# KVPY Examination Class XII Stream SB/SX Held on 05-11-2017 Question Paper With Solutions

KVPY Question Paper 2017 Stream SX Held on 05-11-2017

Part A-Mathematics

1. Let BC be a fixed line segment in the plane. The locus of a point A such that the triangle ABC is isosceles, is (with finitely many possible exceptional points)

(A)  a line

(B)  a circle

(C)  the union of a circle and a line

(D)  the union of two circles and a line

2. The number of solution pairs (x, y) of the simultaneous equations log1/3 (x + y) + log3 (x – y) = 2 and 2y2 = 512x+1 is

(A)  0

(B)  1

(C)  2

(D)  3

3. The value of the limit  is

(A)  −∞

(B)  −1/4

(C)  0

(D)  1/4

4. Let R be a relation on the set of all natural numbers given by a R b ⇔ a divides b2.

Which of the following properties does R satisfy?

I. Reflexivity

II. Symmetry

III. Transitivity

(A)  I only

(B)  III only

(C)  I and III only

(D)  I and II only

(I) This relation is reflexive relation because

every natural no. divides square of itself

a R a ⇔ a divides a2

(II) not symmetric eg. 5 R 10 ⇒ 5 Divide 100

But 10 R 5 ⇏ 10 Divide 25

(III) Not transitivity for example

if 8 R 4 & 4 R 2 ⇏ 8 R 2

only (I) Option

5. The fractional part of a real number x is x –[x], where [x] is the greatest integer less than or equal to x. Let F1 and F2 be the fractional parts of  and   Then F­1 + F2 lies between the numbers

(A)  0 and 0.45

(B)  0.45 and 0.9

(C)  0.9 and 1.35

(D)  1.35 and 1.8

6. The number of real solutions of the equation 2sin 3x + sin 7x – 3 = 0 which lie in the interval [–2π, 2π] is

(A)  1

(B)  2

(C)  3

(D)  4

only possible when sin 3x = 1 & sin 7x = 1

sin 3x = 1

Solving these 1 = 3m – 7n

First solution is m = 5, n = 2

Second solution is m = 12, n = 5

So two solutions are possible

7. Suppose p, q, r are real numbers such that q = p (4 – p), r = q (4 – q), p = r (4 – r). The maximum possible value of p + q + r is

(A)  0

(B)  3

(C)  9

(D)  27

8. The parabola y2 = 4x + 1 divides the disc x2 + y2 ≤ 1 into two regions with areas A1 and A2. Then | A1 – A2 | equals

(A)  1/3

(B)  2/3

(C)  π/4

(D)  π/3

9. A shooter can hit a given target with probability 1/4. She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

(A)  (0.5272, 0.5274)

(B)  (0.2636, 0.2638)

(C)  (0.1317, 0.1319)

(D)  (0.0658, 0.0660)

3rd time target will hit in sixth time

So, In first 5 attempt these will be 3L, 2W and

at 6th attempt shot will be hit

So,

10. Consider the following events :

E1 : Six fair dice are rolled and at least one die shows six.

E2 : Twelve fair dice are rolled and at least two dice show six.

Let p1 be the probability of E1 and p2 be the probability of E2. Which of the following is true ?

(A)  p1 > p2

(B)  p1 = p2 = 0.6651

(C)  p1 < p2

(D)  p1 = p2 = 0.3349

11. For how many different values of a does the following system have at least two distinct solutions ?

ax + y = 0

x + (a + 10) y = 0

(A)  0

(B)  1

(C)  2

(D)  Infinitely many

12. Let R be the set of real numbers and f : R → R be defined  by where [x] is the greatest integer less than or equal to x, and {x} = x – [x]. Which of the following statements are true ?

I. The range of f is a closed interval

II. f is continuous on R.

III. f is one-one on R.

(A)  I only

(B)  II only

(C)  III only

(D)  None of I, II and III

13. Let xn = (2n + 3n)1/2n for all natural numbers n. Then

14. One of the solutions of the equation 8 sin3θ – 7 sin θ + √3 cos θ = 0 lies in the interval

(A) (0, 10°]

(B) (10°, 20°]

(C) (20°, 30°]

(D) (30°, 40°]

15. Let a, b, c, d, e, be real numbers such that a + b < c + d, b + c < d + e, c + d < e + a, d + e < a + b. Then

(A) The largest is a and the smallest is b

(B) The largest is a and the smallest is c

(C) The largest is c and the smallest is e

(D) The largest is c and the smallest is b

(i) a + b < c + d

(ii) b + c < d + e

(iii) c + d < e + a

(iv) d + e < a + b

from (i) & (iii)

a + b < e + a

⇒ b < e

from (ii) & (iv)

b + c < a + b

⇒ c < a

(i) – (ii)

a – c < c – e

⇒ c > e

(i) – (iv)

(a – e) + (b – d) < (c – a) + (d – b)

from thus d > b

(i) + (iii) – (ii)

c > d

overall a is greatest, b is least

16. If a fair coin is tossed 5 times, the probability that heads does not occur two or more times in a row is

(A)  12/25

(B)  13/25

(C)  14/25

(D)  15/25

17. Consider the following parametric equation of a curve :

x (θ) = | cos 4θ| cos θ

Y(θ) = |cos 4θ| sin θ

for 0 ≤ θ ≤ 2π

Which one of the following graphs represents the curve ?

(A)

(B)

(C)

(D)

18. Let A = (a1, a2) and B = (b1, b2) be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between A and B ?

(A)  √65

(B)  √74

(C)  √83

(D)  √97

19. Let  Then the value of the integral  is

(A)  11/3

(B)  13/3

(C)  14/3

(D)  16/3

20. Let  Put   and  Then

(A)

(B)

(C)

(D)

Section 2-Part A-Physics

21. The magnitude of acceleration of the electron in the nth orbit of hydrogen atom is aH and that of singly ionized helium atom is aHe. The ratio

(A)  1 : 8

(B)  1 : 4

(C)  1 : 2

(D)  dependent on n

22. A carrot looks orange in colour because of the β carotene molecule in it. This means that the β carotene molecule absorbs light of wavelengths

(A) longer than 550 nm.

(B) shorter than 550 nm.

(C) longer than 700 nm.

(D) shorter than 700 nm.

VIBG | YOR

400 nm | 700 nm

Absorbed Reflected

therefore seen

23. If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss’s law all the charge resides on the surface. Suppose now that Colomb’s force between two charges varies as 1/r3. Then, for a charged solid metallic sphere

(A) field inside will be zero and charge density inside will be zero.

(B) field inside will not be zero and charge density inside will not be zero.

(C) field inside will not be zero and charge density inside will be zero.

(D) field inside will be zero and charge density inside will not be zero.

For static condition E = 0 in both of conductor

∴ ϕ through a Gaussian surface just under the surface of conductor = 0 but as

So qen = 0 is not correct statement. Some charge will present insider bulk of conductor.

24. Using dimensional analysis the resistivity in terms of fundamental constants h, me, c, e, ε0 can be expressed as

(A)

(B)

(C)

(D)

25. Consider a bowl filled with water on which some black pepper powder have been sprinkled uniformly. Now a drop of liquid soap is added at the centre of the surface of water. The picture of the surface immediately after this will look like

due to soap bubble surface tension is reduced therefore in that area. Black paper powder will sink.

26. It was found that the refractive index of material of a certain prism varied as 1.5 + 0.004/λ2, where λ is the wavelength of light used to measure the refractive index. The same material was then used to construct a thin prism of apex angle 10°. Angles of minimum deviation (δm) of the prism were recorded for the sources with wavelengths λ1 and λ2 Then

(A)  δm1) < δm2) if λ1 < λ2.

(B)  δm1) > δm2) if λ1 > λ2.

(C)  δm1) > δm2) if λ1 < λ2.

(D)  δm is the same in both the cases.

27. Two circularly shaped linear polarisers are placed coaxially. The transmission axis of the first polarizer is at 30° from the vertical while the second one is at 60°, both in the clockwise sense. If an unpolarised beam of light of intensity I = 20 W/m2 is incident on this pair of polarisers, then the intensities I1 and I2 transmitted by the first and the second polarisers, respectively, will be close to

(A) I1 = 10.0 W/m2 and I2 = 7.5 W/m2

(B) I1 = 20.0 W/m2 and I2 = 15 W/m2

(C) I1 = 10.0 W/m2 and I2 = 8.6 W/m2

(D) I1 = 15.0 W/m2 and I2 = 0.0 W/m2

28. An electron in an electron microscope with initial velocity  enters a region of a stray transverse electric field  The time taken for the change in its de-Broglie wavelength from the initial value of λ to λ/3 is proportional to

(A)  E0

(B)  1/E0

(C)  1/√E0

(D)  √E0

29. A bird sitting on a single high tension wire does not get electrocuted because

(A) the circuit is not complete.

(B) the bird feet has an insulating covering.

(C) capacitance of the bird is too small and the line frequency is too small.

(D) resistance of the bird is too high

is very large therefore bird does after very high capacitive reactance in the path of A.C. current.

30. A positive charge q is placed at the center of a neutral hollow cylindrical conducting shell with its cross section as shown in the figure below.

Which one of the following figures correctly indicates the induced charge distribution on the conductor (ignore edge effects).

Option ‘A’ is correct option. According charge conservation & Gauss’s law.

31. A transverse wave of frequency 500 Hz and speed 100 m/s is traveling in the positive x direction on a long string. At time t = 0 s the displacements at x = 0.0 m and at x = 0.25 m are 0.0 m and 0.02 m, respectively. The displacement at x = 0.2 m at t = 5 × 10–4 s is

(A)  −0.04 m

(B)  −0.02 m

(C)  0.04 m

(D)  0.02 m

32. A thin piece of thermal conductor of constant thermal conductivity insulated on the lateral sides connects two reservoirs which are maintained at temperatures T1 and T2 as shown. Assuming that the system is in steady state, which of the following plots best represents the dependence of the rate of change of entropy of the ratio of temperatures T1/T2

33. Which of the following plots represents schematically the dependence of the time period of a pendulum if measured and plotted as a function of its oscillations? (Note : amplitude need not be small)

Time period will increase as the amplitude is increases.

34. On a pulley of mass M hangs a rope with two masses m1 and m2 (m1 > m2) tied at the ends as shown in the figure. The pulley rotates without any friction, whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley ?

35. Two satellites S1 and S2 are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time t = 0, the satellites are farthest apart. The periods of revolution of S1 and S2 are 3 h and 24 h respectively. The radius of the orbit of S1 is 3 × 104 Then the orbital speed of S2 as observed from

(A)  the planet is 4π × 104 km h–1 when S2 is closest from S1.

(B)  the planet is 2π × 104 km h–1 when h–1 when S2 is closest from S1.

(C)  S1 is π × 104 km h–1 when S2 is closest from S1

(D)  S1 is  3π × 104 km h–1 when S2 is closest from S1

36. A rectangular region of dimensions w × l (w < < l) has a constant magnetic field into the plane of the paper as shown. On one side the region is bounded by a screen. On the other side positive ions of mass m and charge q are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference V < 0, and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen ?

(A)  Ions with  will hit the screen.

(B)  Ions with  will hit the screen.

(C)  All ions will hit the screen.

(D)  Only ions with  will hit the screen.

37. Force  applied on a body is written as  is a unit vector. The vector  is equal to

(A)

(B)

(C)

(D)

38. A particle of mass m moves around the origin in a potential  where r is the distance from the origin. Applying the Bohr model in this case, the radius of the particle in its nth orbit in terms of  is

(A)  a√n

(B)  an

(C)  an2

(D)  an√n

39. Two bottles A and B have radii RA and RB and heights hA and hB respectively with RB = 2RA and hB = 2hA. These are filled with hot water at 60°C. Consider that heat loss for the bottles takes place only from side surfaces. If the time the water to cool down to 50°C is tA and tB for the bottles A and B, respectively, then tA and tB are best related as

(A)  tA = tB

(B)  tB = 2tA

(C)  tB = 4tA

(D)  tA = tA/2

40. The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at 20°C and 1 atmospheric pressure is of the order of (kB = 1.4 × 10–23 J/K, and the average mass of an air molecules is 5 × 10–27 kg)

(A)  1027

(B)  1023

(C)  1025

(D)  1029

Section 3-Part A Chemistry

41. The major product formed in the following reaction is

42. Among the α-amino acids – threonine, tyrosine, methionine, arginine and tryptophan, those which contain an aromatic group in their side chain are

(A) threonine and arginine

(B) tyrosine and tryptophan

(C) methionine and tyrosine

(D) arginine and tryptophan

43. The number of stereoisomers possible for the following compound is

CH3-CH=CH-CH(OH)-CH3

(A)  1

(B)  2

(C)  3

(D)  4

44. In electrophilic aromatic substitution reactions of chlorobenzene, the ortho/para-directing ability of chlorine is due to its

(A) positive inductive effects (+I)

(B) negative inductive effect (–I)

(C) positive resonance effect (+R)

(D) negative resonance effect (–R)

45. Among the following,

the antiaromatic compounds are

(A)  I and IV

(B)  III and V

(C)  II and IV

(D)  I and III

46. Upon reaction with CH3MgBr followed by protonation, the compound that produces ethanol is

(A)  CH3CHO

(B)  HCOOH

(C)  HCHO

(D)  (CHO)2

47. Which of the following is NOT an oxidationreduction reaction ?

(A)  H2 + Br2 → 2HBr

(B)  NaCl + AgNO3 → NaNO3 + AgCl

(C)  2Na2S2O3 + I2 → Na2S4O6 + 2NaI

(D)  Cl2 + H­2O → HCl + HOCl

NaCl + AgNO3 → NaNO3 + AgCl is not a oxidation-reduction reaction because there is no change in oxidation state of any element.

48. The thermal stability of alkaline earth metal carbonates–MgCO3, CaCO3, SrCO3 and BaCO3, follows the order

(A) BaCO3 > SrCO3 > CaCO3 > MgCO3

(B) CaCO3 > SrCO3 > BaCO3 > MgCO3

(C) MgCO3 > CaCO3 > SrCO3 > BaCO3

(D) SrCO3 > CaCO3 > MgCO3 > BaCO3

Thermal stability of polyvalent anion salt like CO3 2– increase down the group due to increase in ionic character.

49. When a mixture of diborane and ammonia is heated, the final product is

(A)  BH­3

(B)  NH4BH4

(C)  NH2NH2

(D)  B3N3H6

50. Among the following metals, the strongest reducing agent is

(A)  Ni

(B)  Cu

(C)  Zn

(D)  Fe

According to their SRP value.

51. The molecule which is NOT hydrolysed by water at 25°C is

(A)  AlCl3

(B)  SiCl4

(C)  BF3

(D)  SF6

Due to steric hinderance SF6 is not hydrolysed by H2O at 25ºC

52. Among the following compounds, the one which does NOT produce nitrogen gas upon heating is

(A)  (NH4)2Cr2O7

(B)  NaN3

(C)  NH4NO2

(D)  (NH4)2 (C2O4)

53. Chlorine has two naturally occurring isotopes, 35Cl and 37 If the atomic mass of Cl is 35.45, the ratio of natural abundance of 35Cl and 37Cl is closest to

(A)  3.5 : 1

(B)  3 : 1

(C)  2.5 : 1

(D)  4 : 1

54. The reaction C2H6 (g) ⇌ C2H4(g) + H2(g) is at equilibrium in a closed vessel at 1000 K. The enthalpy change (∆H) for the reaction is 137.0 kJ mol–l. Which one of the following actions would shift the equilibrium to the right ?

(A) Decreasing the volume of the closed reaction vessel

(B) Decreasing the temperature at which the reaction is performed

(C) Adding an inert gas to the closed reaction vessel

(D) Increasing the volume of the closed reaction vessel

According to Lechatelier principal on increasing volume of closed vessel equilibrium will shift towards right.

55. The enthalpy (H) of an elementary exothermic reaction A ⇌ B is schematically plotted against the reaction coordinate. The plots in the presence and absence of a catalyst are shown in dashed and solid lines, respectively. Identify the correct plot for the reaction.

For exothermic reaction

∆H = EP – ER < 0

EB – EA < 0

EB < EA

Catalyst does not changes the initial and final position of the reaction so correct answer is (A).

56. Mg(OH)2 is precipitated when NaOH is added to a solution of Mg2+. If the final concentration of Mg2+ is 10–10 M, the concentration of OH(M) in the solution is

[Solubility product for Mg (OH)2 = 5.6 × 10–12]

(A)  0.056

(B)  0.12

(C)  0.24

(D)  0.025

57. A constant current (0.5 amp) is passed for 1 hour through (i) aqueous AgNO3, (ii) aqueous CuSO4 and (iii) molten AlF3, separately. The ratio of the mass of the metals deposited on the cathode is

[MAg, MCu, MAl are molar masses of the respective metals]

(A) MAg : 2 MCu : 3 MA1

(B) MAg : MCu : MA1

(C) 6 MAg : 3 MCu : 2 MA1

(D) 3 MAg : 2 MCu : MA1

58. A reaction has an activation energy of 209 kJ mol–1. The rate increases 10–fold when the temperature is increased from 27°C to X °C. The temperature X is closest to

[Gas constant, R = 8.314 J mol–1 K–1]

(A)  35

(B)  40

(C)  30

(D)  45

59. A mineral consists of a cubic close-packed structure formed by O2– ions where half the octahedral voids are occupied by Al3+ and oneeighth of the tetrahedral voids are occupied by Mn2+. The chemical formula of the mineral is

(A)  Mn3Al2O6

(B)  MnAl2O4

(C)  MnAl4O7

(D)  Mn2Al2O5

60. For a 4p orbital, the number of radial and angular nodes, respectively, are

(A)  3, 2

(B)  1, 2

(C)  2, 4

(D)  2, 1

no. of radial node = n – ℓ – 1 = 4 – 1 – 1 = 2

no. of angular node = ℓ = 1

Section 4-PartA-Biology

61. Interferons combat viral infection by

(A) inhibiting viral packaging directly.

(B) increasing the binding of antibodies to viruses.

(C) binding to the virus and agglutinating them.

(D) restricting viral spread to the neighboring cells.

In a typical scenario, a virus defected cell will release interferons causing near by cells to heighten their anti-viral defense

62. Leydig cells synthesize

(A)  insulin

(B)  growth hormone

(C)  testosterone

(D)  estrogen

Also know as interstitial cells present in testis between somniferous tubule.

63. Glucagon increases the blood glucose concentration by

(A) promoting glycogenolysis.

(B) increasing the concentration of fructose 2,–6-bisphosphate.

(C) increasing the concentration of pyruvate kinase.

(D) inhibiting gluconeogenesis.

Promote breakdown of Glycogen in liver.

64. Which ONE of the following is NOT essential for Polymerase Chain Reaction (PCR) ?

(A)  Restriction enzyme

(B)  Denaturation of DNA

(C)  Primers

(D)  DNA polymerase

RE is not required in PCR

65. CO2 acts as a greenhouse gas because

(A) it is transparent to heat but traps sunlight.

(B) it is transparent to sunlight but traps heat.

(C) it is transparent to both sunlight and heat.

(D) it traps both sunlight and heat.

Green house effect increases earth’s temperature by trapping heat.

66. A graph of species richness vs area on log-log axes is

(A)  linear

(B)  sigmoidal

(C)  oscillatory

(D)  parabolic

log S = log c + z  log A

67. Concentration of Na+ ions outside a nerve cell is ~100 times more than inside. The concentration of K+ ions is more inside the cells. The levels of Na+ ions and K+ ions are maintained by

(A) free diffusion of Na+ ions and pumping of K+ ions across the membrane.

(B) Na+ and K+ pumps in the membrane.

(C) free diffusion of K+ ions and pumping of Na+ ions across the membrane.

(D) water channels formed by lipids in the membrane.

Energy derived pumps are present in plasma membrane.

68. In a chemical reaction, enzymes catalyze the reaction by

(A) lowering the activation energy.

(B) increasing the activation energy.

(C) decreasing the free energy change between reactants and products.

(D) increasing the free energy change between reactants and products.

Enzyme decreases activation energy in reaction.

69. The rigidity of cellulose is due to

(A)  coiled structure of glucose polymer

(B)  β (1 → 4) glycosidic linkage

(C)  hydrogen bonding with adjacent glucose polymer

(D)  cross=linking between glucose and peptides

Bundle of cellulose fibre are rigid to H-bonds.

70. Antigen-antibody reactions

(A) always result in precipitation of the complex

(B) depend only on covalent interactions.

(C) are irreversible.

(D) depend on ionic and hydrophobic interactions.

Antibody- antigen interaction is essentially Non-Covalent, Electrostatic interaction, Hydrogen Bonds, Vander walls forces and Hydrophobic interactions are all known to be involved depending on the interaction sites.

71. Which ONE of the following combinations of molecular masses of polypeptides are obtained from purified human IgM when analysed on sodium dodecyl suplhate polyacrylamide gel electrophoresis (SDS-PAGE) under reducing conditions?

(A) 55 kDa, 15 kDa

(B) 70 kDa, 25 kDa, 15 kDa

(C) 55 kDa, 25 kDa

(D) 155 kDa

72. For a particular gene that determines the coat color in a diploid organism, there are three different alleles that are codominant. How many different skin colors are possible in such an organism?

(A)  9

(B)  6

(C)  4

(D)  3

73. Two genetic loci controlling two different traits are linked. During the inheritance of these traits, the Mendelian laws that would be affected is/are

(A) Law of dominance, law of segregation and law of independent assortment

(B) Law of segregation and Law of independent assortment

(C) Only Law of independent assortment

(D) Only Law of segregation

Linkage in exception of law of independent assortment

74. Which ONE of the following statements is INCORRECT?

(A) Alleles are different forms of the same gene.

(B) Alleles are present at the same locus.

(C) Alleles code for different isoforms of a protein.

(D) Alleles are non-heritable.

Alleles are alternate form of gives of one character present on same locus.

75. Which ONE of the following statements is INCORRECT about restriction endonucleases?

(A) They serve as primitive form of immune system in bacteria.

(B) They digest the DNA non-randomly.

(C) They digest the DNA at specific location.

(D) They digest the DNA from free ends.

Endonucleases do not cut from free ends.

76. The number of net ATP molecules produced from 1 glucose molecule during glycolysis is

(A)  1

(B)  2

(C)  3

(D)  4

In glycolysis net ATP produced

= 4 – 2 = 2 ATP

77. Which ONE of the following coenzymes is required for the conversion of L-alanine to a racemic mixture of D-and L-alanine ?

(A) Pyridoxal-6-phosphate

(B) Thiamine pyrophosphate

(C) Coenzyme A

Information based question

78. The cyclic electron flow during photosynthesis generates

(C)  ATP alone.

In cyclic photophosphorylation only ATP is formed.

79. Match the type of cells given in Column I with organisms given in Column II. Choose the appropriate combination from the options below.

(A) P-iii, Q-i, R-ii

(B) P-iii, Q-ii, R-i

(C) P-i, Q-ii, R-iii

(D) P-ii, Q-iii, R-i

Flame cells are for secretion and osmoregulation in flatworms.

Collar cells line spongocoel and cavars in sponges and creat water amount.

Cnidocytes are stringing cells and help in defense, affiance and capture of prey these cells also help in attachment with substrate

80. Compared to the atmospheric air, the alveolar air has

(A) more pO2 and less pCO2

(B) less pO2 and pCO2

(C) more pO2 and more pCO2

(D) less pO2 and less pCO2

Pressure gradient is essential for movement of gases in and out of the body.

Section 5 part B Mathematics

81. Let x, y, z be positive integers such that HCF (x, y, z) = 1 and x2 + y2 = 2z2. Which of the following statements are true?

I. 4 divides x or 4 divides y.

II. 3 divides x + y or 3 divides x – y.

III. 5 divides z(x2 – y2)

(A)  I and II only

(B)  II and III only

(C)  II only

(D)  III only

Take combination such as x = 1, y = 7, z = 5

Now, check options

(ii) & (iii) statement are correct.

82. How many different (mutually noncongruent) trapeziums can be constructed using four distinct side lengths from the set {1,3,4,5,6}?

(A)  5

(B)  11

(C)  15

(D)  30

|a – c| < b + d < a + c

(a, c) (b, d) (1, 3) (5, 6)

(1, 3) (4, 5)

and (1, 3) (4, 6)

Now make different combination. Total of 11 combination are possible.

83. A solid hemisphere is mounted on a solid cylinder, both having equal radii. If the whole solid is to have a fixed surface area and the maximum possible volume, then the ratio of the height of the cylinder to the common radius is

(A)  1 : 1

(B)  1 : 2

(C)  2 : 1

(D)  √2 : 1

84. Let ABC be an acute scalene triangle, and O and H be its circumcentre and orthocenter respectively. Further let N be the midpoint of OH. The value of the vector sum  is

(A)

(B)

(C)

(D)

85. The quotient when 1+ x2 + x4 + x6 + …… + x34 is divided by 1 + x + x2 + x3 + ……+ x17 is

(A)  x17 – x15 + x13 – x11 ……. + x

(B)  x17 + x15 + x13 + x11 + ……+ x

(C)  x17 + x16 + x15 + x14 + ……+ 1

(D)  x17 – x16 + x15 – x14 + …….−1

86. Let R be the region of the disc x2+y2 ≥1 in the first quadrant. Then the area of the largest possible circle contained in R is

(A)  π(3 – 2√2)

(B)  π(4 – 3√2)

(C)  π/6

(D)  π(2√2 – 2)

87. Let R be the set of real numbers and f : R→ R be given by  We now make the following assertions :

I. There exists a real number A such that f(x) ≤ A for all x.

II. There exists a real number B such that f(x) ≥ B for all x.

(A) I is true and II is false

(B) I is false and II is true

(C) I and II both are true

(D)  I and II both are false

88. Define  for all real x, where

Then

(A) g(x) is not continuous everywhere

(B) g(x) is continuous everywhere but differentiable nowhere

(C) g(x) is continuous everywhere and differentiable everywhere except at x = 0,1

(D) g(x) is continuous everywhere and differentiable everywhere except at x = 0,1,2

89. The integer part of the number  is

(A)  50

(B)  52

(C)  57

(D)  59

90. The number of continuous functions f:[0,1]→R that satisfy

(A)  0

(B)  1

(C)  2

(D)  infinity

Given equation can be written as

Section 6 part B Physics

91. One end of a rod of length L=1 m is fixed to a point on the circumference of a wheel of radius R = 1/√3 m. The other end is sliding freely along a straight channel passing through the center O of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity ω about O.

The speed of the sliding end P when θ = 60° is

(A)  2ω/3

(B)  ω/3

(C)  2ω/√3

(D)  ω/√3

92. One mole of an ideal monatomic gas undergoes the following four reversible processes :

Step1 : It is first compressed adiabatically from volume V1 to 1m3.

Step 2 : then expanded isothermally to volume 10 m3.

Step 3 : then expanded adiabatically to volume V3.

Step 4 : then compressed isothermally to volume V1.

If the efficiency of the above cycle is 3/4 then V1 is,

(A)  2m3

(B)  4m3

(C)  6m3

(D)  8m3

93. A neutron star with magnetic moment of magnitude m is spin in with angular velocity ω about its magnetic axis. The electromagnetic power P radiated by it is given by  where μ0 and c are the permeability and speed of light in free space, respectively. Then

(A) x = 1, y = 2, z = 4 and u = –3

(B) x = 1, y = 2, z = 4 and u = 3

(C) x = –1, y = 2, z = 4 and u = –3

(D) x = –1, y = 2, z = 4 and u = 3

P = [M L2 T–3]

μ0 = [M L T–2 I–2]

m = [I L2]

ω = [T–1]

C = [L T–1]

∴ [M L2 T–3] = [M L T–2 I–2]x [I L2]y [T–1]z [LT–1]u

x = 1, y = 2, z = 4, u = –3

94. A solid cube of wood of side 2a and mass M is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis AB. A bullet of mass m (<<M) and speed v is shot horizontally at the face opposite to ABCD at a height 4a/3 from the surface to impart the cube an angular speed ω. It strike the face and embeds in the cube. Then ωc is close to (note : the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is 2Ma2/3)

(A)  Mv/ma

(B)  Mv/2ma

(C)  mv/Ma

(D)  mv/2Ma

95. A gas obeying the equation of state PV = RT undergoes a hypothetical reversible process described by the equation,  where c1 and E0 are dimensioned constants. Then, for this process, the thermal compressibility at thigh temperature

(A) approaches a constant value.

(B) is proportional to T.

(C) is proportional to T1/2

(D) is proportional to T2.

96. To calculate the size of a hydrogen anion using the Bohr model, we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum h = h/2π, and taking electron interaction into account the radius of the orbit in terms of the Bohr radius of hydrogen atom  is

(A)  aB

(B)

(C)

(D)

97. A square-shaped conducting wire loop of dimension a moving parallel to the x-axis approaches a square region of size b (a < b) where a uniform magnetic field B exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed (ν) as a function of x is

inside B speed will be constant therefore B option is correct, representation of speed

98. The figure of a centimeter scale below shows a particular position of the vernier calipers. In this position the value of x shown in the figure is ( figure is not to scale)

(A)  0.02 cm

(B)  3.65 cm

(C)  4.15 cm

(D)  0.03 cm

99. A parallel beam of light is incident on a tank filled with water up to a height of 61.5 mm as shown in the figure below. Ultrasonic waves of frequency 0.5 MHz are sent along the length of the water column using a transducer placed at the top, and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen ? Take the speed of sound in water to be 1,500 m/s.

100. A star of mass M (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the center of mass of the star-planet system is shown below :

The radius of the planet’s orbit is closest to

(1 A. U. = Earth-Sun distance)

(A)  0.004 A.U.

(B)  0.008 A.U.

(C)  0.004 A.U.

(D)  0.12 A.U.

Section 7 Part B-Chemistry

101. In the following reaction sequence

X and Y are

102. In the following reactions

103. Which of the following alkenes can generate optically active compounds upon hydrogenation ?

(A)  I, III and IV

(B)  II and III

(C)  I and III

(D)  II and IV

104. When heated in air, brown copper powder turns black. This black powder would turn brown again when heated with

(A)  CO

(B)  O2

(C)  H2

(D)  NH3

H2 is reducing agent

105. The geometry and magnetic property of [NiCl4]2–, respectively, are

(A) tetrahedral, paramagnetic

(B) tetrahedral, diamagnetic

(C) square planar, paramagnetic

(D) square planar, diamagnetic

[NiCl4]2 sp3 hybrid, Tetrahedral

106. Among (i) [Cr(en)3]3+, (ii) trans-[Cr(en)2 Cl2]+ , (iii) Cis-[Cr(en)2 Cl2]+ (iv) [Co(NH3)4Cl2]+ the optically active complexes are

(A)  i and ii

(B)  i and iii

(C)  ii and iii

(D)  ii and iv

107. 227Ac has a half-life of 22 years with respect to radioactive decay . The decay follows two parallel paths : 227Ac → 227Th and 227Ac → 223 If the percentage of the two daughter nuclides are 2.0 and 98.0, respectively, the decay constant (in year–1) for 227Ac → 227Th path is closest to

(A)  6.3 × 10−2

(B)  6.3 × 10−3

(C)  6.3 × 10−1

(D)  6.3 × 10−4

108. A system consisting of 1 mol of an ideal gas undergoes a reversible process, A → B → C → A (schematically indicated in the figure below). If the temperature at the starting point A is 300 K and the work done in the process B → C is 1 L atm, the heat exchanged in the entire process in L atm is

(A)  1.0

(B)  0.0

(C)  1.5

(D)  0.5

For process A → C, W = 0, ∆E = 0, q = 0

For process A → B

W = –1 (1.5 – 1) = –0.5 lit. atm

∆E = q + W

0 = q + W

q = –W = – (– 0.5) = 0.5 lit. atm

For process B → C, W = 1 atm

∆E = q + W

0 = q – W

–q = W = –1 atm

∴ Total heat exchanged = 1.5

109. A mixture of toluene and benzene boils at 100°C. Assuming ideal behaviour, the mole fraction of toluene in the mixture is closest to [Vapour pressures of pure toluene and pure benzene at 100°C are 0.742 and 1.800 bar respectively. 1 atm = 1.013 bar]

(A)  0.824

(B)  0.744

(C)  0.544

(D)  0.624

1.013 = 0.742 Xt + 1.8 Xb

1.013 = 0.742(1 – Xb) + 1.8 Xb

Xb = 0.256

∴ Xt = 1 – Xb = 0.744

110. A two-dimensional solid pattern formed by two different atoms X and Y is shown below. The black and white squares represent atoms X and Y, respectively. The simplest formula for the compound based on the unit cell from the pattern is

(A)  XY8

(B)  X4Y9

(C)  XY2

(D)  XY4

The unit cell of the above pattern will consist of

8 white square and 1 black square i.e. it will

form centre unit cell.

∴ No. of white square Y = 8

No. of black square X = 1

∴ Formula XY8

Section 8 Part B Biology

111. The genetic distance between genes A and B is 10 cm. An organism with Ab combination of the alleles is crossed with the organism with aB combination of alleles. What will be the percentage of the gametes with AB allele combination by an F1 individual ?

(A)  1

(B)  5

(C)  10

(D)  50

Recombinants formed = 10% (AB 5% & ab 5%)

112. Proteins P, Q, and R are associated with intact organellar membrane in a cell. If the intact organelle is treated with a high ionic strength buffer, only protein R remained associated with the membrane fraction. Based on this, one could conclude that

(A) P and Q are peripheral membrane proteins.

(B) R is a peripheral membrane protein.

(C) P and Q are integral membrane bound proteins.

(D) P is peripheral and Q is integral membrane protein.

Peripheral proteins can be detached earily

113. In photosynthesis, oxygen is produced by

(A) photosystem I from carbon dioxide.

(B) photosystem II from carbon dioxide.

(C) photosystem I from water.

(D) photosystem II from water.

photosynthesis at Ps II in lumen of thylakoid

114. How many different proteins consisting of 100 amino acids can be formed from 20 different amino acids ?

(A) 20100

(B) 10020

(C) 220

(D) 20 × 100

20100

115. Molecular weight of Coli DNA is 3.1 × 109 g/mol. Average molecular weight of nucleotide pair is 660 g/mol and each nucleotide pair contributes to 0.34 nm to the length of DNA. The length of E. coli DNA molecule will be approximately

(A) 0.8 nm

(B) 1.6 nm

(C) 1 .6 μm

(D) 1.6 mm

116. Which ONE of the following options is TRUE with respect to Emigration ?

(A) It is the difference between the births and deaths in a population.

(B) It is the difference between individuals who have come to a habitat and who have left the habitat.

(C) It involves individuals of different species coming to a habitat from elsewhere during the period under consideration

(D) It involves individuals of a population leaving a habitat during the time period under consideration.

117. Choose the CORRECT combination of statements given below related to cysteine residue in proteins.

i. Cysteine can be linked to tyrosine by S-O bond.

ii. Cysteine can be linked to another cysteine by S-S bond.

iii. Cysteine can complex with Zn2+.

iv Cysteine can be linked to methionine by S-S bond

(A) i and ii

(B) ii and iii

(C) iii and iv

(D) i and iv

118. The minimum number of plants to be screened to obtain a plant of the genotype AabbCcDd from a cross between plants of genotypes AaBbCcDd and AABbCCDd is

(A) 8

(B) 16

(C) 32

(D) 64

119. When a pure bred, red flower-producing plant of genotype RR is crossed with a pure bred, white flower-producing plant of genotype rr, all the F1 plants produced pink flowers If all the plants in each generation from F1 to F6 are selfed, what will be the percentage of plants with red and white flowers in the final population consisting of a large number of individuals ? (Consider that flower colour has no effect on reproduction and survival.)

(A) 3 – 4

(B) 12 – 13

(C) 49 – 51

(D) 97 – 100

After selfing homozygous individual produces All white & red offspring and heterozygous also produces 50%. Red & White flower.

120. The schematic below describes the status of lac operon in the absence of lactose. Which ONE of the following happens when lactose is present in the cell ?

(A) Lactose binds to Pi and stops the transcription of i.

(B) Lactose is converted to allolactose, which binds to Plac and results in the displacements of the repressor from O.

(C) Lactose is converted to allolactose, which binds to the repressor protein and prevents its interaction with O.

(D) Lactose has no effect on the status of the lac operon.