KVPY Exam Online Mock Test Set A

1. For a spontaneous process

2. Among the following, the correct statement about cathode ray discharge tube is

3. The number of moles of water present in a spherical water droplet of radius 1.0 cm is
[Given: density of water in the droplet = 1.0 g cm–3]

4. During the free expansion of an ideal gas in an isolated chamber,

5. The plot of concentration of a reactant vs. time for a chemical reaction is shown below: The order of this reaction with respect to the reactant is

6. The element whose salts cannot be detected by flame test is

7. The oxide which is neither acidic nor basic is

8. For a multi-electron atom, the highest energy among the following is

9. The most polarizable ion among the following is

10. Treatment with lime can remove hardness of water caused by

11. In water-gas shift reaction, hydrogen gas is produced from the reaction of steam with

12. IUPAC name of the following compound is

13. The major product of the following reaction is

14. The following compounds are

15. The hybridizations of N, C and O shown in the following compound respectively, are

16.

17.

18. Mumbai needs 1.4 X 10¹² litres of water annually. Its effective surface area is 600 km² and it receives an average rainfall of 2.4 m annually. If 10% of this rain water is conserved it will meet approximately

19. Which one of the following schematic graphs best represents the variation of PV (in Joules) versus T (in Kelvin) of one mole of an ideal gas? (The dotted line represents PV = T.)

20. Two masses M₁ and M₂ carry positive charges Q₁ and Q₂, respectively. They are dropped to the floor in a laboratory setup from the same height where there is a constant electric field vertically upwards. M₁ hits the floor before M₂. Then,

21. The electrostatic energy of a nucleus of charge Ze is equal to kz²e²/R, where k is a constant and R is the nuclear radius. The nucleus divides into two daughter nuclei of charges Ze/2 and equal radii. The change in electrostatic energy in the process when they are far apart is

22. The nuclear radius is given by R = r₀A^1/3, where r₀ is constant and A is the atomic mass number. Then,

23. A particle slides from the top of a smooth hemispherical surface of radius R which is fixed on a horizontal surface. If it separates from the hemisphere at a height h from the horizontal surface then the speed of the particle is

24. A ball is moving uniformly in a circular path of radius 1 m with a time period of 1.5 s. If the ball is suddenly stopped at t = 8.3 s, the magnitude of the displacement of the ball with respect to its position at t = 0 s is closest to

25. Consider two equivalent, triangular hollow prisms A and B made of thin glass plates and arranged with negligible spacing as shown in the figure. A beam of white light is incident on prism A from the left. Given that the refractive index of water is inversely related to temperature, the beam to the right of prism B would NOT appear white if

26. Frosted glass is widely used for translucent windows. The region where a transparent adhesive tape is stuck over the frosted glass becomes transparent. The most reasonable explanation for this is,

27. A student in a town in India, where the price per unit (1 unit = 1 kW-h) of electricity is ` 5.00, purchases a 1 kVA UPS (uninterrupted power supply) battery. A day before the exam, 10 friends arrive to the student’s home with their laptops and all connect their laptops to the UPS. Assume that each laptop has a constant power requirement of 90 W. Consider the following statements
I All the 10 laptops can be powered by the UPS if connected directly.
II All the 10 laptops can be powered if connected using an extension box with a 3A fuse.
III If all the 10 friends use the laptop for 5 hours, then the cost of the consumed electricity is about ` 22.50.
Select the correct option with the true statements.

28. A steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown below. The terminal velocity of the ball is closest to :

29. A specially designed Vernier calliper has the main scale least count of 1 mm. On the Vernier scale there are 10 equal divisions and they match with 11 main scale divisions. Then, the least count of the Vernier calliper is

30. Various optical processes are involved in the formation of a rainbow. Which of the following provides the correct order in time in which these processes occur ?

31.

32. Let l > 0 be a real number, C denote a circle with circumference l, and T denote a triangle with perimeter l. Then

33. Let N₁ = 2⁵⁵ + 1 and N₂ = 165. Then

34. The number of non-negative integer solutions of the equations 6x + 4y + z = 200 and x + y + z = 100 is

35. Let P be an interior point of a convex quadrilateral ABCD and K, L, M, N be the midpoints of AB, BC, CD, DA respectively. If Area(PKAN) = 25, Area(PLBK) = 36, and Area(PMDN) = 41 then Area(PLCM) is

36. A two-digit number ab is called almost prime if one obtains a two-digit prime number by changing at most one of its digits a and b. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is

37. The number of cubic polynomials P(x) satisfying P(l) = 2, P(2) = 4, P(3) = 6, P(4) = 8 is

38. Let x₁, x₂ , ..., x₁₁ be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

39. Let N be the least positive integer such that whenever a non-zero digit c is written after the last digit of N, the resulting number is divisible by c. The sum of the digits of N is

40.

41.

42. Let a_n, n≥1, be an arithmetic progression with first term 2 and common difference 4. Let M_n be the average of the first n terms. then the sum

43. Let p(x) = x² + ax + b have two distinct real roots, where a, b are real numbers. Defin g(x) = p(x³) for all real numbers x. Then which of the following statements are true?
I. g has exactly two distinct real roots
II. g can have more than two distinct real roots
III. There exists a real number α such that g(x) ≥ α for all real x

44.

45. Let ABC be an equilateral triangle with side length a. Let R and r denote the radii of the circumcircle and the incircle of triangle ABC respectively. Then, as a function of a, the ratio R/r

46. Match the plant hormones in Column I with their primary function in Column II. Choose the CORRECT combination.

47. If the gene pool of the locus X in the human genome is 4, then what would be the highest possible number of genotypes in a large population?

48. Solid and dotted lines represent the activities of pepsin and salivary amylase enzymes of the digestive tract, respectively. Which one of the following graphs best represents their activity vs pH?

49. Papaya is a dioecious species with XY sexual genotype for male and XX for female. What will be the genotype of the embryos and endosperm nuclei after double fertilization?

50. A cell weighing 1 mg grows to double its initial mass before dividing into two daughter cells of equal mass. Assuming no death, at the end of 100 divisions what will be the ratio of the mass
of the entire population of these cells to that of the mass of the Earth? Assume that mass of the Earth is 10²⁴ kg and 2¹⁰ is approximately equal to 1000.

51. An organic compound X with molecular formula C₆H₁₀, when treated with HBr, forms a gem dibromide. The compound X upon warming with HgSO₄ and dil. H₂SO₄, produces a ketone which
gives a positive iodoform test. The compound X is

52. An organic compound contains 46.78% of a halogen X. When 2.00 g of this compound is heated with fuming HNO₃ in the presence of AgNO₃, 2.21 g AgX was formed. The halogen X is [Given: atomic weight of Ag = 108, F = 19, Cl = 35.5, Bi = 80, I = 127]

53. The correct statements among the following
i. E_2s (H) > E_2s (Li) > E_2s (Na) > E_2s (K)
ii. The maximum number of electrons in the shell with principal quantum number n is equal to 2n².
iii. Extra stability of half-filled subshell is due to smaller exchange energy
iv. Only two electrons, irrespective of their spin, may exist in the same orbital are

54. [Given: “a”, “b” are standard parameters for van der Waals gas]

55. PbO₂ is obtained from

56. A healthy adult of height 1.7 m has an average blood pressure (BP) of 100 mm of Hg. The heart is typically at a height of 1.3 m from the foot. Take the density of blood to be 10³ kg/m³ and note that 100 mm of Hg is equivalent to 13.3 kPa (kilo Pascals). The ratio of BP in the foot region to that in the head region is close to.

57. A hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with diameter of 11.7 m and the mass of the balloon and the payload (without the hot air inside) is 210 kg. Temperature and pressure of outside air are 27 °C and 1 atm = 10⁵ N/m² respectively. Molar mass of dry air is 30 g. The temperature of the hot air inside is close to, [The gas constant R = 8.31 J/K/mol]

58. A student uses the resistance of a known resistor (1 Ω) to calibrate a voltmeter and an ammeter using the circuits shown below. The student measures the ratio of the voltage to current to be 1 X 10³ Ω in circuit (a) and 0.999 Ω in circuit (b). From these measurements, the resistances (in Ω) of the voltmeter and ammeter are found to be close to:

59. In an hour-glass approximately 100 grains of sand fall per second (starting from rest), and it takes 2 sec for each sand particle to reach the bottom of the hour-glass. If the average mass of each sand particle is 0.2 g then the average force exerted by the falling sand on the bottom of the hour-glass is close to.

60. A water-proof laser pointer of length 10 cm Placed in a water tank rotates about a horizontal axis passing through its center of mass in a vertical plane as shown in the figure. The time period of rotation is 60 s. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to (Refractive index of water =1.33)

61.

62. A prime number p is called special if there exist primes p₁, p₂, p₃, p₄ such that
p = p₁ + p₂ = p₃ – p₄. The number of special primes is

63.

64. Let S = {1, 2, 3, ..., 100). Suppose b and c are chosen at random from the set S. The probability that 4x² + bx + c has equal roots is

65. Let a, b, c, d be distinct real numbers such that a, b are roots of x² – 5cx – 6d = 0 and c, d are roots of x² – 5ax – 6b = 0. Then b + d is

66. During oogenesis in mammals, the second meiotic division occurs

67. Which one of the following organisms is a bryophyte?

68. Which one of the following parts of the eye is affected in cataract?

69. Which one of the following anatomical structures is involved in guttation?

70. Which one of the following organs is NOT a site for the production of white blood cells?

71. Which one of the following sequences represents the CORRECT taxonomical hierarchy?

72. In a diploid organism, when the locus X is Inactivated, transcription of the locus Y is triggered. Based on this observation, which one of the following statements is CORRECT?

73. Where are the proximal and distal convoluted tubules located within the human body?

74. Which one of the following metabolic conversions requires oxygen?

75. The mode of speciation mediated by geographical isolation is referred to as

76. Which one of the following genetic phenomena is represented by the blood group AB?

77. Microscopic examination of a blood smear reveals an abnormal increase in the number of granular cells with multiple nuclear lobes. Which one of the following cell types has increased in number?

78. Removal of the pancreas impairs the breakdown of

79. The crypts of Lieberkühn are found in which one of the following parts of the human digestive tract?

80. Which one of the following is a CORRECT statement about primate evolution?