = tan–1

76

, then the value of 'n' is equal to

(A) 2 (B) 3 (C) 4 (D) 5

82. Range of the function f(x) = |xcos|cos||xsin|sin| 11 is

(A) {0} (B) 2/,0 (C) ,0 (D) none of these

83. If f(x) = x3 + 2x2 + 3x + 4 and g(x) is the inverse of f(x) then g(4) is equal to -

(A) 41

(B) 0 (C) 31

(D) 4

84. Let 0xlim 2

2

x]x[

= and 0xlim 2

2

x]x[

= m, then

(A) exists but m does not (B) m exists but does not(C) and m both exist (D) neither nor m exists

85. The function f(x) is defined by f(x) =

1xif4

1xor1x43if)5x2x(log 2

3x4 is

(A) continuous at x = 1(B) discontinuous at x = 1 since f(1+) does not exist though f(1–) exists.(C) discontinuous at x = 1 since f(1–) does not exist though f(1+) exists.(D) discontinuous since neither f(1–) nor f(1+) exists.

86. The value of 0xlim

x/1

xlnx

xx)12ln(x

exsin)12(e

x

is equal to-

(A) e (B) 2 n e (C) e n 2 (D) None of these

87. The jump of discontinuity for the function at x = 0, (where [.] denotes greatest integer function and{.} denotes fractional part of x).

(Page No. : 15 of 20)

f (x) =

is :

(A) e1 e 1 (B) e1 e 2 (C) 1 (D) 1 + e e1

88.x1

0x xxcos1xlim

is equal to

(A) – 21

(B) 4 (C) 21

e

(D) 41

e

89. If nlim

n

2k

1

)1k(kk)1k)(2k)(1k(1

cos = k

120, find the value of k.

(A) 702 (B) 720 (C) 620 (D) 420

90. Find the number of points at which the function

f(x) =

1x,2xsin

1x,]x[|3x2|

is not differentiable in [0, 2]

(A) 1 (B) 2 (C) 3 (D) 4

91. If A =

22

, B =

5

6, C =

11

are such that AB = C, then absolute value of |A| is

(A) 61

(B) –30 (C) 272

(D) 361

92. If 7x4x1x23

x32xx7x24x2x73x2x

2

2

2

= ax6 + bx5 + cx4 + dx3 + ex2 + fx + g, then

the value of g is(A) 2 (B) 1 (C) 2 (D) none of these

93. Given

= n 2, then the value of

dx is equal to :

(A) n 2 (B) n 2 (C)

n 2 (D) + n 2

94. nlim

33

2

1n1

+ 33

2

2n2

+ 33

2

3n3

+ .................. + n94

is equal to

(A) n 3 (B) 23n2 (C) 3

2n3 (D) n 2

95.

3

1 dx)x(cotcot is equal to

(A) 22 (B) 32 (C) 92 (D) 162

(Page No. : 16 of 20)

96. A =

112121321

, then det(Adj (AdjA))

(A) 16 (B) 162 (C) 163 (D) 164

97. If f : [0, 1] (0, ) such that 1

0

1dx)x(f , 1

0

xdx)x(fx and 1

0

22 xdx)x(fx , then

(A) f(x) = 5 (B) f(x) = 8(C) f(x) is not possible (D) f(x) = 2x – 1

98. The solution of the differential equation(x2 sin3 y – y2 cos x) dx + (x3 cos y sin2 y – 2y sin x) dy = 0 is

(A) x3 sin3 y = 3y2 sin x + C (B) x3 sin3 y + 3y2 sin x = C(C) x2 sin3 y + y3 sin x = C (D) 2x2 sin y + y2 sin x = C

99. Let f(x) be defined as

f(x) =

–1 2tan – 5x , 0 x 1–6x, x 1

f(x) can have a maximum at x = 1 if value of is(A) 0 (B) –1 (C) –tan 1 (D) –2

100. 1 1 1 1f x sin cosec sin x cos sec cos x has

(A) exactly two values (B) one value

(C) undefined (D) infinite values

101. Number of solutions to equation

1 1| sin | cos | | | cos | sin ||x x- -+1 1sin | cos | cos | sin |,x x- -= - if 0,4x pÎ is

(A) 1 (B) 2 (C) 4 (D) 8

102. Range of the function ‘f ’ defined by 1

cosf x

xé ù

= ê úë û

, where [.] and {.} denotes the greatest integer and

fractional part function respectively is .....

(A) set of integers (B) set of all natural numbers

(C) {2, 3, 4, ......} (D) {1}

103. If 20

ax x

x

e e xLt bx

(finite) then _____

(A) 2, 0a b (B) 30,2

a b (C) 32,2

a b (D) 0, 2a b

(Page No. : 17 of 20)

104. Let cos ,f x x

π x1,-sinx

π][0, x,xt0:f(t)minimumg(x) , then

(A) g(x) is discontinuous at x (B) g(x) is continuous for [0, )x

(C) g(x) is differentiable at x (D) g(x) is differentiable for [0, )x

105. If f(x) = [x] + [x + 1/3] + [x + 2/3], then ([.] denotes the greatest integer function)

(A) f(x) is continuous at x = 1, 10, 15 (B) f(x) is continuous at x = n/3, where n is any integer

(C) 3/2

0dx)x(f = 1/3 (D) 3/2x

lim f(x) = 2

106. The set of all values of a for which the function 54 1 3 log 5

1af x x x

a

de-

creases for all real values of x is

(A) , (B) 1,

(C) 5 273, 2,

2

(D) 3 214, 1,

2

107. If 0(3)f'R,x0,(x)f" and 2tan 2 tan 4 ,0 ,2

g x f x x x then g x increas-

ing in

(A) 0.4

(B) ,6 3

(C) 0,3

(D) ,4 2

108. The position vector of a point P is r xi y j zk where x, y, z N and a i 2 j k

.

If r . a 20

, the number of possible position of P is

(A) 81 (B) 49 (C) 100 (D) 36109. The differential equation of all parabolas with axis parallel to the y-axis is

(A) 2

2 2d y y xdx

(B) 3

3 2d y ydx

(C) 32

2

d y dydx dx

(D)

3

3 0d ydx

110. The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissaand the intercept of the normal on x-axis and passing through (2, 1) is

(A) 2 2x y x 0 (B) 2 24x 2y 9y 0

(C) 2 22x 4y 9x 0 (D) 2 24x 2y 9x 0

(Page No. : 18 of 20)

REASONING111. The nth term of a sequence is n

2P =1

nn

, where

n = 2, 3, 4,....Find the value of P15 × P16 ×.............× P48

(a)105

8 (b) 70

(c) 35 (d)4815

112. On a circular racing track, points P and Q arediametrically opposite. If A starts running from Ptowards Q along the circular track. he takes 10minutes more than he would have taken had herun along the straight path. This difference in timewould be 6 minutes for B. If A and B start runningfrom P at the same time but in opposite directions,they will meet in_______minutes. (Take = 3)(a) 22.5 (b) 35.5(c) 16.5 (d) None of theseDirections for questions 113 to 116 Answer thequestions on the basis of the informationgiven below.The following table records the number of danceperformances by five dancers D1, D2, D3, D4 andD5 in five months M1, M2, M3, M4, M5.

M1 M2 M3 M4 M5

Average number of

perform ances by a dancer

over 5 m onths

D1 5 4 7 9 5.6

D2 6 4 3

D3 5 7 2 1

D4 6 5 5.6

D5 3 3 5 7 2

Average number of

dance perform ances

in a m onth

4.6

(i) Average number of dance performances by D2over the given five months is 90% of theaverage of D5 over these five months

(ii) D4 performed 8 dances in the month M1(iii) In two consecutive months, D4 has performed

5 dances

(iv) The average number of dances performed in M3is 5.4

(v) No two months have the same average numberof dances performed

113. Dancers who have given more than five danceperformances in M2 or who have an average of thenumber of dance performances greater than 5 areselected for a show. How many dancers areselected?(a) 1 (b) 2(c) 4 (d) 5

114. If the number of dance performances given by D5in the months M2 and M3 are interchanged thenwhat will be the difference in the number ofdancers selected for the show mentioned inprevious question?(a) 2 (b) 1(c) 0 (d) 3

115. If the number of dance performances by eachdancer in the months M3 and M4 are interchangedthen how many dancers perform more dances inM4 compared to that in M3?(a) 2 (b) 1(c) 3 (d) 4

116. If instead of 7, D1 performs only 3 dances in M3,then in how many ways can the remaining fourperformances together be adjusted in any one ofthe other months so that the number of dances byD1 in any month may not exceed the number ofdances by D2 in that month by 7 or more?(a) 1 (b) 2(c) 3 (d) 4

117. In a family of four, the father’s age is 43

times the

age of the mother. Two years before, the mother’sage was five times the age of the son, three yearslater, father’s age would be thrice his daughter’spresent age. The sum of the current ages of allmembers in family is 83. Find the current age ofson.(a) 22 years (b) 7 years(c) 12 years (d) 17 years

118. The average age of a group of people is increasedby 10 when a person aged 19 years is replaced bya new person aged 59 years. How many peopleare there in the group?(a) 10 (b) 14(c) 4 (d) 15

(Page No. : 19 of 20)

119. A clock gains 5 minutes in 24 hours. It was setright at 10 a.m. on Monday. What will be the truetime when the clock indicates 10:30 a.m. on thenext Sunday?(a) 10 a.m.(b) 11 a.m.(c) 25 minutes past 10 a.m.(d) 5 minutes to 11 a.m.

120. A man 50 years old has 8 sons born at equalintervals. The sum of the age of the father andsons is 186. What is the age of the eldest son ifthe youngest is 3 year old?(a) 33(b) 28(c) 31(d) 29

(Page No. : 20 of 20)